WV - Purdue Engineering · x [> } [%& [%& / \ )

$Page 1: WV - Purdue Engineering · x [> } [%& [%& / \ )$
� ��

�� ! "#� $

%'&)()*,+.-/&1032145&76)89*,:<;=-/>@?=*BAC-D*E(GFH*E>JILK.+.MN6C&1;OFPKRQS:<&7TVUWA);O*,?XILKY-OKR&7QZ>@QC(GK.QP:[&1T/UHA);=*[?X\1?]>@UWF)^KY:[-,_VàQb\1?]>@UWFHK.:,-[cd;=FH*X&16H89*,:e;#TfAW-9;#6g*X?O*,UH?=*,-O*[QL;O*E(K.Qh>i-D;O?=AW:e;=AH?O*X-OAHKR;=>@6W+R*V0j&1?#?=*[QC()*[?=KRQW\i>1QW(()KY-DUW+.>JM7_lkmFW*nT/&L-9;o:[&1T/T/&1QB-OAW:]Fp-9;=?OAC:e;OAW?O*�KY-q;OFH*r274sTV*E-DFtcW>/:<&1+.+.*,:e;=KR&7QB&10uUg&1+.Mv\1&1QC-q:[&1QW-OKY-9;O^K.QH\'&@0w214xUC&7KRQL;]-r>@QW(b;=FH*y*E()\1*E-�;OFW>@;w89&1K.Qh;OFW*[Tp_zn?=>1UHFHKY:[-#FW>1?=(H{q>1?O*VAW-OAW>@+.+RMh-OAHUHUg&1?O;=-�;=FHK.-?=*[UH?=*,-O*[QL;=>@;OK.&1Q|_h}H&7?V-OT/&v&@;OFW*[?/>@QW(C~�&1?V-DK.T/UH+R*,?V-OAH?O0�>1:[*,-,c�&@;OFW*[?V\1?]>@UHFHKY:[-�?O*,UH?=*,-O*[QL;=>@;OK.&1QW-�KRQ)^:<+.AW()*��LAW>1(H?OKY:o-OAH?O0�>1:<*E-[cv��^�-OUH+.KRQW*3-OAH?D0�>7:<*E-[c)>@QC(y-DAW6g()K.IvK.-OK.&1QB-OAH?O0�>1:[*,-,_uàQi>1(H()KR;OK.&1Q�;O&V214s-DFC>@Ug*K.Q)0j&1?=TX>�;OK.&1Qtc�\1?]>@UHFHKY:[-n?=*[UH?=*,-O*[QL;]>�;OK.&1QC-3:,>@Q�:[&1QL;=>1KRQh:<&7+R&7?e~J;O*[�L;=AH?=*�K.Q)0j&1?=TX>�;OK.&1Q�{�FHKY:]F�KY-n;OFH*,Q� ;=*<�v;OAW?O*[^�TX>@UWUC*E(H��&7QL;O&f;OFH*�?=*[QW()*,?O*E(y&76)89*,:<;q6vMX;=FH*�\1?]>@UHFHKY:[-qFW>1?=(H{q>1?O*7_u}�KR\7AH?=*f�,�W_.�n-OFH&�{w-q>?=&1AH\7Ff214ST/*E-DFV&@0d>w;=&�M�()&1\�>@QC(f>o;O*[�L;=AH?=*<^�T/>1UHUg*,(f?O*,QW()*[?=*,(�KRTX>1\1*q0j?O&7Ts;OFH*w-=>@T/*qIvKR*,{�UC&7KRQL;,_àQ�:[&1T/UHA);=*[?�IvK.-OKR&7Q|cC;OFH*V&16)89*E:e;�?O*,UH?=*,-O*[QL;=>@;OK.&1Q'T�AC-9;�6C*/-OAHK�;]>@6H+.*r0j&7?3AC-D*VKRQ�&16)89*E:e;n?O*E:<&1\1^QHKR;OK.&1Q|cg{�FHKY:]F'T/*,>@QC-�;OFC>�;w;=FH*[?=*rT�AC-9;n6C*�-O&1T/*rUg&@;=*[QL;OKY>@+�:<&7?O?=*,-OUC&7QW()*,QW:<*#6g*<;9{q*[*,Qp;OFH*r?=*[UW?O*[^-O*[QL;=>@;OK.&1Q�>1QW(X;=FH*o0j*E>�;=AH?O*E-�;=FW>�;�:[>1Q�6g*3*[�v;O?]>1:e;=*,(/0j?=&1T�>1Q�K.T/>1\1*7_��o&�{�*,I1*[?Ec@;=FH*[?=*�>@?=*3-O*[I1*,?=>1+()KR�g*,?O*,QL;q;9MvUg*,-m&10�K.TX>@\1*E-m:<&1T/T/&1QW+RMXAW-O*,(iK.Qi274s&16)89*E:e;�?=*,:<&7\1QHKR;OK.&1QtcLK.QpUW>@?O;OKY:<AW+.>1?,��\1?]>JML^�-=:[>1+R*K.T/>1\1*E-[c�:[&1+.&1?VKRTX>@\7*,-,c�>@QC(G?]>@QH\7*�K.T/>1\1*E-[_G}WAH?D;=FH*[?=T/&1?=*1c�KR;XK.-VQH&�{�:[&1T/T/&1QG;=&�FC>JI1*�*,K�;=FH*[?\1?]>JML^�-=:[>1+R*�&1?#:<&7+R&7?3K.TX>@\1*E-n?O*,\1KY-9;=*[?=*,(';=&p?=>1QH\1*V(H>�;]>Hc|UH?=&�IvK.(HKRQH\B?O*E:<&7\1QHKR;OK.&1Qb>@+.\1&1?=KR;OFHTX-n{�K�;=F>X?=K.:]FW*[?3-O*<;n&@0l0j*,>@;OAH?=*,-,_o%'&L-9;�214�&16)89*E:e;n>1+R\7&1?=K�;=FHTX-w>@?=*rQH&1;3\7*[QH*,?=>1+|*[QH&7AH\1Fp;=&�FW>1QW()+.*�-OAW:]F

}�KR\7AH?=*y�[�C_R�7��214�T/*,-OF'&@0�>/;=&�Mi(H&1\y>@QC(p;O*[�L;=AH?=*<^�T/>1UHUg*,(p?=*[QW()*,?O*E(pKRTX>1\1*1_o��&7AH?D;=*,-OMB&10��#>@?=K��AW+R+.K _

¡ �J¢

¡ � � �� ! #"$"%"

>�IJ>1?OK.*<;9MN&10o0j*E>�;OAW?O*E-[c�6WA);XKRQW-D;O*E>1(Z{�*,?O*p()*E-DK.\1QH*E(N0j&7?/>�UW>1?D;=K.:[AH+.>1?/?O*,UH?O*E-D*,QL;=>�;=KR&7Q|_GkmFvAW-/KR;KY-rK.TVUg&1?O;=>1QL;�;O&�+R&v&%&h>�;�;OFH*i:<&1T/T/&1QN?=*[UW?O*E-D*,Q7;]>�;=KR&7QW-�6C*[0j&1?=*�()KY-O:[AW-=-DK.QH\�274x&76)89*,:<;�?O*E:<&7\1QHKR^;OK.&1Qt_�àQ/\7*[QH*,?=>1+W:[>@;O*[\7&1?=KR*E-[cJ;=FH*[?=*o>1?O*m\1*,&1T/*<;=?OKY:m?=*[UH?=*,-O*[QL;=>@;OK.&1QW-�K.Q/;O*,?OTX-�&10gUg&1K.QL;=-,c7+.K.QH*,-,c7>1QW(-OAH?D0�>7:<*E-('g-DMvT�6g&1+.KY:#?O*,UH?=*,-O*[QL;=>@;OK.&1QW-mK.Q';O*,?OTX-o&@0�UH?=KRT/KR;OK.I1*�:[&1T/UC&7QH*[QL;]-o>@QC(i;OFH*,KR?�-DUC>�;OKY>@+t?O*,+.>@^;OK.&1QC-DFHK.UW-)'u>1QW(0jAWQW:e;=KR&7QW>@+�?=*[UH?=*,-O*[QL;]>�;OK.&1QC-oK.Qb;O*[?=TX-n&@0�0jAWQW:e;=KR&7QW>@+�UC>@?O;=-�>@QW(�;OFW*[K.?�0jAHQW:e;=KR&7QW>@+?=*[+Y>�;OK.&1QC-DFHK.UW-,_�*b*V{�K.+.+�6C*,\1K.Q�{�KR;OFN>i-DAH?=I1*,M'&@0�;=FH*/T/&7-D;#:[&1T/T/&1Q�TV*[;OFH&)(H-n0j&7?#?O*,UH?=*,-O*[QL;OK.QH\214 &16)89*E:e;=-�>1QW(�;OFH*,QiUW?O&):<*,*,(�;O&/;=FH*#?O*,UH?=*,-O*[QL;=>@;OK.&1QW-�?O*E�LAHKR?=*,(B6vMX;OFW*#TV&L-9;o:[&1T/T/&1QB;9MvUC*E-m&@0&16H89*,:e;�?=*,:[&1\1QWK�;=KR&7Qi>1+R\7&1?=K�;=FHTX-[_

+-,/.(+ 0214357698;:7<>=?:7@A@A:7BDCE6!F43�6!GH6!B�I�JKIL(:7BNM 6OI�P4:RQSG

��&1T/UHAH;O*[?pIvKY-DK.&1Q 6g*[\L>@Q {�KR;OF ;OFH*h{q&1?T&Z&107U�&76C*,?D;]-�K.Q��WV%X ¡ &1Q ?=*,:[&1\7QHK�;=KR&7Q &@0�Ug&1+.MvFH*,(H?=>1+&16H89*,:e;]-[c�AC-DK.QH\p-DK.T/UH+R*V{�K.?O*[^ 0j?]>@T/*�T/&)()*,+.-�>@QC(�TX>�;]:]FHK.QH\y;=&p-D;O?]>@K.\1FL;n+RK.QH*/-D*,\1T/*[QL;=-n*[�L;=?=>7:e;=*,(0j?=&1TxK.TX>@\7*,-,_ZY|K.QH*<â-O*[\1T/*,Q7;O^�6C>1-O*,(yT/&)()*,+.-oFW>JI1*�?=*[TX>@K.QH*,(iUg&1UHAW+.>1?�*[I1*,Qi;O&)(H>JM1cW6HA);w;=FH*[?=*r>@?=*>@+Y-O&/>VQvAHTf6C*,?w&@0l>@+R;O*[?=QW>@;OK.I1*,-q;=FW>�;o>@;D;=*[T/U);�;O&XT/&7?O*#:<+.&7-O*[+.My?=*[UH?=*,-O*[QL;m;OFW*r(H>�;]>�0j?=&1T!&16)89*E:e;]-;OFC>�;X:[>@QZFW>JI1*i:<AH?=I1*E(G>@QC(G*[I7*[Q 0j?O*,*<^�0j&1?=T -OAH?O0�>1:[*,-,_bàQ ;OFHKY-X-O*,:e;=KR&7Q|c�{q*�{�K.+R+�+.&v&%&N>�;/T/*,-OFT/&)()*[+Y-[c|-OAH?O0�>1:[*<^�*,()\7*<^�I1*[?O;O*[�BT/&)()*[+Y-,c�I1&J�)*[+l>@QW(�&):e;O?=*[*fT/&v(H*[+Y-[c�\7*[QH*,?=>1+RK�[[*E(v^�:[Mv+RK.QW()*,?oT/&)()*[+Y-[c-OAHUC*,?=�LAW>7()?=K.:nT/&)()*[+Y-[cC>@QW(p()*[0j&1?=T/>16H+.*#TV&)()*,+.-,_�*b*r{�K.+R+t>1+.-O&/+R&v&$&B>�;�;=FH*�()KY-D;OK.QW:e;=KR&7Qi6g*<;9{q*[*,Q;O?=AH*X214�T/&)()*,+.-�>@QC(�:]FW>1?=>7:e;=*[?=K.-D;OKY:e^�IvKR*,{�TV&)()*,+.-3;=FW>�;r?=*[UH?=*,-O*[QL;�>i274�&16)89*E:e;�6vM�>B-O*<;#&10O\@4IvKR*,{w-[_]_^-`�]�à] b�cedgf�h#iEdgj9k-f�l�hm 214�T/*,-OFbK.-#>BI1*,?OM-OKRT/UH+.*/\1*,&1T/*<;=?OKY:�?=*[UW?O*E-D*,Q7;]>�;=KR&7Q';OFW>@;r()*,-=:<?=KR6g*,-�>1Q�&76)89*,:<;n6vM�>i-D*[;#&@0I1*,?D;=K.:[*,-3>@QW('*E()\1*E-�;=FW>�;3;O&1\7*<;=FH*[?30j&1?=T!Ug&1+.Mv\1&7QW-wK.Q�214oâ-DUW>7:<*7_ m Qb>@?=6HK�;=?=>1?OMBT/*,-OFTX>JMBFW>JI7*>@?=6HKR;O?]>@?=MrUg&1+.ML\7&1QW-,_ mon�p q%rtsvuwn-xyp{za| K.-�:<&7TVUg&7-O*,(/&10�UC&7+RMv\1&7QW-�>1+R+g&@0�&1QW*�;9MvUC*7_�}3QW*o:<&7TVT/&7QH+RMAW-O*,(BT/*,-OFBKY-�>�~ n��uw�#q�rts�uwn�xyp�z�| c){�FWK.:]FiK.-�:[&1T/Ug&7-O*,(y*,QL;OK.?O*,+RMy&10|;O?=KY>@QH\7+R*E-('L;OFW*#TV*E-DFp-OFH&�{�Q�K.Q}�KR\7AH?=*V�,�W_.��K.-�>V;=?OKY>@QH\7AH+Y>@?mT/*,-OF|_�%'*,-OFH*E-w:[>1QB?=*[UH?=*,-O*[QL;w>@Qi&16H89*,:e;o>@;�IJ>1?OK.&1AC-�()K��d*[?=*[QL;w+.*[I7*[+Y-&@0�?O*E-D&7+RAH;OK.&1Q|cv0j?=&1Tx>/:[&7>@?]-O*o*,-D;OK.TX>�;=*#&@0t;=FH*#&16H89*,:e;m;=&/>VI7*[?=M��WQH*#+.*[I1*,+�&@0l()*<;]>@K.+ _�}�K.\1AH?=*f�,�W_�\-OFH&�{w-�;=FH?=*[*3(HK��d*[?=*[QL;mTV*E-DFW*,-�?O*,UH?O*E-D*,QL;OK.QH\f()KR�d*[?=*[QL;�+.*[I7*[+Y-�&10t?O*E-D&7+RAH;OK.&1Qy&10�;OFH*�()&1\C_�kmFH*[MX:[>1Q6g*oAW-O*,(/6g&@;=FX0j&1?�\7?=>1UHFHKY:[-�?=*[QC()*[?=KRQW\#&1?�0j&7?�&76)89*,:<;�?O*E:<&7\1QHKR;OK.&1Q/IvK.>�?]>@QW\1*w(H>@;=>H_* FH*,QXAW-O*,(/0j&7??=*,:<&7\1QHKR;OK.&1Qtc@0j*,>@;OAH?=*w*[�L;=?=>7:e;=KR&7QX&1Ug*[?]>�;O&7?=-�T�AW-D;�6g*3()*(�WQH*E(/;O&f*<�v;O?]>1:<;�0j*,>@;OAH?=*,-�0j?O&7T�;=FH*o?]>@QH\7*(H>@;=>f;OFW>@;o:[>1QB6g*#AW-O*,(iKRQpTX>�;]:]FHK.QH\W_��vAW:]Fi0j*E>�;OAW?O*E-m{�KR+.+�6C*r(HK.-=:<AW-=-O*,(i+.>@;O*,?�KRQB;OFHKY-w:]FW>1U);O*,?,_]_^-`�]�`�� O�!��f_�W�Sk-��f_�)��f��#f��dgj9k-fHlah�vK.QW:<*�TX>@QvMy&10t;=FH*#*,>1?O+.My214sIvKY-DK.&1Qp-DM)-D;O*,T/-m{q&1?T&1*E(X{�KR;OFpUC&7+RMv\7&1QW>1+g&76)89*,:<;=-,c)*,()\7*,-mFW>JI7*36g*[*,Q;OFW*#T/>1KRQp+.&):[>@+d0j*E>�;=AH?O*#AC-D*E(�0j&7?�?O*E:<&7\1QHKR;OK.&1Qi&1?�Ug&7-O*�*,-D;OK.T/>@;OK.&1Q|_ m ;OFH?=*[*{�v()K.T/*[QW-OKR&7QW>@+d&76)89*,:<;T/&)()*[+W;OFW>@;�:<&1QC-DKY-9;]-�&@0d&1QW+RM�;OFH*w*E()\1*E-�>@QC(fI7*[?O;OKY:<*E-l&@0d;OFH*o&16)89*E:e;�KY-�:[>1+R+.*,(/>�� n�p(��n�uwxyp TV&)()*,+ _kmFH*r{�K.?=*<^�0j?=>1TV*#?=*[UW?O*E-D*,Q7;]>�;=KR&7Qi>7-O-OAHT/*,-m;=FW>�;o;OFH*V-DAH?O0�>1:[*,-�&10l;OFH*r&76)89*,:<;3>@?=*#UH+Y>@QW>1?o>@QC(i;OFW>@;;OFW*#&16)89*E:e;�FW>1-m&7QH+.MB-D;O?]>@K.\1FL;q*E()\1*E-[_

m AW-D*[0jAH+�\1*,QH*[?]>@+.K�[,>�;=KR&7QX&@0u;OFH*n{�KR?=*<^�0j?]>@T/*oT/&)()*[+d;=FW>�;�FW>7-�6g*[*,QBFW*,>JIvKR+.MXAW-O*,(�KRQi:<&1T/UHAH;O*[?IvK.-OK.&1Q KY-X;OFW* z�rtn��{u% �p(¡¢p�£(q¢p{¡$¤�p(n ~ p�¥ ?=*[UH?=*,-O*[QL;]>�;OK.&1Qt_skmFW*�?=*[UH?=*,-O*[QL;=>@;OK.&1QPK.-i>G(H>@;=>G-D;O?=AW:<;OAH?=*:<&7QL;=>@K.QHK.QH\i;OFH*XI7*[?O;OKY:<*E-3&10�;=FH*X&16H89*,:e;Ec�;OFW*y-DAH?O0�>1:[*,-�&10�;OFW*X&16)89*E:e;,ct;OFH*X*E()\1*X-O*[\7TV*,QL;=-�&@0q;OFW*&16H89*,:e;EcH>@QW(|c)AW-DAC>@+.+RM7cv;OFH*�;=&1Ug&1+.&1\1KY:[>1+d?O*,+.>@;OK.&1QW-OFHK.UW-�;OFW>@;�-OUg*,:<KR0jMy;=FH*r-OAH?D0�>7:<*E-�&7QB*,K�;=FH*[?w-OKY()*�&@0>@Q'*E()\1*V>@QW(i;=FH*�I7*[?O;OKY:<*E-w&1Q'*,K�;=FH*[?n*[QC(p&@0�>@Q'*E()\1*V-D*,\1T/*[QL;E_9* FH*[Q';=FH*�&76)89*,:<;3KY-wUg&1+.Mv\1&1QC>@+�c;OFW*p-OAH?O0�>1:[*,-/>@?=*�UH+Y>@QC>@?X>@QW(G;OFH*p*E()\1*'-O*[\1T/*,Q7;]-f>1?O*p-D;O?]>@K.\1FL;V+.K.QH*i-O*[\7T/*[QL;=-,_Z�o&�{�*,I1*[?Ecl;OFW*

�� )�� w�� ¢�R�� ¡ �WV

}uK.\1AW?O*/�[�C_ \H��kmFH?O*,*�TV*E-DFW*,-m&@0�;OFW*r()&1\X>�;w()KR�d*[?=*[QL;w?O*E-D&7+RAH;OK.&1QW-,_��&7AH?O;O*,-OMy&10��#>@?=K|��AW+R+.K _

T/&)()*[+|\7*[QH*,?=>1+RK�[[*E-�;O&/KRQC:<+.AW()*r:<AW?OI7*,(B*,()\7*�-O*[\7T/*[QL;=-�>1QW(C~J&7?�:<AH?=I1*E(�-OAH?D0�>7:<*E-[_}�KR\7AH?=*��[�C_ 2�KR+.+.AW-9;=?=>@;O*E-�>V-O>1T/UH+R*n-DAW?D0�>7:<*<^�*,(H\1*<^�I1*,?D;=*<�/(H>�;]>f-D;O?=AW:e;=AH?=*oAW-O*,(y0j&1?m?O*,UH?=*,-O*[QL;OK.QH\>X(H>@;=>@6C>1-O*3&10�&76)89*,:<;wTV&)()*,+.-wKRQ'>X214 &16)89*E:e;�?O*E:<&7\1QHKR;OK.&1Qp-DM)-D;O*,Ti_�kmFH*r(H>�;]>/-9;=?OAW:<;OAH?=*#KY-�FHK.*[?O^>@?]:]FHKY:[>1+ c76C*,\1K.QHQHK.QH\f{�KR;OF�;OFH*n{q&1?=+.(y>@;�;=FH*o;=&1UB+R*,I1*[+d>@QC(y:<&7Q7;=KRQvAHK.QH\V()&�{�QX;O&f;OFW*n-OAH?O0�>1:<*E-�>1QW(>@?]:[-q>�;�;OFH*�+.&�{�*E-9;�+R*,I1*[+�_làQB}�K.\1AH?=*��,�W_ 2#;OFW*36g&J�)*,-�{�K�;=F��W*,+.(W-�+Y>@6g*[+.*,( QW>1T/*1cL;9MvUC*7c��*[QL;OKR;9M� #c;O?]>@QC-90��gKRQC()K.:,>�;=*�;OFH*o*[+.*[T/*[QL;=-�&@0|>r-O*<;�&10|:<+Y>1-=-��*[QL;OKR;9M� #_��>1:]F/*[+.*[T/*[QL;�&10d;OFH*o-O*<;�FW>1-�>�QW>@T/*1c>f;9MvUC*7cH>fUg&1K.QL;O*,?m;O&X>@Q��*[QL;OKR;9M� #cH>@QW(i>f274s;O?]>@QC-90j&7?OTX>�;=KR&7QX;OFC>�;�K.-�>1UHUH+.KR*E(B;O&f;OFH*��*,Q7;=K�;9M� ;O&i&16H;=>@K.Qh>�Ug&@;=*[QL;OKY>@+.+RM'?=&@;]>�;=*,(�>1QW(�;O?]>@QW-O+.>@;O*E('KRQC-9;]>@QW:[*1_f}W&1?�*<�H>1TVUW+R*7cd;OFH*/{q&1?=+.(�FW>1-�>i-D*[;:[>1+R+.*,(�� p� ~ z _�àQi;OFC>�;o-O*<;o>@?=*�QW>@T/*E(BK.QW-D;=>1QW:<*E-m&@0lIJ>1?OK.&1AC-�214�&76)89*,:<;mT/&)()*,+.-,_ m QvMB\1K.I1*[Qi&16H^89*,:<;�T/&)()*[+CK.-�()*{�CQH*,(/K.QyKR;=-�&�{�QX:[&L&7?=(HKRQW>@;O*w-OM)-9;=*[Tp_�kmFH*�;O?]>@QC-90j&7?OTX>�;=KR&7QV>1+R+.&�{w-�*E>1:]F/KRQC-9;]>@QW:[*;O&/6g*#KRQC()*[Ug*[QW(H*[QL;O+.MBUg&7-OKR;OK.&1QH*E(�K.Qi;OFH*#{q&1?=+.(|_kmFH*V&16)89*E:e;�T/&v(H*[+Y-�*,>1:]F�FW>JI1*f;OFH?=*[*/-O*<;=-,�w;=FH*[K.?#*,(H\1*,-,cg;OFH*,KR?#I7*[?O;OKY:<*E-[c�>@QC(';OFW*[K.?�0�>1:<*E-[_ mI1*,?D;=*<�VFW>1-�>@QX>1-=-D&):[K.>@;O*,(/274 Ug&1K.Q7;m>@QW(X>#-O*<;�&@0�*,()\7*,-�;OFW>@;�T/*[*<;m>�;�;=FW>�;qUC&7KRQL;,_ m QX*,()\7*wFW>1-�>-D;=>@?O;lUC&7KRQL;,c@>1Q�*,QW(�Ug&1K.QL;,c1>o0�>1:[*�;=&3KR;=-�+.*<0 ;Ec1>w0�>7:<*�;O&nK�;]-l?OK.\1FL;Ec@>@QW(f>@Qf>1?=:�;OFW>@;�()*{�WQW*,-�K�;]-u0j&1?=TicKR0�KR;nKY-nQH&@;#>B-D;O?]>@K.\1FL;n+RK.QH*1_ m 0�>7:<*�FC>1-�>B-OAH?O0�>1:[*r;OFC>�;#()*{�WQW*,-nK�;]-�-DFW>1UC*/>@QC(�>i-D*[;n&10�6C&7AHQW(v^>@?=K.*,-rK.QW:[+RAW(HKRQH\�K�;]-�&7A);O*,?f6g&1AWQW(H>@?=K.*,-�>1QW(NFH&7+R*�6C&7AHQW(H>1?OK.*,-,_ m 6C&7AHQW(H>1?OMbFW>1-V>@QG>7-O-O&):<KY>�;=*,(0�>1:[*r>@QW(p>X-O*<;w&10l*E()\1*E-[_�kmFH*#+R&�{q*,-D;w+.*[I1*,+�*[QL;OKR;OK.*,- �v>1?=:,-[cH-OAH?O0�>1:[*,-,cW>@QW(iUg&1K.QL;=- �v>@?=*nQH&@;3(H*{�WQH*E(FH*,?O*7_Uw*[UH?=*,-O*[QL;=>@;OK.&1QW-�0j&1?q-DAH?O0�>1:[*,-q>@QW(�>@?]:[-�{�K.+.+g()*,UC*,QW(y&7Qy;=FH*3>1UHUH+.K.:,>�;OK.&1QB>@QW(X&7QX;OFW*n>7:[:<AH^?]>1:<Mp>@QC(-DT/&v&@;=FHQH*E-O-3?O*E�LAHKR?=*,(|_okmFH*[M'T/K.\1FL;36g*�?=*[UW?O*E-D*,Q7;=*,(p6vMp*,�LAW>@;OK.&1QW-3&1?o0jAH?D;=FH*[?n6H?=&%&7*[Q()&�{�QrK.QL;O&�-DAW?D0�>7:<*�UC>�;=:]FW*,-�>@QW(r>1?=:�-D*,\1T/*[QL;]-[_��l&1K.Q7;]-t>1?O*�TV*,?O*,+RM�I7*,:e;=&1?]-t&10�� c M1c [��u:<&v&1?]()K.QW>�;=*,-,_}�KR\7AH?=* �[�C_ �P-DFW&�{w-B>Z-DK.T/UH+R*N274 &76)89*,:<;B;=FW>�;':[>1Q 6g*�?=*[UW?O*E-D*,Q7;=*,( K.Q ;=FHKY-pT/>1QHQH*,?,_�ku&

¡ \ � �� ! #"$"%"

POINT

FACE

POINTPOINTFACE

point

FACE

objects

faces

edges

vertices

name type object transf

name type face transf name type vertex transf name type edge transf

boundaries edges

left face

right face

start pt.

end pt.surface

arcname type boundary transf

edges

boundary set

face

SURFACE

ARC

VERTEX

WORLD

OBJECT

FACE EDGE

BOUNDARY

object set

face set vertex set edge set

}uK.\1AW?O*/�[�C_ 2W��vAH?O0�>1:<*[^�*E()\1*[^�I7*[?O;O*[�/(H>@;=>X-D;O?=AW:e;=AH?=*1_

E3

E2

V2

V1E1

F3

F2

F1

F4 F5

}uK.\1AW?O*/�[�C_ �C��H>@T/UH+.*r214s&16H89*,:e;w{�KR;OFpUH+Y>@QC>@?�>@QW(p:[ML+.K.QW()?=K.:,>@+|-OAH?D0�>7:<*E-[_

�� )�� w�� ¢�R�� ¡ \H�-OKRT/UH+.K�0jMb;=FH*�K.+R+.AW-D;O?]>�;=KR&7Q|c�&1QH+.Mh>p0j*[{�IvKY-DK.6H+.*B-OAH?D0�>7:<*E-�>@QC(h*,()\7*,-V>@?=*y()K.-=:<AC-O-O*,(�_�kmFH*�IvKY-DK.6H+.*-OAH?D0�>7:<*E-n>1?O*/}q�1c|}�\)cu}�2Wct}��Wct>1QW(�} ¡ _V}q�1c|}l2Wct}��Wct>1QW(�} ¡ >@?=*fUW+.>1QW>@?#-OAH?D0�>7:<*E-[c�{�FHK.+.*/}�\�K.->i:<Mv+RK.QW()?=KY:[>@+l-OAH?D0�>7:<*7_r}��VKY-�6C&7AHQW()*E(6vM>B-OK.QH\1+.*f6g&1AWQW(H>@?=M':<&7TVUg&7-O*,(�&@0�>i-OKRQH\7+R*V*,(H\1*f;OFW>@;:[>1QX6C*n?=*[UH?=*,-O*[QL;O*E(V6LMX>r:[KR?]:<AW+.>1?�>@?]:@_l}�\�KY-�6g&1AHQC()*,(X6vMV;9{q&�-DAC:]FX6C&7AHQW(H>1?OK.*,-,_�}l2�K.-�6C&7AHQW()*E(6vM�>1Q�&7A);O*,?#6C&7AHQW(H>1?OM�:[&1T/Ug&7-O*,(b&@0�0j&1AH?�-D;O?]>@K.\1FL;�*,()\7*,-#>1QW(h>BFW&1+.*X6C&7AHQW(H>1?OM�:[&1T/Ug&7-O*,(�&@0>X-OKRQH\7+R*f:<K.?=:[AH+.>1?w>@?]:@_m}��WcC>1QW(p} ¡ >@?=*#*,>7:]Fi6g&1AWQW()*,(p6vMp>X-DK.QH\7+R*#6g&1AHQC(H>@?=MB:[&1T/UC&L-D*E(p&@0�0j&1AH?-D;O?]>@K.\1FL;r*,()\7*,-,_ ��()\1* �o�y-D*,UW>@?]>�;=*,-n0�>7:<*,-�}�2�>@QW(N} ¡ _i`�0�{�*y;=>�&7*XI1*,?D;=*<��f�X;O&'6g*�KR;=-f-9;]>@?O;Ug&1K.Q7;w>1QW(�� \#;=&/6C*�KR;=-m*[QC(�Ug&1K.QL;,cv;OFW*[Qp}�2VKY-mK�;]-m+R*[0 ;m0�>1:<*�>@QC(B} ¡ K.-qKR;=-m?=KR\7FL;�0�>7:<*1_��*,?D;=*<�� \FW>7-q;OFH?=*[*#>1-=-O&v:[K.>@;O*E(�*E()\1*E-��w�1c � \)cH>@QC( ��2H_�� S�vAH?O0�>1:[*<^�*,()\7*<^�I1*[?O;O*[�y-9;=?OAW:<;OAH?=*�o-OK.QH\r;=FH*o?=*[UH?=*,-O*[QL;]>�;OK.&1Q/&10t}uK.\1AW?O*r�,�W_ 2Hcv:<?=*,>@;O*o>#T/&)()*,+C&10�;OFH*3*[QL;OK.?O*3&16)89*E:e;�-OFH&�{�QyK.Q�}�K.\1AH?=*�[�C_ �Cc1QW>1T/KRQH\�*,>1:]F/0�>7:<*7c7*E()\1*7cL>1QW(XI1*,?D;=*<�VKRQX;=FH*30jAH+R+d214�&16H89*,:e;EcL>1QW(/AW-OKRQW\r;OFW*,-O*wQW>@T/*E-�K.QX;OFW*-D;O?=AW:e;=AH?O*7_

]_^-`�]�`�b � f��-f��l��_f�k9�! �"-l#��!k!f�� dgj9k-fHlahm q$p(� p(n�u�s��%$WpT£ '&ws �� £%p(n K.-#>BI1&7+RAWTV*[;O?=K.:VUH?=K.TVKR;OK.I1*/()*(�WQH*,(b6vM>p-DUC>1:<*/:<AW?OI7*V>@�vKY-�>@QW(b>p:<?=&7-=--O*,:e;=KR&7Qr0jAHQC:e;OK.&1QV>�;l*,>7:]FrUC&7KRQL;l&@0H;=FH*�>��)KY-[_�kmFH*q:[?O&L-O-u-D*E:e;=KR&7Q�KY-�-O{q*[U);l>@+.&1QH\o;OFH*m>��)KY-�:[?O*E>�;=KRQH\3>-O&1+.K.(/&10d?=*[I7&1+.A);OK.&1Qt_u}H&7?�*<�H>1TVUW+R*7cL>#:[&1T/T/&1Qy:<K.?]:<AH+Y>@?�:[ML+.K.QW()*[?�K.-�>#\1*,QH*[?]>@+.K�[[*,(V:<Mv+.KRQC()*[?�{�FH&7-O*>��)KY-qK.-m>V-9;=?=>1KR\7F7;m+.KRQH*�-O*[\1T/*,Q7;�>@QC(�{�FH&7+R*�:<?=&7-=-q-D*E:e;OK.&1QBK.-�>V:<K.?]:<+.*3&10u:<&7QW-9;]>@QL;m?=>7()KRAC-[_ m :<&7QH*KY-3>X\7*[QH*,?=>1+RK�[[*E(':<Mv+.KRQW(H*[?o{�FW&7-O*f>��)KY-wKY-3>�-9;=?=>1KR\7F7;3+RK.QH*f-O*[\7T/*[QL;n>1QW(p{�FH&7-O*f:[?O&L-O-o-D*E:e;OK.&1Q�K.-3>:<K.?]:<+.*�{�FH&7-O*�?=>7()K.AW-�-9;]>@?O;=-�&7A);Z[,*[?=&�>@;�&1QH*�*,QW(/Ug&1K.Q7;�&@0g;OFH*o>@�)K.-�>1QW(V\1?=&�{w-�;O&#KR;=-�T/>@�)KRTfAHT�>@;;OFW*q&1;OFH*,?l*[QW(fUC&7KRQL;E_ m ?=*,:e;]>@QH\7AH+Y>@?l-D&7+RKY(�KY-l>n\1*[QW*[?]>@+.Kv[,*,(r:[ML+.K.QW()*[?l{�FH&L-D*m>��)KY-�K.-�>n-9;=?=>1KR\7FL;�+.KRQW*-O*[\1T/*,Q7;�>@QW({�FH&7-O*�:<?=&7-=-o-O*,:<;OK.&1QKY-n>�:<&7QW-D;=>@QL;n?O*E:e;=>1QH\1+.*1_ m ;=&1?=AW-oKY-n>y\1*,QH*[?]>@+.K�[[*,(p:[ML+.K.QW()*[?{�FH&L-D*#>��)KY-mK.-�>/:[KR?]:<+.*#>@QW(i{�FH&L-D*#:<?=&7-=-m-D*E:e;=KR&7QBKY-w>/:<&7QW-9;]>@QL;w:<K.?=:[+R*7_

m \1*,QH*[?]>@+.Kv[,*,(y:[Mv+RK.QW()*,?qT/&)()*,+�&@0u>1QB&76)89*,:<;qK.QW:<+.AW()*E-�()*,-=:<?=K.U);OK.&1QW-q&10|;OFH*�\7*[QH*,?=>1+RK�[[*E(y:<Mv+.KRQ)^()*,?=-r>1QW(�;OFH*B-DUW>@;OKY>@+�?=*[+Y>�;=KR&7QW-OFHKRUC-#>@T/&1QH\i;=FH*[TpclUH+.AW-#\1+.&16C>@+�UH?=&1Ug*[?O;OK.*,-#&10�;=FH*y&76)89*,:<;,_BkmFW*:<Mv+.KRQC()*[?]-o:,>@Qp6C*V()*,-=:<?=K.6C*E(p6LMi+.*[QH\1;OF'&@0�>@�vKY-,cC>JI1*,?=>1\1*#:<?=&7-=- �v-O*,:e;=KR&7Q�{�KY(v;OFtcg?]>�;=KR&X&10l;OFH*�;9{�&Cc>@QC(i:[&1QH*#>1QH\1+.*1_��&7QHQH*,:<;OK.IvK�;9MyKY-m;=FH*rT/&7-D;w:<&1T/T/&1Q'-OUW>�;=K.>1+�?O*,+.>@;OK.&1QW-OFHK.U|_�àQ'>1(H(HK�;=KR&7Q�;=&X*[QW(vÛg&1K.Q7;X:<&7QHQH*E:e;OK.IvK�;9M7c�:<Mv+.KRQW(H*[?]-�TX>JMh6C*p:<&7QHQH*E:e;O*E(G-O&;OFC>�;V;OFH*i*[QW( UC&7KRQL;]-�&10o&1QH*i:<&7QHQH*,:<;�;=&>@QNK.QL;O*,?OK.&1?fUC&7KRQL;f&10o>@QH&1;OFH*,?,_'àQG;OFHKY-f:,>1-O*1c�;OFW*�UW>1?=>1TV*[;O*,?=-#&10�;OFH*i:<&7QHQH*,:<;OK.&1Q|c�-OAW:]F >7-#;OFW*Ug&7-OK�;=KR&7Qi>@;q{�FHKY:]FB;OFH*#:<Mv+.KRQC()*[?]-q;O&7AW:]F|cL;OFH*#K.QW:[+RK.QW>�;=KR&7Qi>1QH\1+.*1c)>1QW(X;=FH*#\1K.?=(H+R*�>@QH\7+R*�()*E-O:[?OK.6HK.QH\;OFW*3?=&@;]>�;OK.&1QX&10|&1QH*3>@6g&1A);q;OFH*3&@;=FH*[?qTX>JMf6g*3AC-D*E(/;O&V()*,-=:<?=KR6g*w;=FH*3:[&1QHQW*,:e;=KR&7Q|_�zn+R&76W>@+CUH?=&1Ug*[?O^;OK.*,-q&10u>@QB&16)89*E:e;mT/>JM/K.QW:<+.AW()*nQvAHT�6g*[?m&10tUHK.*,:<*E- ��:<Mv+.KRQC()*[?]- �<cvQLAWT�6g*[?m&@0t*,+R&7QH\7>@;O*E(XUHK.*,:<*E-[c)>1QW(-OMLT/T/*<;=?OM'&10�;=FH*X:<&1QWQH*,:<;OK.&1QW-,_��wK.*[?]>@?]:]FHKY:[>1+u\7*[QH*,?=>1+RK�[[*E(:<Mv+.KRQW(H*[?#T/&)()*[+Y-[c�K.Qb{�FHK.:]Fh()KR�g*,?O*,QL;+.*[I1*,+.-�&@0|()*<;]>@K.+W>@?=*�\1K.I1*,QX>�;�()KR�d*[?=*[QL;�+R*,I1*,+.-�&10d;OFH*wFWKR*,?=>1?=:]FvM1c7>@?=*m>1+.-O&#Ug&7-=-DK.6H+.*1_l}H&1?�*<�H>@T/UH+.*1cL>Ug*[?]-D&7QyT/KR\7F7;q6C*3T/&v(H*[+.*,(yI7*[?=Mf?=&1AW\1FH+.MV>7-�>f-9;=K.:�& �W\7AH?O* ��>1-q-OFH&�{�QyK.Q�}�KR\7AH?O*f�[�C_ ¡ ��:<&7QW-DKY-D;OK.QH\&@0�:<Mv+RK.QW()*,?=-�0j&1?�;OFW*nFW*,>1(|c7;=&1?]-D&Cc7>1?OTX-,cv>1QW(X+.*[\L-[_ m ;q;OFH*nQH*<�v;�+.*[I1*,+C&10|;OFW*3FHK.*[?]>@?]:]FvM1c1;OFH*3;O&7?=-O&T/KR\7FL;w6C*�(HKRIvKY()*,(pK.QL;O&y>/QH*E:�&B>@QC(B+.&�{q*[?m;O&7?=-O&Wcv;=FH*�>1?OTX-mK.Q7;=&/;OFH?=*[*f:<Mv+RK.QW()*,?=-q0j&7?wAHUHUg*[?n>@?=Tpc+.&�{�*,?w>@?=Ticg>@QW(pFC>@QW(�cg>@QW(i;=FH*r+.*[\L-w-DK.T/KR+Y>@?=+.M1_ m ;w;OFW*rQH*<�v;o+.*[I7*[+�cH;=FH*rFW>1QW(H-wT/K.\1FL;o6g*r6H?=&%&7*[QK.Q7;=&>iT/>1KRQhUHK.*,:[*X>@QW( �WI7*7�CQH\1*,?=-,cu>1QW(�&7QH*X+.*[I1*,+�()*[*,UC*,?,ct;OFH*��CQH\1*,?=-�T/K.\1FL;r6C*X6W?O&$&1*[Q�KRQL;=&;OFW?O*,*nUWKR*E:<*,-o>@QW(�;OFH*�;=FvAHT�6pK.Q7;=&V;9{�&C_m ;OFH?=*[*{�v()K.T/*[QW-OKR&7QW>@+n\1*,QH*[?]>@+.K�[[*,( :<Mv+RK.QW()*,?':[>@Q�UH?=&@89*,:<;�;=& ;9{q&P(HK��d*[?=*[QL;4&LK.QW(H-i&10r;9{�&��()K.T/*[QW-OKR&7QW>@+�?O*,\1K.&1QW-r&1QG>@QNK.TX>@\7*1��?=K.6H6C&7QW-�>1QW(h*[+.+.KRUW-O*,-,_ mEn�� KY-�;OFH*yUW?O&189*,:e;=KR&7Qh&@0�;OFW*

¡ \$\ �� ! #"$"%"

}�KR\7AH?=*X�[�W_ ¡ ��Uw&1AH\7Fi\7*[QH*,?=>1+RK�[[*E(p:<Mv+RK.QW()*,?wT/&)()*[+u&@0�>/UC*,?=-O&1Q|_qkmFH*�()&1;D;=*,(p+.KRQH*E-�?=*[UH?=*,-O*[QL;�;OFW*>��)*E-m&@0t;=FH*r:<Mv+.KRQC()*[?]-[_

}�KR\7AH?=*i�,�W_ XH��kmFH*/UH?=&v:[*,-=-n&@0�:<&1QC-9;=?OAW:<;OK.QH\p>B\7*[QH*,?=>1+RK�[[*E(�:[ML+.K.QW()*[?r>1UHUH?=&J�)KRTX>�;=KR&7Q'0j?=&1T >S\@4-OFW>@Ug*1_ � ��H>@T/UH+.*#:<&1AW?D;=*,-OMX&@0�zn*[?]>@?](�%'*E()KR&7QHK�_ �

+.&1QH\�Ug&1?O;OK.&1QV&@0g;OFH*w:[ML+.K.QW()*[?Ec@{�FHK.+.*w>@Q p{s�s � � z(p KY-l;OFW*�UH?O&189*,:<;OK.&1QV&@0W;=FH*w:<?=&7-=-�-O*,:e;=KR&7Q|_�}o0g:<&7AH?]-D*7c;OFW*V:[?O&L-O-3-D*E:e;OK.&1Q�K.-3QH&@;#>@+.{m>JMv-o:<K.?=:[AH+.>1?,cd-O&�KR;=-nUH?=&@89*,:<;OK.&1Q'KY-nQH&@;�>@+.{q>JM)-w*,+R+.K.U);OKY:[>1+ c�>@QC(�-O&1T/*\1*,QH*[?]>@+.K�[[*,(V:<Mv+.KRQC()*[?]-�>@?=*�:<&1T/UH+.*<;=*[+.M�-OMLT/T/*<;=?OKY:@cL-D&n;=FH*[MfFW>JI1*mQH&#+.&1QH\7*[?l&1?�-OFH&7?D;=*[?�UW>1?D;]-[_l}H&7?;OFW&7-O*m;OFW>@;�()&WcL>@+.\1&7?OKR;OFHTX-lFW>JI7*�6C*,*[Qy()*,I1*,+R&7UC*E(�;=& �WQW(V;=FH*w?=KR6H6g&1QC-�KRQXK.TX>@\7*,-l&@0d;=FH*wT/&)()*[+.+R*E(&16H89*,:e;]-[_�kmFH*E-D*�>@+.\1&7?OKR;OFWT/-q\7*[QH*,?=>1+R+.M/+R&v&%&/0j&7?m+R&7QH\f?=*[\7KR&7QW-�;OFW>@;�:,>@Qi-DAHUWUC&7?D;q;OFH*�QH&1;OK.&1Qi&@0u>1Q>��)KY-[_f}uK.\1AW?O*i�[�C_ Xi-DFW&�{w-w;=FH*/UH?O&):[*,-=-3&10�()*[;O*[?=T/KRQWKRQH\pUg&@;=*[QL;OKY>@+�>��)*E-3&10�\7*[QH*,?=>1+RK�[[*E(:<Mv+.KRQW(H*[?]-0j?=&1Tx>y\@4�-DFW>1UC*7_

}�KR\7AH?=*��[�C_ ¢'-DFH&�{w-V-D;O*[UC-fK.QZ:[?O*E>�;=KRQH\b>�()*[;=>1KR+.*,( TV&)()*,+m&@03>�UW>@?O;OKY:<AH+Y>@?VFvAHTX>@QG6g&)()MN0j&7?;OFW*rUHAH?=UC&L-D*#&10�T/>%&vKRQH\X{q*[+.+R^��H;O;OK.QH\y:<+.&@;=FHK.QH\W_ m -OUC*E:<KY>@+t-O*[QW-OK.QH\X*[QvIvKR?=&1QWTV*,QL;�:[&1Tf6HKRQW*,-�K.QHUHA);0j?=&1T ;9{q*[+.I1*y:,>@T/*[?]>1-,_/�)K��N:[>1TV*,?=>7-�IvKR*,{�;=FH*yFvAHTX>@QN>@;�*,�LAW>1+�KRQL;=*[?=IJ>1+.-r&@0w> \�T :<Mv+.KRQW(H?OKY:[>1+?=&L&7Tp�l;OFH*,?O*rKY-w>/+.&�{�-O*<;3>1QW(iFHK.\1F'-D*[;o-D&/;=FW>�;n>R\�T�;]>@+.+|Ug*[?]-D&7Qp:,>@Qp6g*#ILK.*[{q*,(|_ m -o-DFH&�{�QpK.Q}�KR\7AH?=*V�,�W_ ¢vc)-OKR+.FH&1AW*<;D;=*,-q0j?=&1Tx-OKR�i:[>1T/*[?]>1-q>@?=*nAC-D*E(y;=&��H;w*[+.+RK.U);=K.:,>@+|:<?=&7-=-m-D*E:e;=KR&7QW-q;O&/&16H;=>@K.Qp>:<Mv+.KRQC()?OKY:[>1+�T/&v(H*[+�_ m +.KR\7FL;�\7?OKY(�K.-#>1+.-O&BAC-D*E(b-O&B;OFW>@;#;O?=K.>1QH\1AH+Y>�;=KR&7Q�:,>@Qb6C*XAW-O*,(�;O&':[&1T/UHA);=*214�-DAH?O0�>1:[*�UC&7KRQL;=-wKRQ'>1(W()K�;=KR&7Qi;O&/UC&7KRQL;]-�&1Qi;OFW*r-DK.+RFW&1AH*[;D;O*E-[_m��&1QW:,>JILKR;OK.*,-m>1?O*#()*,I1*[+.&1Ug*,(BAW-OKRQW\;OFW*r-9;=?OAW:<;OAH?=*,(B+.KR\7F7;o(W>�;=>WcH>@QW(BAH+R;OK.TX>�;O*,+RMi>/()*<;]>@K.+R*E(BT/*E-DFp&@0u;O?=K.>1QH\1+.*,-mKY-�:<&7T/UHA);O*E(�_

�� )�� w�� ¢�R�� ¡ \12

}�KR\7AH?=*i�,�W_ ¢v� �L;O*,UW-#K.Q�TX>�&vK.QH\'>iTV&)()*,+�&@0m>BFvAHTX>1Q�6g&)()M'0j&1? �W;D;OK.QH\:[+R&1;OFHK.QH\W_ ��ku&1U ��kmFH?O*,*:<?=&7-=-q-D*E:e;OK.&1Qp:<AW?OI7*,-m>@+.&1QH\f{�K�;=F':<?=&7-=-�-O*,:<;OK.&1Qp-DK.+RFW&1AH*[;D;O*E-q0j?O&7T�-DKR�B:,>@T/*[?]>1-�IvKR*,{�KRQH\f;OFW*#6C&)()M� ;=FH*m-9;=?=>1KR\7F7;|+.K.QH*,-uUH?=&@89*,:<;|;OFW*q-OKR+.FH&7AH*<;O;O*�;=&�{q>1?=(3;=FH*�:,>@T/*[?]>1- �e_H�v;O?=AW:e;=AH?O*E(#+.KR\7F7;u0j*,>@;OAH?=*,-u>@+.+R&�{214 UC&7KRQL;=-�;O&y6g*r:<&7TVUWA);O*E(pKRQ':<&7QW:[>JIvKR;OK.*,-,_ ��q&1;D;O&7T ��zn*[QH*,?=>1+RK�[[*E(i:[Mv+RK.QW()*,?�TV&)()*,+u:[?O*E>�;O*E(�6vM�H;O;OK.QH\y*[+.+.KRU);=K.:,>@+l:<?=&7-=-�-D*E:e;=KR&7QW-m;O&y;OFH*V-DKR�i-OKR+.FH&7AH*<;O;O*,-,cg?O*E-DAH+R;OK.QH\/;=?OKY>@QH\7AH+Y>@?�T/*,-OF|cd>@QW(p-OFW>1()*E(K.T/>1\1*7_ ��&1AH?O;O*E-DM�&@0��w*[+.*[Q �vFW*[QN>@QW(b:<&7+R+.*,>1\1AH*E-�>�;#;OFW*y4o*,U);,_y&10��&7TVUWA);O*,?7�):<K.*[QC:<*1c��w&7QH\��&1QW\ �oQHKRI7*[?]-DKR;9M'&@09�):<K.*[QC:<*X>@QW(�kt*E:]FHQH&7+R&7\1Md�oUH?=&@89*E:e;#-DAWUHUC&7?D;=*,(�6vM\1?]>@QL; m }�~v� � 2L~�VL¢f0j?=&1T;OFW*#àQW()AW-D;O?=M�>@QC(iku*,:]FWQH&1+.&1\7My4o*,I1*[+.&1UWTV*,QL;o��&7AHQW:[KR+�&10l�o&1QH\X��&1QW\Wc�� m Us&10��FHK.QW>/K.Qh�)V%Vv¢v_ �

¡ \@� �� ! #"$"%"

�� zn*[QH*,?=>1+RK�[[*E(B:[Mv+RK.QW()*,?�TV&)()*,+.-��&1QC-9;=?OAW:<;q>#\7*[QH*,?=>1+RK�[[*E(X:<Mv+.KRQW(H*[?qTV&)()*,+C&10t>@Q�>1KR?=UH+Y>@QH*7_�kmFW*3>@K.?=UH+.>1QH*o-OFH&1AW+.(XFC>JI1*o>r0jAW-D*,+.>1\1*7c{�K.QH\7-,c�>@QC( >�;=>@K.+�_GkmFH*p{�KRQH\L-f-OFH&7AH+.( *,>7:]F FW>JI7*B>@QP>�;O;=>1:]FW*,(NT/&@;=&1?E_Gkt?=Mh;O&h()*E-O:[?OK.6C*B;OFW*:<&7QHQH*E:e;OK.IvK�;9M�?O*,+.>@;OK.&1QW-OFHK.UW-m6C*[;9{�*,*[QiUW>@K.?]-m&@0u\7*[QH*,?=>1+RK�[[*E(B:[Mv+RK.QW()*,?=-,_

F EP F PE

F E

P

PP

F F F F E E F F F F F F E E F F

1 5

740

2 6

OCTREE

NUMBERING SCHEME

F F F F EEF F FFF E F F

OBJECT

}�KR\7AH?=*V�,�W_ � � m -DK.T/UH+.*�;OFH?=*[*{�v()K.T/*[QW-OKR&7QW>@+d&76)89*,:<;o>@QW(BK�;]-�&):e;=?O*,*n*,QW:<&)()K.QH\C_

]_^-`�]�`�^ � � �#��f�f�hm Q � ~ n�p�p KY-�>3FWKR*,?=>1?=:]FHKY:[>1+ � �v>1?OMn;=?O*,*m-D;O?=AW:<;OAH?=*1_ ��>1:]FVQH&)()*mK.Qf;=FH*q;O?=*[*�:<&7?O?=*,-OUg&1QW(H-u;=&�>�:[AH6HKY:?=*[\1K.&1Qp&10�;=FH*�AWQHKRI7*[?]-D*7_wkmFH* svu � p{s &@0�>XQH&)()*rKY-3*[KR;OFH*,? ��rts�s cdKR0�;OFH*�:[AH6g*�KY-3:[&1T/UH+.*<;O*,+RMi*[QC:<+.&7-O*,(6vMr;=FH*m;OFH?=*[*{�v()K.T/*[QW-OK.&1QW>1+)&16)89*E:e;,c p{x � ~ & K�0g;OFW*o:<AH6g*w:<&7QL;=>@K.QW-lQH&#UC>@?O;�&@0g;OFH*w&76)89*,:<;,c@&7? � uwn ~ ��uws cKR0u;=FH*r:<AH6g*#UW>1?D;=+RMyK.QL;O*,?=-O*,:<;=-q;OFW*n&76)89*,:<;,_ m QH&)()*#{�KR;OFp+Y>@6g*[+ ��rts�s &1? p(x � ~ & FW>7-mQH&X:]FHK.+.()?=*[Qt_ mQH&)()*�{�KR;OF/+Y>@6g*[+ � uwn ~ ��uws FW>7-�*[K.\1FL;�:]FHK.+.(H?O*,QV?=*[UW?O*E-D*,Q7;=KRQW\o;=FH*�UW>@?O;OKR;OK.&1Q/&10W;OFW*o:<AH6g*�K.Q7;=&#&):e;=>1QL;=-,_

m ;OFH?=*[*{�v()K.T/*[QW-OK.&1QW>1+7&76)89*,:<;�:,>@Qf6C*�?=*[UH?=*,-O*[QL;=*,(#6vM�> \��K\��K\��#;OFH?=*[*{�v()K.T/*[QW-OKR&7QW>@+v>@?=?]>JM0j&1?3-D&7TV*#K.QL;O*,\1*[?��_�kmFH*r*,+R*,T/*[QL;=-�&10l;OFH*�>1?O?]>JMy>@?=*r:[>1+R+.*,( ¤ � ¥#p(s�z >1QW(iFW>JI1*r>/I�>1+RAH*#&10�� 0jAH+.+ �&1? � �j*[T/U);9M��<cCK.QW()KY:[>@;OK.QH\X;OFW*rUH?=*,-O*[QW:[*#&1?o>16W-D*,QW:<*#&10l;OFH*r&76)89*,:<;,_mkmFH*r&):e;=?O*,*#*[QW:[&)()KRQW\y&@0l;OFW*&16H89*,:e;�KY-�*,�LAHK.I�>@+.*[QL;l;O&�;=FH*m;OFH?=*[*{�v()K.T/*[QW-OK.&1QW>1+v>1?O?]>JM�?O*,UH?=*,-O*[QL;=>@;OK.&1Q|c�6HAH;�{�KR+.+H\1*,QH*[?]>@+.+.M#?O*E�7AWKR?=*T�AC:]F+R*E-O-n-OUW>1:[*1_�}uK.\1AW?O*B�[�W_ � \7KRI7*,-o>B-DK.T/UH+.*f*[�)>1T/UH+R*f&@0�>1Q&16)89*E:e;#>@QW(K�;]-3&):<;O?=*[*r*,QW:<&)()K.QH\WcAW-OKRQW\f;=FH*#&):e;]>@QL;wQvAHT�6g*[?=KRQW\/-=:]FH*,TV*�&10�L>1:�&vKRQC-q>1QW(pku>1QHK.TV&1;O&C_

�� }n:e;=?O*,*,-}�KR\7AH?=*'�[�W_.�1�X-OFH&�{w-�;9{q&'IvKR*,{w-#&@0w>-OKRT/UH+.*�:]FW>1KR?E_p��&7QW-D;O?=AW:e;�>1QN&v:<;O?=*[*XT/&)()*[+�&@0m;OFW*�:]FW>@K.?E_m -=-OAHT/*f;=FW>�;n;OFW*/-O*,>@;�>1QW(6C>1:�&>@?=*�6g&@;=F��iI1&J�)*,+.-36vM'�BI7&J�v*,+.-36vMN�fI7&J�)*[+l>@QW(�;OFW>@;n*E>1:]F�&@0;OFW*#+R*,\7-mKY-�2/I1&J�)*[+Y-�6vM��nI7&J�)*[+d6vM�#I1&J�)*[+�_

�� )�� w�� ¢�R�� ¡ \ ¡]_^-`�]�`�� O��f��O�-��k-� �a�_h�vAHUg*[?]�LAW>1(H?OKY:[-�>1?O*�T/&)()*[+Y-w&7?OK.\1K.QW>@+.+.My()*[I7*[+.&1Ug*,(B0j&1?o:[&1T/UHA);=*[?�\7?=>1UHFHKY:[-�>@QC(BUW?O&7UC&L-D*E(�0j&7?�AW-O*K.Qf:<&7T/UHA);O*,?uIvKY-DK.&1Q#6vMr�l*,Q7;=+.>1QW(�_H�)AHUC*,?=�LAW>7()?=K.:,-t:[>1Q�K.QL;OAHKR;OK.I1*,+RM�6g*�;=FH&1AH\7FL;u&@0W>7-t+.AHT/UW-�&@0W:[+.>JM;OFC>�;�:,>@Q/6C*w(H*<0j&1?=T/*,(/>@QC(/\1+.AH*,(f;O&7\1*[;OFH*,?�KRQL;O&#&76)89*,:<;�T/&v(H*[+Y-[_�%>@;OFH*,T/>@;OKY:[>1+R+.M�-OAHUC*,?=�LAW>7()?=K.:,-0j&1?=Ts>�UW>@?]>@T/*[;O*[?=K�[[*,(o0�>@T/K.+RM�&10)-OFW>1UC*E-[_ m -DAWUC*,?=�LAW>7()?OKY:�-OAH?D0�>7:<*�KY-u(H*{�WQH*E(�6vMn>�I7*,:<;O&1?��i{�FH&7-O*�� >@QW(��X:<&7T/UC&7QH*[QL;=-�>1?O*#-OUC*E:<Kv�W*,(p>7-q0jAHQW:e;=KR&7QW-�&10t;OFW*r>@QH\7+R*E-��>@QW(��PILKY>f;OFH*#*E�LAW>�;=KR&7Q

�� :<&7- �"! �#��):<&L- ��$ �#� ��&% :[&7- � ! �#��)-OKRQ ��$ �#� ��&' -OK.Q � ! �#��

��9�[�C_R� �

0j&1?)(+* %-, � , * % >1QW(.(0/ , � �1/32ukmFH*XUW>@?]>@T/*[;O*[?]- �� &% >@QW( � ' -OUC*E:<KR0jM;OFW*y-DK�[[*/&@0q;OFW*-OAHUC*,?=�LAW>7()?=K.:nK.QB;=FH* �45� >1QW(6�y()K.?O*E:e;=KR&7QW-[c)?=*,-OUg*,:e;=KRI7*[+.M1_�kmFW*#UW>@?]>@T/*<;=*[?]-07 � >@QW(67 % ?O*,UH?=*,-O*[QL;;OFW*r-O�LAW>1?O*,QH*,-=-qKRQi;OFW*#+.>@;OKR;OAW()*r>1QW(B+R&7QH\1KR;OAW(H*nUW+.>1QH*,-,_�vAHUg*[?]�LAW>1(H?OKY:[-�:,>@Q/T/&v(H*[+W>#-O*<;�&10dAC-D*[0jAH+H6HAHK.+Y()KRQW\r6H+.&v:�&)-�-OAW:]FX>1-�-OUHFH*,?O*E-[c7*[+.+RK.UW-O&1KY(H-,c1:<Mv+.KRQ)^()*,?=-,clUW>@?]>@+.+R*,+R*,UHK.UC*E(H-[c�>1QW(hKRQH^�6g*<;9{q*[*,Q -DFC>@Ug*,-,_ * FH*[Q-7 � >@QW(.7 % >@?=*y6g&@;OF �1c�;OFH*B\1*,QH*[?]>�;=*,(-OAH?D0�>7:<*3K.-q>@Qy*,+R+.K.UW-D&7K.(|cv>1QW(XKR0 �� &% � � ' c)>�-OUHFH*,?O*7_�* FW*[Q�7 � � ��3>@QC(87 % �s�7c7;=FH*�-DAH?O0�>1:[*+.&L&$&)-m+RK�&1*#>/:<Mv+.KRQW(H*[?E_kmFH*wUg&�{q*[?�&10g;=FH*3-OAHUg*[?]�LAW>1()?=KY:m?O*,UH?O*E-D*,QL;=>�;=KR&7Qf+.K.*,-�QW&@;�K.QyKR;=-�>16HK.+RKR;9M�;=&rT/&)()*[+gUC*,?D0j*E:e;�\7*[&1^T/*<;=?OKY:�-DFW>1UC*E-[cv6HAH;wKRQiK�;]-�>@6HK.+.K�;9MX;=&fT/&)()*,+|()*<0j&7?OT/*,(B\1*,&1T/*<;=?OKY:n-DFW>1UC*E-�;OFH?=&1AH\7FB()*[0j&1?=TX>�;OK.&1QC--OAW:]F�>1-Z~ u � p(n��¢q >1QW( � p{��£w��¢q:9 YtKRQH*E>@?t;=>@Ug*[?=K.QH\o>@+.&1QW\�;OFH* [��)>��)K.-tK.-u\1K.I1*,Q#6vMo;=FH*�;=?=>1QW-D0j&1?=T/>@;OK.&1Q

�<; � = >@?ACB �ED �GF �� ; � = >IHA B �JD � F �� ; � �

{�FH*,?O*LKNMV>@QW(�KNO �5(#� , KPM KNO , � ��>1?O*o;OFH*o;=>@Ug*[?=K.QH\�UW>1?=>1T/*<;O*,?=-�{�K�;=F�?=*,-OUC*E:e;q;O&�;OFH* � >1QW( �UH+Y>@QH*E-[cW?O*E-DUg*,:<;OK.I1*[+.M1cC?O*,+.>@;OK.I1*n;O&/;=FH*Q�y(HKR?=*,:<;OK.&1Q|_mkmFH*#6g*[QW()K.QH\�(H*<0j&1?=TX>�;=KR&7QiKY-w()*(�WQH*E(p6LMB;OFW*;O?]>@QC-90j&7?OTX>�;=KR&7Q�R; � � DG:[&7- ��S � ��TU(WV � � ; � � D -DK.Q��S � ��TU(WV � � ; � -OKRQ��YX�� > (ZV �

{�FH*,?O*[K'KY-o;=FH*/:<AH?=I�>�;OAW?O*7cRV�K.-o;OFH*/UH?=&@89*E:e;=KR&7Q'&@0�;=FH* � >1QW( � :<&7T/UC&7QH*[QL;=-3&1QL;=&y;OFW*V6g*[QC()KRQW\UH+Y>@QH*\�\(ZVV\1K.I1*[QB6vM V]� :[&7- = S^(�;]>@Q`_ � = �� F F[a � % D � % T�KY-m;OFW*�;O?]>@QW-D0j&1?=TX>�;OK.&1QB&@0�Vf\7KRI7*[Qi6LMTb�cK _ � (b:[&7- �YX��3d"K _ � (ZVfe

>@QC(+X�KY-q;OFW*#6C*,QW()K.QH\y>@QH\7+R* X��c�:K _ � 2

¡ \%X �� ! #"$"%"

}�KR\7AH?=*y�[�C_ VW�q}�KR;D;O*E('+.*<0 ;D^�I1*,QL;O?=K.:[+R*rT/&)()*,+.-n>�;-�CI1*#;=KRT/*VUC&7KRQL;=-3()AH?=KRQW\�-DM)-D;O&7+R*7cCAW-OK.QH\y*<�v;=*[QW()*E(-OAHUC*,?=�LAW>7()?=K.:,-�{�KR;OFpUW>1?=>1T/*<;O*,?q0jAHQW:e;=KR&7QW- � :<&1AW?D;=*,-OMy&@0 �1K.QW>1Fi��>1?�&y>1QW(B43T/K�;=?OKY-w%'*[;=>@�)>7- �<_

�vAHUg*[?]�LAW>1(H?OKY:#T/&)()*[+Y-3>1?O*#TX>1KRQH+.Mi0j&1?3AW-D*f{�K�;=F?]>@QH\7*r(H>�;]>�>@QC('-D*,I1*[?]>@+tUH?O&):[*,()AH?=*,-w0j&1?3?O*E:<&�IL^*[?=K.QH\';OFW*BUW>1?=>1T/*<;O*,?=-r&@03>-OAHUg*[?]�LAW>1()?=KY:y�H;f;O&�>�-DAW?D0�>7:<*yFW>JI7*y6g*[*[QZUH?=&1Ug&7-O*,(�_b}uK.\1AW?O*�,�W_ VK.+R+.AW-D;O?]>�;O*E-�-OAHUg*[?]�LAW>1()?=KY:9�H;]-�;=&V274s(H>�;]>#0j?=&1T�;OFH*�+.*<0 ;mI1*,Q7;=?OKY:<+.*o&10u>rFW*,>@?O;�>�;Z�CI1*3;OK.TV*nUg&1K.Q7;]-[_kmFH*E-D*r>1?O*n*<�v;O*,QW()*E(i-OAHUg*[?]�LAW>1()?=KY:[-m{�KR;OFpUW>@?]>@T/*[;O*[?q0jAHQC:e;OK.&1QC-[cC{�FH*[?=*n;OFH*#UW>1?=>1T/*<;O*,?=-m>1?O*�QH&1;:<&7QW-D;=>@QL;]-m6HA);�0jAHQW:<;OK.&1QW-,_

+-,/.�� 3�146�� M :RQS6��(G 5 6-3�G14G L{6�� =��{J�G�G M :�QS6��{G

m +.+�&@0�;OFW*f>@6g&�I1*#&76)89*,:<;3?=*[UH?=*,-O*[QL;]>�;OK.&1QC-m*[T/UHFW>7-DK�[[*#;=FH*r;=FH?=*[*��)()K.TV*,QW-OKR&7QW>@+uQW>�;=AH?O*�&@0�;OFW*�&16H^89*,:<;=-,c)6HA);wK.\1QH&7?O*o;OFH*#UW?O&76H+R*,T�&@0�?O*E:<&1\7QHK�[[K.QH\f>1QB&76)89*,:<;�0j?=&1Tx>�;9{q&w�v(HKRT/*[QC-DK.&1QW>1+dKRTX>@\7*o;]>�&7*[Q0j?=&1T!>1Q>@?=6HKR;O?]>@?=MXILK.*[{�Ug&1K.QL;,_�%'&L-9;w&76)89*,:<;=-�+.&v&%&B(HK��d*[?=*[QL;o{�FH*,Q'IvKR*,{�*E(�0j?=&1T5()KR�g*,?O*,QL;oIvKR*,{mÛg&1K.Q7;]-[_ m :<Mv+RK.QW()*,?�;OFW>@;lUW?O&189*,:e;]-|;=&n>3?=KR6H6g&1Q ��-O*[*�>@6g&�I1* ��K.Q�&7QH*q-O*<;�&10WIvKR*,{�UC&7KRQL;=-l>1+.-O&oUH?=&@89*E:e;]-;O&n>@Q#*,+R+.KRUC-D*�KRQ�>1QH&@;=FH*[?�-D*[;u&10HILK.*[{�Ug&1K.QL;=-,_tàQr\7*[QH*,?=>1+ cE{q*�:[>1QrUW>1?D;=K�;=KR&7Q�;OFH*q-DUW>7:<*�&@0)IvKR*,{�UC&7KRQL;=-K.Q7;=&f>��WQHKR;O*�-D*[;q&10 ¤)��p � {svuwz�z{p{z � cv*E>1:]FyIvK.*[{ :<+Y>1-=-�?O*,UH?O*E-D*,QL;OK.QH\�>�-O*<;q&@0|IvK.*[{�Ug&1K.Q7;]-�;=FW>�;�-OFW>@?=*-O&1T/*#UH?=&1Ug*[?O;9M1_�kmFH*#UW?O&7UC*,?D;9MyTX>JMB6C*�;=FW>�;w;=FH*�-=>@T/*#-DAW?D0�>7:<*,-m&10l;OFH*#&76)89*,:<;o>@?=*#ILKY-OKR6H+.*#K.Qp>1QK.T/>1\1*q;=>%&1*,Q�0j?=&1T�;OFW>@;�-D*[;�&@0dILK.*[{�Ug&1K.QL;=-,c@;=FH*w-O>1T/*q+.K.QH*w-D*,\1T/*[QL;]-�>@?=*qIvKY-DK.6H+.*1c7&1?l;OFW*�?O*,+.>@;OK.&1QW>1+()KY-9;]>@QW:[* ��-O*[*o��FW>@UH;O*[?��7��u6g*<;9{q*[*[QV?=*[+Y>�;OK.&1QC>@+)-9;=?OAC:e;OAW?O*E-u*[�v;O?]>1:e;=*,(�0j?O&7T +.KRQH*�()?]>J{�K.QH\7-l>�;�*E>1:]F&@0q;OFW*yIvKR*,{�UC&7KRQL;=-rK.-r-OTX>@+.+�*[QW&1AH\7F|_�}�KR\7AH?=*'�[�W_.� � -OFH&�{w-n;OFH*�ILK.*[{�:<+Y>1-=-O*,-�&@0�>':<AW6C*�(H*{�WQH*E(6vM'\1?=&1AHUWKRQH\�;O&7\1*<;=FH*[?3;OFW&7-O*fIvK.*[{�Ug&1K.Q7;]-n{�FHK.:]FbUH?=&)()AW:<*V+.KRQH*/()?]>J{�KRQW\7-o;OFW>@;�>1?O*f;O&7UC&7+R&7\1KY:[>@+.+.MKY-D&7TV&7?OUWFHK.:1_�}�K.\1AH?=*��,�W_.�1�w-OFH&�{w-�;9{q&�IvK.*[{w-�&@0t>f:]FW>@K.?�K.Qy{�FHKY:]FyT/&7-D;,cv6HA);mQH&1;q>@+.+�cL&10�;OFH*�-=>@T/*-OAH?D0�>7:<*E-�>@?=*wIvK.-OK.6H+R*7_�kmFW*,-O*wIvKR*,{w-�:<&7AH+Y(X6C*o\1?=&1AHUg*,(V;=&1\1*[;OFH*,?�IvKY>#>r:<+.AW-D;O*[?=K.QH\�>@+.\1&7?OKR;OFWT�AW-OKRQW\;OFW*[K.?�?O*,+.>@;OK.&1QW>1+L()KY-D;=>@QC:<*m()*{�WQW*,(f&�I1*[?�?=*[\1K.&1QfUH?=KRT/KR;OK.I1*,-l>1QW(#;=FH*m?O*,\1K.&1Qf>7(J8D>1:[*[QW:[M#?O*,+.>@;OK.&1Q�>7-l>6W>7-DKY-�0j&7?�:<+.&7-O*[QH*E-O-,_�kmFW*[My>@?=*�>@T/&1QH\fTX>@QvMX()K��d*[?=*[QL;w-OKRT/K.+.>1?�IvK.*[{w-�;OFW>@;�;=&1\7*<;OFW*[?q0j&1?=T�>�IvK.*[{:<+Y>1-=-)'d;OFH*/QvAHT�6g*[?�&10�IvKR*,{w-3KY-nUC&1;O*,Q7;=K.>1+R+.M'K.Qt�WQHKR;O*7_fkmFH*VTX>@K.Q�Ug&1K.Q7;�KY-n;OFW>@;n&7QW:<*f;OFH*/:<&7?O?=*,:<;IvKR*,{N:<+Y>1-=-|FW>7-|6g*[*[Qf()*<;=*[?=TVK.QH*E(�0j&1?�>@Q#&16H89*,:e;EcE;OFH*�T/>@;=:]FHK.QH\�;=&3()*[;O*,?OT/K.QH*�;OFW*�:<&7?O?=*,-OUg&1QW()*,QW:<*E-QH*E:<*,-=-=>@?=Mo0j&7?uUg&7-O*�()*[;O*,?OT/K.QW>�;=KR&7Q�KY-u>oFHKR\7FH+.M%�):<&7QW-9;=?=>1KRQW*,(�c,;9{�&��v()K.T/*[QW-OK.&1QW>1+%&vKRQC(r&@0CT/>@;=:]FHK.QH\C_kmFH*�AW-O*�&@0uIvK.*[{ :<+Y>1-=-D*E-�{m>1-qUH?=&1Ug&7-O*,(�6vM��&v*[QW()*,?OK.Q�&y>1QW(�I�>1Qi43&v&1?=Q �D�)VL¢�V��<_lkmFW*�-D;O?=AW:<^;OAW?O*3;OFH*,MXUH?=&1Ug&7-O*,(XKY-m:[>@+.+.*,(�>1Q uwz � p� ~ q�nTu � | _ m Q u�z � pT ~�KY-q(H*{�WQH*E(�>7-�>V�LAW>@+.K�;]>�;=KRI7*[+.M/(HK.-D;OK.QW:e;IvKR*,{ &@0u>1Qy&16H89*,:e;m>1-q-D*,*[QX0j?=&1T�>f-D*[;�&@0�:<&1QWQH*,:<;O*,(yILK.*[{�Ug&1K.QL;=-,_�kmFH*oQH&)()*E-�&10u>@QB>1-OUC*E:e;�\7?=>1UHF?=*[UH?=*,-O*[QL;o>1-OUg*,:e;]-o>1QW(i;OFH*f>@?]:[-w:[&1QHQH*E:e;3>7(J8D>1:[*[QL;3>7-DUg*,:<;=-,_mkmFW*�:]FW>@QW\1*#K.Q�>@UHUg*,>1?=>1QW:<*r>@;w;OFW*6g&1AHQW(W>@?=My6C*[;9{�*,*[Qi;9{q&/>7-DUg*,:<;=-mKY-w:[>1+R+.*,(p> ¤W� z�r�u�s�p(¤�p(� ~�_ m +.\1&7?OKR;OFWT/-�0j&1?w>@AH;O&1TX>@;OKY:n:[&1QW-D;O?=AW:<^;OK.&1Qp&10�>1-OUg*,:e;�\7?=>1UHFW-q{�*,?O*#()*,I1*,+R&7UC*E(�K.Qi;OFH*�+Y>�;O*X�WV � � -,c76HAH;w6C*E:[>@AC-D*n;OFW*r-9;=?OAW:<;OAH?=*,-�>1?O*nI1*,?OM��! "��#��$%��#�&��'$�&��)(*&��+,��-

�� )�� w�� ¢�R�� ¡ \L¢

Class 2Class 1 Class 3

}�KR\7AH?=*#�[�W_.� � �tkmFH*�;=FH?=*[*wIvK.*[{ :<+Y>1-=-D*E-l&@0|>r:[AH6C*3()*{�WQW*,(/6vMf\7?O&7AHUHK.QH\n;O&7\1*<;=FH*[?�ILK.*[{�Ug&1K.QL;=-�;OFW>@;UH?=&)()AW:<*n;=&1Ug&1+.&1\1KY:[>1+R+.MXKY-D&7TV&7?OUWFHK.:3+.KRQH*r(H?=>J{�K.QH\7-,_

}�KR\7AH?=*Z�,�W_.�1�1�Zkm{�&P:]FW>@K.?pILK.*[{w-B;=FW>�;p6C*,+R&7QH\Z;O&P;OFH*N-=>@T/*�IvK.*[{ :<+Y>1-=-�6W>7-D*E( &7Q ;OFW*[K.?'+R&�{?=*[+Y>�;OK.&1QC>@+�()KY-9;]>@QW:[*1_

¡ \ � �� ! #"$"%"

}�KR\7AH?=*i�,�W_.�W\H� ��Y|*[0 ; ��\14 � 6W>1+R+.&v&1QW�i&7? u% ~ ��¤wp4 � � ~ � rtn 6C*,KRQH\'6W+R&�{�QhAHUb;O&4�W;r;OFH*�\14�Ug&1K.Q7;]-[_��UwKR\7F7; �9\@4 � ?OAW6H6C*,?m6W>@QW(W�X-9;=?O*[;=:]FH*E(�&�I7*[?�;OFH*#&7A);=-OK.(H*#&@0t;=FH* \@4 UC&7KRQL;=-,_

+Y>@?=\1*f0j&1?#?=*,>@+.KY-9;=K.:f&16)89*E:e;]-[c�;=FH*[M�FW>JI1*/QH&1;�6g*[*,QhAW-D*E(�TfAW:]FbKRQb&16)89*E:e;#?=*,:<&7\1QHKR;OK.&1Qt_VkmFH*/IvK.*[{:<+Y>1-=-m&1?�:]FW>1?=>7:e;=*[?=K.-D;OKY:oIvK.*[{ :<&1QC:<*[UH;wFW>1-m6g*[*,QiFW*,>JIvKR+.MXAW-O*,(iK.QW-9;=*,>7(�_�� oK.*[{mâ:<+Y>1-=-mT/&v(H*[+Y-kmFH*�;9{�&�:]FC>@K.?=-#&10o}�KR\7AH?O*��[�W_.�1�X6g&@;=FG6g*[+.&1QH\';=&�>-OK.QH\1+.*yIvKR*,{�:<+Y>1-=-#&@0o>';OFH?=*[*[^�()K.T/*[QW-OK.&1QW>1+&16H89*,:e;E_�4o?]>J{ UHKY:e;=AH?=*,-�&10t;OFW?O*,*#TV&7?O*#:[&1T/T/&1QiILK.*[{mâ:<+Y>1-=-O*,-�&@0�;OFH*r:]FW>1KR?E_

+-,/. � � P�82G�L��9G ��4J�G�6-Q J�B4Q � 6!<�: 3�@AJ�� {6 M :RQS6��{G

��FvM)-OK.:,-9^�6W>1-O*,(fT/&)()*[+Y-�:,>@QX6g*oAW-O*,(V;=&rT/&)()*[+C;OFH*n>@UHUg*,>1?=>1QW:<*w>1QW(/6g*[FW>JIvK.&1?�&10t>@Qy>1:<;OAW>1+WUHFvM)-D^KY:[>@+t&16)89*E:e;w6g*[K.QH\XKRTX>1\1*,(|_ m Q'*[�)>1T/UH+R*�KY-w\7KRI7*[Qi6C*,+R&�{ {�FH*[?=*n;OFH*�&16)89*E:e;wKY-m;OFH*�FLAWT/>1QpFH*,>1?D;E_}o0 ;O*,Q|c@;=FH*�UH?=KRQC:<K.UH+R*E-�&@0gUHFvM)-DKY:[-�>1?O*mQH&1;�AW-D*E(r;=&#T/&v(H*[+W>1QV>7:e;OAC>@+HUHFvM)-OK.:,>@+)-DM)-D;O*,Tic76HA);�K.QW-D;O*,>7(>@?=*mAW-O*,(VKRQX>1QW>@+.&1\7M�;O&r-OKRTfAH+.>@;O*�-O&1T/*�KRTX>1\1*�>@QW>1+RM)-OK.-u;]>1-�&g_ m QX*[�H>@T/UH+.*qKY-�\7KRI7*[QV6C*,+R&�{#c7{�FH*[?=*>�T/*,-OF#&@0v;=?OKY>@QH\7+R*E-�KY- � s �w� ��r � >7-|>�6W>1+R+.&v&1Qn;O&-�H;�274 (H>@;=>mUg&1K.Q7;]-�;]>�&1*,Q�0j?O&7T >q;=*[+.*[UHFW&1QH*�FC>@QW(v^-O*<;,_�àQ/;OFW*�TV&)()*,+RK.QH\#&10C;=FH*�FH*,>1?D;Ec@;=FH*�&16)89*E:e;=KRI7*�K.-�;=&#TV&)()*,+H;=FH*w:]FW>@QW\1K.QH\#-DFW>1UC*w>1QW(f6C*,FW>JIvKR&7?&@0�>@Qb&16H89*,:e;r&�I7*[?n;OK.T/*y-D&i;=FW>�;rKR;=-�0jAWQW:e;=KR&7QHKRQW\:[>@Qb6g*XAHQW()*,?=-D;O&v&)(�_XàQb;OFH*XT/&)()*,+RK.QH\'&@0q;OFW*;O*,+R*,UHFH&7QH*mFW>@QW(W-D*[;,c�;=FH*�&16)89*E:e;=KRI7*�KY-l;O&�&76);=>1KRQV>3\7&v&v(fT/*,-OFfT/&)()*,+)&@0W;=FH*w-D;=>�;=K.:qT/*,>7-DAW?O*,TV*,QL;=-,_

m ;O*,?OT�;=FW>�;�KY-�-D;O?=&1QH\7+RM�?=*[+Y>�;O*E(r;=&n;OFH*m;=*[?=T � | &�z�� {z�� u�z(p�£ x � £%p(s KY- £%p�� n�xyu � svpKx � £$p{s _lkmFW*+Y>�;D;=*[?m;=*[?=Tx*[T/UHFC>1-OKv[,*,-q;OFC>�;�;OFW*r:]FW>@QH\7*3K.Qp&16)89*E:e;w-OFW>@Ug*#K.-q;=&X6C*#T/&)()*,+R*E(�_kmFH*,?O*3FW>1-q6g*[*[Qi\1&v&)(XUH?=&1\7?O*E-O-�?O*E:<*,Q7;=+RMXK.QiUHFvMv-OKY:[-D^�6W>7-D*E(X>@QW(B()*<0j&7?OTX>16H+R*nT/&)()*[+.KRQW\W_�kmFH*<^&1?=Mp>@QW(�>@UHUH+.KY:[>�;=KR&7QW-o>1?O*f?OKY:]F�>1QW('T/&1?=*�:<&7T/UH+R*[�';OFW>1Q';OFW*f&1;OFH*,?n>1?O*E>1-o:[&�I1*,?O*E(BK.Q;=FHKY-o;=*<�v;,_kmFH*m6H?=KR*[0d:[&�I1*,?=>1\1*�\7KRI7*[Q�FW*[?=*qKY-l&1QW+RM#0j&7?�;OFH*�UHAW?OUg&7-O*m&@0CK.QL;O?=&)()AW:<K.QH\3;OFH*m;=&1UHKY:m>@QW(fT/&@;=KRI�>�;=KRQW\;OFW*r-9;=AW()*[QL;�;=&/(H&X&1A);]-DKY()*�?O*E>1()K.QH\/K.Q�;=FH*#?=>1UHKY()+RMB()*[I7*[+.&1UHK.QH\/+RKR;O*,?=>@;OAH?=*1_

]_^-` bOà] � �!��Zf�h�� Zf j � �tjZ�-� dgj9k-fHlah%'&L-9;�&10gAW-�FW>JI1*mUH+Y>1:[*,(/>n?OAH6W6C*,?�6W>@QC(V>1?O&7AHQW(f&1AH?�&1A);]-9;=?O*[;=:]FH*E(��WQW\1*[?]-,_�}3AH?�CQH\1*,?=-�>1?O*�>@QC>@+R^&1\7&1AW-u;=& �WI1*mUg&1K.Q7;]-�K.Qy\14 >@QW(f;=FH*�?OAW6H6C*,?�6W>1QW(�KY-�>�:<+.&7-O*,(V:<&7QL;O&1AW? � ;OFW?O&7AH\1FW�o;OFW*O�WI1*mUg&1K.Q7;]-[_

�� )�� w�� ¢�R�� ¡ \%V

. .

. .

.P

P

P

Q Q

Qj-1, t

j , t+1P.

.Qj , t+1

j-1, t

j+1 , t

j , t

j , tj+1 , t.

}�KR\7AH?=*X�[�W_.�,2W� ��Yt*<0 ; ��}H&7?=:[*,-�&7Q>/UC&7KRQL;o&10�>X-D;O?=*<;]:]FH*,(i?=AH6H6g*[?36W>@QW(B;=*[QW(p;=&XT/&�I1*�;OFC>�;oUg&1K.QL;K.QL{m>@?](�_ ��U�KR\7FL; � m Q K.Q � >@;OK.&1QW>1?OM�0j&1?]:<*y&7Q >'Ug&1K.Q7;V&@0o>'6C>@+.+R&v&1Qh;=*[QW(W-r;=&�T/&�I1*XKR;V&7A);9{m>@?](�cUH?=&�IvK.()*E(y;=FH*#*[+Y>1-D;OKY:30j&1?]:<*E-�0j?=&1T!QH*[K.\1Fv6g&1?=KRQW\fUg&1K.QL;=-�>@?=*�*<�H:<*,*,()*E(�_

kmFH*y>7:e;OK.&1Qb&@0q;OFW*X?OAH6W6C*,?r6W>@QC(b:,>@Qb6C*y-OK.T�AH+Y>�;=*,(b6vM�>@Q u% ~ ��¤�p/ � � ~ � rtn {�FHKY:]FhTV&�I7*,-nK.Qh>1QK.T/>1\1*�;O&�{m>@?](�>nT/KRQWKRTfAHT�*,QH*[?=\1Mr-D;=>@;O*1_ m ?OAW6H6C*,?�6W>@QC(r;=*[QW(H-�;O&#:<&7Q7;=?=>7:e;�;O&�?=*,()AW:[*mK�;]-�-9;=&1?=*,(*[QW*[?=\1M1c�>�;�+.*,>7-9;fAHQL;OK.+�KR;fFW>7-#T/*<;�{�KR;OF -OAHUHUg&1?O;OK.QH\p0j&7?=:[*,- �j;OFH*��WQH\1*,?=- �e_p}�KR\7AH?=*'�[�W_.�W\ �j?=KR\7FL; �K.+R+.AW-D;O?]>�;O*E-�;OFHKY-�:<&7QW:<*,U);,_lkmFH*w-OTX>@+.+H(H>@?T&#?O*,\1K.&1QW-l>1?O*m>@QW>1+R&7\1&7AW-|;=&�&1AH?�WQW\1*[?]-,��;OFH*w:[&1QL;O?]>1:<;OK.&1Q&@0�;=FH*�?=AH6H6g*[?n6W>1QW('KY-3-D;O&7UHUC*E('6vM�;=FH*,-O*�?=*[\7KR&7QW-,_ m QH&1;OFH*,?n>7-DUg*,:<;o&@0�;=FH*/>@QW>1+R&7\1M�KY-�;=FW>�;n;OFW*?=AH6H6g*[?m6W>@QC(y{�K.+R+�QH&1;qFC>JI1*oK.Qt�WQWK�;=*�:[AH?=IJ>@;OAH?=*%'v*,I1*[QBK�0�-9;=&1UHUg*,(B6vMy>f-OKRQW\1+.*3Ug&1K.QL; ��&1?m{�KR?=*��;OFW*?=AH6H6g*[?�6C>@QW(/{�K.+R+g-DT/&v&@;=FH+.M�{�?]>@Uy>@?=&1AWQW(f;OFW>@;�UC&7KRQL;E_l��?O*,I1*,Q7;=KRQW\n&7?�UHAHQWK.-OFHK.QH\rFHK.\1Fy:[AH?OI�>@;OAH?=*:[>1Qh6C*y()&7QH*y()AH?=K.QH\-DK.T�AW+.>@;OK.&1Q|_�}�K.\1AH?=*'�[�C_R��\��+R*[0 ; ��-OFH&�{w-�{�FW>�;r{q&1AW+.(bFW>1UHUC*,QhK�0w>p6W>1+R+.&v&1Q{q*[?=*X6H+R&�{�QNAWUGKRQC-DKY()*y&7AH?rFW>1QW(h{�K�;=F �WQH\7*[?]-#Ug&7-O*,(N>1-�K�0�\7?=>7-DUHK.QH\>'6C>@+.+ _ m QC>@+.&1\1&7AW-O+RM7ct{q*:<&7AH+Y(B-OKRTfAH+Y>�;O*r>VIvK.?D;=AW>@+�6W>1+R+.&v&1Qi6C*,KRQW\V6W+R&�{�QpAHUpK.QW-DKY()*#-O&1T/*�KRTX>@\7*�?O*,\1K.&1QW-q&1?�Ug&1K.QL;=-,_}�KR\7AH?=*#�[�W_.�W\3K.+R+.AW-D;O?]>�;=*,-�>#:[?OKR;OKY:[>1+W>1()I�>1Q7;]>@\7*q&10|>1:e;=KRI7*w:<&7Q7;=&1AH?]-,�|;OFW*o:<&7Q7;=&1AH?�KY-�>#:[&1T/UH+.*<;=*-D;O?=AW:e;=AH?O*o*[I1*,QV;OFH&7AH\1F/;=FH*3(H>@;=>#6g*[K.QH\��W;�TX>JM�6g*o6W>7()+.Mr0j?]>@\1T/*,Q7;=*,(�_l%'&7?O*,&�I1*[?Ec@&1;OFH*,?�:]FW>@?]>1:<^;O*,?OKY-D;OKY:[-�:[>1Qp6C*#*,Q)0j&1?]:<*E(�;=&1U)â()&�{�Q|cH-OAW:]Fp>1-w-OT/&v&@;OFWQH*,-=-[c)Ug*[?=K.TV*[;O*,?w+RK.T/K�;]-[cC>@QW(B;OFW*#UH?O&7UC*,?D;9M&@0d6g*[K.QH\�>#-OKRT/UH+.*w:<AH?=I1*7_H*b*�QH&�{P\1K.I1*w>�6H?=K.*<0�-a&7*<;=:]F/&10gFH&�{Z;OFW*�6C*,FW>JIvKR&7?�&@0|>@QX>1:<;OK.I1*�:<&7QL;O&1AW?:[>1QB6g*r-OKRTfAH+.>@;O*E(B6vM�>/:[&1T/UHA);=*[?w>@+.\1&7?OKR;OFWTi_ku&i-OKRTfAH+Y>�;O*f;OFW*V6g*[FC>JILK.&1?n&@0q>@Qh>1:e;=KRI7*f:[&1QL;O&7AH?�&16)89*E:e;,c�{q*7�W?=-D;�QH*[*E(�>BT/*[T/&1?=M-9;]>�;=*�;=&()*(�WQH*V;OFH*X-D;O?=AW:e;=AH?=*f>@QC(�+.&):[>�;=KR&7Q&@0�;OFH*X:[&1QL;O&7AH?,_f��&7QW-OK.()*,?o;=FH*X-DK.T/UH+.*/:,>1-O*�{�FH*,?O*V{q*fFW>JI7*>4�H�)*E(G-D*[;�&@0��Ug&1K.QL;=-f>�;r;=KRT/*��ec�*E>1:]Fh+.&v:,>�;=*,(N>�;�� #>@QW(h*E>1:]FG:<K.?]:<AH+Y>@?=+RM�?O*,+.>@;O*E(b;O&';9{q&QH*,KR\7FL6g&1?]-�� _ � ��>@QW(�� e_làQ/;OFH*n:[>1-O*�&@0|>#IvK.?D;=AW>@+C?OAW6H6C*,?�6W>1QW(�cL*,>7:]FVUg&1K.QL;�{�K.+R+C6C*n-DAW6)89*,:<;;O&r>nUHAW+R+.KRQW\�0j&1?]:<*m0j?=&1T�;=FH*m;9{�&#QW*[K.\1Fv6C&7?=-,cJ;OFW*�?O*E-DAH+R;�&@0d{�FHKY:]F/{�KR+.+W>1:,:<*,+R*,?=>@;O*�;OFH*wUg&1K.QL;�� |;=&>VQH*[{ Ug&7-OK�;=KR&7Q�� _�}�K.\1AH?=*/�[�W_.�,2 �j+.*<0 ; ��K.+.+RAW-D;O?]>�;=*,-q;=FHK.-,_�*b*#AW-OAW>@+.+RMi:<&7QW-DKY()*,?q*E>1:]FiUC&7KRQL;�;=&FW>JI7*nAWQHK�;3T/>7-O-o-D&X{q*r:[>1Qi*E>1-OKR+.M�:[&1T/UHA);=*�>1:,:<*[+.*[?]>�;=KR&7Q�K.Qp;O*,?OTX-�&10u0j&7?=:[*1_ �3-DK.QH\y>7:[:<*,+R*,?=>@;OK.&1Q{q*f:<&7T/UHA);O*VI1*,+R&):[K�;9M7cg>1QW(AW-OK.QH\�I7*[+.&v:[K�;9Mp{q*f:[&1T/UHA);=*fUg&7-OK�;=KR&7Q|_�kmFLAC-[cd&1AW?3T/*[T/&7?OM'-D;=>�;=*f>@;;OK.T/*��-DFH&7AH+Y(y>@+Y-D&f:<&1QL;]>@K.QX;OFH*�>1:,:<*,+R*,?=>@;OK.&1Qy>@QC(XI1*,+R&):<KR;9M/&@0|*E>1:]FyUg&1K.QL;,�lT/&1?=*[&�I1*,?,c@;OFH*E-D*nQH*[*E(QH&1;f6g*2[,*[?=&�>�;f;OFH*p-D;=>@?O;�&10w;OFH*p-OKRTfAH+.>@;OK.&1Q|_ }3QH*�T/&7?O*i(H>�;]>T/*[Tf6C*,?fKY-VQH*[*E()*,(��X{q*�AC-D*i>�q&v&1+.*,>@Q'I�>1?OKY>@6H+.*#;=&�K.QW()KY:[>�;=*�{�FH*[;OFH*,?3&7?3QW&@;o;=FH*�Ug&1K.QL;nFC>1-o-D;O&7UHUg*,(T/&�IvK.QH\�()AH*�;O&B?OAHQWQHKRQW\K.Q7;=&V-O&1T/*n(H>�;]>�Ug&1K.QL; � :[>@+.+.*,(�> |�u�n�£� � ��z ~ nTuw�� ~ �e_làQi>1(H()KR;OK.&1Q�;O&V&1AH?�>7:e;OK.I1*n:<&7Q7;=&1AH?q&16H89*,:e;Ecv&@0:<&7AH?]-D*7cW{q*�QH*,*,(p;=&B-D;O&1?=*#;=FH*f(H>@;=>/;=&�6g*fT/&)()*,+R*E(��q;OFHKY-3:[&1AH+Y('6g*V>y\1?=*[M)-O:,>@+.*#KRTX>1\1*1cd>y-O*<;n&@0

\@4 *E()\1*nUC&7KRQL;]-[c)>V-D*[;q&10u214s-OAH?D0�>7:<*3UC&7KRQL;=-,cv*<;]:@_�?=*[UH?=*,-O*[QL;O*E(/KRQp-O&1T/*oTX>@QWQH*[?�>1-q()*E-O:[?OK.6C*E(yK.Q;OFWK.-w:]FC>@U);=*[?�&1?mK.Q��FW>@U);=*[?]--\f&1?#� � _

¡ 2 � �� ! #"$"%"

m -OKRT/UH+.*r>@+.\1&7?OKR;OFHT�0j&1?�T/&�IvKRQH\X>7:e;OK.I1*r:[&1QL;O&7AH?mUC&7KRQL;]-�K.-o-a&7*<;=:]FW*,(i6C*,+R&�{#_��&7QL;O&1AW?�UC&7KRQL;=-T/&�I1*BAHQL;OK.+�;OFH*,MNT/*[*<;XFW>1?=(Z:<&7QW-9;=?=>1KRQL;]-�&7?VAWQ7;=KR+m;=FH*p?O*E-DAW+�;]>@QL;f0j&7?=:[*B&7QG;=FH*[T�K.- [[*,?O&C_ }3?EcUg*[?=FW>@UW-�;OFH*3>@+.\1&1?=KR;OFHT�QH*[I7*[?�-D;O&7UW-,c7>1-�KRQ/;=FH*3:,>1-O*�{�FH*[?=*�;=FH*3>7:e;OK.I1*w:[&1QL;O&7AH?�KY-�;=?=>7:�&LK.QH\r>#UC>@K.?&@0�-OUC*E>�&vKRQW\f+.KRUC- �� &@;O*�;=FW>�;o>1QBK.QHKR;OKY>@+|Ug&7-OKR;OK.&1QB0j&1?m;OFW*r:<&1QL;=&1AH?�KY-m?O*E�LAHKR?=*,(|_

�� ! � (H>@;=>VUg&1K.Q7;]-�>�;�;=KRT/* ��'H*E>1:]F�� FW>7-mI1*[+.&):<KR;9M#" �� >1QW(i>1:[:[*[+.*[?]>�;=KR&7Q#$ � �e_% ��&�'��! � (H>@;=>nUC&7KRQL;]-�>�;l;OK.T/* � Dp�$'1*,>7:]F � �� FC>1-lI1*,+R&):[K�;9M�" �� >1QW(V>1:[:[*[+.*[?]>�;=KR&7Q�$ � �� _�o-OK.QH\V;OK.TV*r-D;O*,U)( �ecC()&X>�;w*,>7:]FBUg&1K.QL;�� ;=FW>�;wFW>7-mQH&@;w-D;O&7UHUC*E(p>�;w>/FW>@?](i:<&1QC-9;=?=>1KRQL;,��7_3��&1T/UHA);=*3;=FH*#?=*,-OAH+�;]>@QL;m0j&1?]:<*�&1Q�� qAW-DK.QH\/KR;=-�QH*,KR\7Fv6C&7?=-,_\H_ �o-OKRQH\V;=FH*�0j&1?]:<*7cH:<&1T/UHAH;O*�;OFW*r>1:[:[*[+.*[?]>�;=KR&7QyI1*E:e;O&7?*$ � �� _2W_3��&1T/UHA);=*nI7*[+.&):<KR;9M#" � �� +" � � D,$ � � ( �

�C_3��&1T/UHA);=*nQW*[{ UC&L-DKR;OK.&1Q�� `D-" �� .( �

¡ _�`�0 � �� KY-m{�KR;OFHK.Qp;O&7+R*,?=>1QW:<*n&@0�-D&7T/*�(W>�;=>VUg&1K.QL;,cv0j?=*[*([,*�;OFHKY-�Ug&7-OK�;=KR&7Q|_/#0�1 � �� 2 3 �45!O�)KRQH\7+R*#AWUg(H>@;O*r-D;=>1\1*30j&1?w>@Q'>7:e;OK.I1*#:[&1QL;O&7AH?,_

m +.\1&7?OKR;OFWT!�L2y-a&7*<;]:]FH*,-3>�-OKRT/UH+.*f-D;=>1\1*r&10�>@Q ��AH+R*,?3>1+R\7&1?=K�;=FHTx;=FW>�;�:<&7TVUWA);O*E-[cC0j&1?�>y-OT/>1+R+;OK.T/*'-9;=*[U|cm>1:,:<*[+.*[?]>�;=KR&7QN0j?=&1T 0j&1?]:<*7c�I7*[+.&v:[K�;9Mh0j?=&1T�>7:[:[*[+.*[?]>�;OK.&1QZ>@QW(ZUC&L-DKR;OK.&1Q 0j?O&7T�I1*,+R&):[K�;9M7_m UC&7KRQL;�6 -�Ug&7-OK�;=KR&7Q�KY-n0j?=&%[[*,Q�{�FW*[QbK�;r:<&7+R+.KY()*,-�{�KR;OFh>p(H>�;]>BUg&1K.QL;,c|*E()\1*7c|&1?#-OAH?O0�>1:<*VUW>@;=:]F|_VàQ\1*,QH*[?]>@+�cg;OFHKY-#:[>1Q�6g*X>B:[&7-D;O+.M:<&7TVUWA);=>@;OK.&1Q;=FW>�;#?=*,�LAHK.?O*E-3-O*,>1?=:]F�;OFH?=&1AW\1F';=FH*X(H>�;]>i-D;O?=AW:<;OAH?=*&1?�K.TX>@\7*3;=& �WQW(p-DAC:]Fi>/Ug&1K.QL;,_

�w&v&$&1*�6 -RYu>J{ T/&)()*,+.-i>G-OUH?OK.QH\Cc�{�FHK.:]F K.-i>G:<&7T/TV&7Q *[+.*[T/*[QL;i&@0rUHFvM)-DKY:[-D^�6W>1-O*,(PT/&)()*[+Y-[_�vAHUWUC&L-D*#>/-DUW?OK.QH\/&@0�QW>�;=AH?=>1+�+R*,QH\@;=F87P:[&1QHQW*,:e;]-mUC&7KRQL;]- ��r>@QW( � > _�kmFH*�0j&1?]:<*:9�>1:e;=KRQW\V&7Q � �KY-�UH?=&1Ug&1?O;OK.&1QC>@+H;=&fFW&�{S;OFH*�-DUW?OK.QH\rKY-m-9;=?O*[;=:]FH*E( �j&7?q:[&1T/UH?=*,-=-D*E( ��?=*[+Y>�;=KRI7*�;O&fK�;]-�QC>�;OAW?=>1+C+.*[QH\1;OF|_

9 � ( K�; �=< � ��( � > < (>7 � �� ( � >< � � ( � > < �9�[�C_ \��

kmFHKY-f-OFH&7AH+.(N-OA@?y:<*�;O&b-DK.T�AH+Y>�;=*y&1AW?f?=AH6H6g*[?f6W>@QW(|_ m (W>@T/UHK.QH\0j&7?=:[*�-DFW&1AH+Y(h6C*p>1(W()*,(hKR0oKR;KY-rUg&7-=-DK.6H+.*X;OFW>@;�;=FH*B-OUH?=KRQH\-OM)-9;=*[T :<&7AH+.(G&7-=:<K.+R+Y>�;=*XKRQW(H*{�WQHKR;O*,+RM7_ m ?=*[TX>1KRQHK.QH\'UH?=&16W+R*,T KY-#;=&()*[;O*[?=T/KRQW*�>'\1&v&)(h+.*[QH\1;OFA7w_'`�0�{q*�>@?=*yT/&)()*[+.K.QH\�>S&vQH&�{�Qh&16H89*,:e;Ec�-DAW:]FG>7-#;]>@+�&LK.QH\'+.KRUC-[cl{q*-OFH&1AH+Y(y6g*#>@6H+.*3;O&/()*<;=*[?=TVK.QH*nUH?]>1:e;=K.:,>@+gI�>@+.AH*,-�0j&1? �Nc@7P>@QW(�K�;l_ KB;'KY-m> � -9;=K��dQH*,-=-=��UW>1?=>1T/*<;O*,?;OFC>�;w?=*[+Y>�;O*E-�0j&1?]:<*n;O&y()*[0j&1?=TX>�;OK.&1Qt_

C � f �-f��"ED �#��FD ��-� ��j��GDo� l �� j �m +R;OFW&1AH\7Fy;OFW*nQW&@;OK.&1QB&@0u>1QB>7:e;OK.I1*n:<&7Q7;=&1AH?qFW>7(y6g*[*[QiAW-O*,(�UH?O*,IvKR&7AW-D+.M/6vMX&@;OFW*[?]-[cv>��WV � ¢�UW>1UC*,?6vMy�#>1-=-[c¢* KR;�&vKRQp>@QC(ykt*,?�[,&1Ug&1AH+.&7-q-O*[*[T/*E(/;O&VKR\7QHKR;O*3;OFH*�K.Q7;=*[?=*,-D;�&10|;OFH*#:[&1T/UHA);=*[?qILKY-OKR&7QB:<&7TV^T�AWQHK�;9M7_�%AW:]F/&@0g;OFH*w()KY-=:<AW-=-DK.&1Q/>@6g&�I1*q{m>1-lT/&@;=KRI�>�;=*,(V6vMr;=FH*[K.?�IvKR*,{Z&10 � -DQW>%&1*E-O�WcJ>7-�;OFH*,M�{q*[?=*

�� )�� w�� ¢�R�� ¡ 2W�:[>1+R+.*,(|_l}�KR;D;=KRQH\y>/-OQW>�&7*o;=&V(W>�;=>V{m>1-m()*(�WQH*,(i>1-�>1QB&7U);OK.T/Kv[E>�;=KR&7Q�UH?=&16H+.*[T�;OFW>@;�-O&1AW\1FL;m>VT/K.QHK�^T�AWT�*[QH*,?O\7M36g&1AHQC(H>@?=M#-DAH6H89*,:e;�;O&�-O&1T/*�FW>1?=(�:<&1QC-9;=?=>1KRQL;=-,_ m -tAW-O*<0jAW+70j&7?OTfAH+Y>�;OK.&1Q�K.-u;O&n:<&7QW-DKY()*,?;OFC>�;�;O&1;=>@+l*,QH*[?=\1M'KY-�>i-OAHT &10�;OFW?O*,*V:[&1T/UC&7QH*[QL;]-(' �9�� ~ p(n�� uwsZ � � ~ � rtnyp{��p{n�q!& :]FC>@?]>1:e;=*[?=Kv[,*,(6vMV;OFH*n-9;=?O*[;=:]FHK.QH\�>1QW(/6C*,QW()K.QH\�&10�;OFH*n:<&7Q7;=&1AH?�K�;]-D*,+�09c�� \ � ��xyu(q¢p�p(� p(n�q!& ;OFW>@;q:]FW>1?=>7:e;O*,?OK�[[*E-�FH&�{;OFW*o:<&7Q7;=&1AH?��H;=-�;O&#;=FH*wK.TX>@\1*�K.QL;O*,QW-DKR;9MV&1?�\7?=>7()KR*,QL;,c7>1QW( ��2 � pT¥ ~ p(n�� uws_p(� p(n�q & ()AW*�;O&�:[&1QW-D;O?]>@K.QL;0j&1?]:<*E-[_��&7QW-9;=?=>1KRQL;]-q>1?O*nAW-O*,(B;O&X>1UHUH+.MyKRQH0j&1?=T/>@;OK.&1QB0j?O&7Tx>@QiK.Q7;=*[?]>1:<;OK.I1*nAW-D*,?�&1?w>VFHK.\1FH*,?�+R*,I1*,+� ��UH?=&):<*,-=-,_

m :<&1QL;=&1AH?nUW>@?]>@T/*[;O*[?=K�[[*,(p6vM �� lKY- � � � �J� � � � � 5� � � � ��c|{�FHKY:]F�KY-�89AW-D;#>y0jAHQW:<;OK.&1Qb&@0?=*,>@+lI�>@?=KY>@6H+.* � _XkmFH*/UH?=&16H+.*[T K.-n;=&2�CQW(�;OFH*/0jAHQC:e;OK.&1Q�;OFC>�;rT/KRQWKRT/K�[[*,-n;=FH*X*[QW*[?=\1M()*(�WQH*,(h>7-0j&1+.+.&�{w-[_��

�� A�� D�� A�� D�� A � � � � �� 2 �9�[�C_ 2 �� A�� S � � �� ; � � �� % D� � � �!� � ; ; � � �!� % �9�[�C_ ��

kmFH*r-OQW>�&7*#:[>@Qp6g*�:<&7QL;O?=&1+.+R*E(y;=&XUW>1-=-�QH*E>@?w-O&1T/*r()*,-OK.\1QW>@;O*,(BUg&1K.Q7;]-�6vMB>7(H()K.QH\XKRQp;=FH*r-=�7AC>@?=*,(()KY-9;]>@QW:[*�6C*[;9{�*,*[QX*E>1:]F/UC&7KRQL;�>1QW(V;OFH*3-DQW>%&1*mAW-OKRQW\"� �� #� � A � � � � _$� �%� A�� qT/KR\7FL;|89AW-D;�6C*w;OFH*o-OAHT&@0m;=FH*B-=�LAW>@?=*,(N()KY-D;=>@QC:<*,-r6C*[;9{�*,*[Q >-OQW>%&1*XUg&1K.Q7;/>@QW(b;=FH*B:[+R&L-D*E-9;f*,()\7*yUC&7KRQL;E_kmFH*�K.QL;O*[?=QW>1+*[QW*[?=\1M�(H*{�WQHKR;OK.&1Q K.-�UC*,?OFW>1UW-rT/&7?O*yK.QL;O*,?O*E-9;=KRQH\C_'kmFH*R�W?]-D;�UW>@?O;�&10&�� A�� UHAHQHKY-OFH*,-fFHK.\1FH*,?I�>@?=K.>1QW:<*#K.Qp;OFW*�+.*[QH\1;OFW-o&@0�-DTX>1+R+�:<&1QL;=&1AH?w-O*[\7TV*,QL;=-�'�+R&�{q*[?o*[QH*,?O\7MyT/*,>@QC-o-OT/>1+R+uI�>@?=K.>1QW:<*#K.Q;OFW*[K.?o+.*[QH\1;OFW-,_qkmFW*�-D*E:<&7QW(iUW>@?O;wUHAHQHKY-OFH*,-3:<AH?=I�>�;OAW?O*7_qkmFH*�{�*,KR\7F7;=KRQW\/0jAHQW:e;=KR&7QW-�S � � �o>@QW(( � � �>@?=*nAW-D*E(B0j&1?�6H+.*[QW(HKRQH\X>1QW(p:[>@Qp>@+Y-O&V>1+R+.&�{ ;OFW*#UH?O&):[*,-=-q;O&V0j&1?=Tx>/-DFC>@?=Ui:[&1?=QH*[?m{�FH*,?O*�>X:<&7?OQH*,?()*[;O*,:<;O&7?�FW>1-q0j&7AHQW(i&1QH*�&7?m;O&V;=>%&1*#>/+R&7QH\V+R*E>@Up&�I1*,?�6H+Y>@QC(�;=*<�v;OAW?O*7_kmFH* �H;D;=KRQW\n&10g>7:e;OK.I1*m:<&7QL;O&1AW?=-t;O&�K.T/>1\1*E-u:,>@Q�6g*m?O*,+.>@;O*E(r;=&o;=FH*mT/>%&vKRQH\n&@0d>@K.?D0j&7KR+Y-u&1?�:[>1QH&v*,-,_}�KR\7AH?=*#�[�W_.�[��-OFH&�{w-�{�FW>@;�FW>@UHUg*[QC-�{�FH*,Q/>#-D;O?=K.UX&@0d{�&v&)(VK.-�QC>@K.+R*E(X>�;�?=*[\1AW+.>1?�KRQL;O*,?OI�>1+.-�;=&�:<?=&7-=--O*,:e;=KR&7QW-�FW*[+Y(yK.QyUH+Y>1:<*36vM/> � -D;O?=&1QH\76W>1:�&)�W_|kmFH*3{q&v&)(/6C*,QW(H-�;O&V-DT/&v&@;=FH+RM7�H;q;OFH* ��>1KR? ��-OUW>1:[*oK.Q6g*<;9{q*[*[QB;OFW*r:<?=&7-=-q-O*,:<;OK.&1QW-qTX>�&vK.QH\X>/-DT/&v&@;=FB6HAH;wUC&L-O-OKR6W+RM�:[&1T/UH+.*<��:[AH?OI7*1_��&1QL;]>1:e;�{�KR;OFi;OFW*:<?=&7-=-�-O*,:<;OK.&1QW-�*[Q)0j&7?=:[*,-�>rFW>1?=(y:[&1QW-D;O?]>@K.QL;,_l�wK.\1F�:[AH?=IJ>@;OAH?=*wKY-�?=*,(HAW:<*E(y>1-�;OFH*3{�&v&)(y()KY-D;O?=KR6HAH;O*,-;OFW*n6g*[QC()KRQW\X*[QH*,?O\7MX&�I1*[?qTX>@QvMyUg&1K.QL;=-,_��&7T/UHA);O*,?w>@+.\1&7?OKR;OFHTX-m:[>1Q�*E>1-OKR+.MyUH?=&)()AW:<*�-OAW:]F z � s�� p:<AW?OI7*,-)' K.QB0�>7:e;EcW}�KR\7AH?O*/�,�W_.�[��{m>1-mUW?O&)()AW:[*,(B6vMB-OAW:]Fi>1Qi>1+R\7&1?=K�;=FHT�K.Qi;OFH*+*�,.-V;O&v&1+ �kmFH*o>1UHUH?=&7>7:]FH*,-l;=&�T/K.QHKRT/K�[[K.QH\r;=FH*o*,QH*[?=\1MV&@0|>f:<&1QL;=&1AH?�>1?O*o6C*,M1&1QC(X&1AH?q-O:[&1Ug*wFH*,?O*7_��q>1?O*[^0jAH+�QLAWTV*,?OKY:[>1+�UH?=&1\1?]>@T/T/K.QH\BKY-#QH*,*,()*E(�;O&'&16H;=>@K.Qh\1&v&)(�:[&1QL;O?=&1+�&10m>1QN>1:e;=KRI7*X:<&1QL;=&1AH?E_y}�KRQHKR;O**[+.*[T/*,Q7;]-qUW>1:�&�>@\7*,-q:[>1Q�6g*3AW-O*,(|_ m 0 ;O*,?#�)V � ¢vcL-D*,I1*,?=>1+CQH*,{ {q&1?T&v-q>@UWUC*E>@?=*,(/;=FW>�;�AW-O*,(B()MvQW>@T/KY:UH?=&1\7?=>1TVT/K.QH\WcgK.QW-9;=*,>7('&@0�;=FH*X-O:,>@+.*f-OUW>1:[*f>1UHUH?=&7>1:]F'UW?O&7UC&L-D*E('6vM�#>1-=- p ~ uws _rkmFW*fK.QL;O*[?=*,-D;O*E(?=*,>1(H*[?�:[>1Q��WQC(BTX>1QLM�KRQL;O*,?O*E-9;=KRQW\V{q&1?T&)-qKRQi;OFW*#+RKR;O*,?=>@;OAH?=*1_

]_^-` bO`�� / ��lal jOj ��dgj9k-fHlah ��j�� b�cm 6W>1+R+.&v&1QNT/&)()*[+q:[>1QN6C*�>TV*E-DFNTX>7()*y6vM�>1UHUH?=&J�vK.TX>�;=KRQH\>'-OUHFH*,?O*7_'%'&7-D;f-O&v:,:<*,?#6W>@+.+.-f>@?=*TX>1()*30j?=&1T5�W\rUC*,Q7;]>@\7&1QW>1+g>1QW(�\ � FH*<�H>1\1&1QC>@+WUWKR*E:<*,-,cv*,>7:]Fy&@0t{�FWK.:]Fi:[>@Q�6C*�()K.ILKY()*E(yK.Q7;=&�;=?OKY>@QH^\1+.*,-,_ ��()\7*,-�&@0g;OFH*m;=?OKY>@QW\1+.*,-l:[>1QV6g*�T/&)()*[+.*,(V6vM�-OUH?OK.QH\L-�-D&n;OFC>�;�;OFW*w-DFW>1UC*m&10C;=FH*�*[QL;OK.?=*m-OM)-9;=*[T:[>1QB()*[0j&1?=Tpc)*[KR;OFH*,?q6vMX*[�vUC>@QW()K.QH\V&1?m:<&7Q7;=?=>7:e;=KRQH\C_�}�K.\1AH?=*V�[�W_.� ¡ -DFW&�{w-�-OAW:]FB>V-OUHFH*[?=KY:[>@+dT/&)()*[+*<�)UW>1QW()K.QH\#K.QW-DKY()*n>#:<+.&1AW(/&10�274�(W>�;=>�Ug&1K.QL;=-�;=>�&7*[QX6vM/-D*,QW-DK.QH\r>�;=*[+.*[UHFW&1QH*wFC>@QW(H-O*<;E_�kmFH*o>@+.\1&1^?=K�;=FHT�0j?=*[*([,*,-�;OFH*�Ug&7-OK�;=KR&7Q�&10u>�I7*[?O;O*[�/{�FW*[QiK�;mTX>�&1*E-�:[&1QL;=>7:e;m{�K�;=Fi-O*[QC-D*E(�(H>@;=>H_ m QiK.Q � >�;=KRQW\0j&1?]:<*/KY-r>@UWUH+RK.*,(�;=&'*,>1:]FbI1*,?D;=*<��K.Qb;OFH*B()KR?=*,:<;OK.&1Qb&@0q;OFH*y-OAH?O0�>1:[*XQH&1?=TX>@+lKRQL;=*[?=UC&7+.>@;O*,(h>@;#;OFW>@;I1*,?D;=*<��_�kt&X()*[;O*E:e;o:<&7QL;=>1:<;q{�KR;OF'-O*[QW-O*,(i(H>@;=>Hcv;=FH*r(H>@;=>/>@?=*#-D*E>@?]:]FH*,(�&1QH+.MyK.Qi>/()K.?O*E:e;=KR&7Qi>1+R&7QH\

¡ 2¢\ �� ! #"$"%"

strongback

cross sections

wood strip(spline)

}�KR\7AH?=*P�,�W_.�[�C� m {�&v&)(�-D;O?=K.Us>@;D;]>1:]FH*E( ;=& :<?=&7-=-'-D*E:e;OK.&1QC-pT/>%&1*E-'> � +.&�{ *[QW*[?=\1M)�Z:[&1QL;O&7AH?E_��)TV&v&1;OF'-DUW+RK.QH*r:<&7AH?O;O*,-OMX&@0 *�,.- � �;OFWK.-�QH&1?=TX>@+�_H* FH*,Qy>@Q/K.Q � >�;=KRQW\#;O?=K.>1QH\1+.*�6g*,:<&7T/*,-�+Y>@?=\1*7c�;OFH*3>@+.\1&1?=KR;OFHT�-DAH6d()K.IvK.()*E-�KR;�K.Q7;=&�0j&1AH?;O?=KY>@QH\7+R*E-[_uàQf;=FHKY-�TX>@QHQH*,?,c1;OFH*w-OUHFH*,?O*w:,>@QVKRQ � >�;=*m;O&�;OFW*�*[+.&1QH\L>�;O*E(f-OFW>1UC*�&10C;=FH*w(H>�;]>#>1-�-OFH&�{�QK.QG}uK.\1AW?O*'�,�W_.� ¡ ��6 �ec ��:��e_'kmFH*y274x(H>@;=>'Ug&1K.QL;=-r{q*[?=*/&16);]>@K.QH*,(b0j?=&1T -O*[I1*,?=>1+�()KR�g*,?O*,Q7;fILK.*[{w-r&@0;OFW*y&16)89*E:e;f-OAH?O0�>1:[*XAW-DK.QH\>p?]>@QH\7*y-O:,>@QHQW*[?Ect*,>7:]Fh?OK.\1KY()+.M;O?]>@QC-90j&7?OT/*,(�;=&>'\1+.&16W>1+�:<&v&1?]()K.QW>�;=*-OMv-D;O*,Tp_ àTX>@\1K.QH*p;=FH*()K ?X:[AH+R;9M &@0 � -O*[{�K.QH\b;O&7\1*[;OFH*,?=��;OFW*�-D*,I1*,?=>1+m(HK��d*[?=*[QL;�-OAH?D0�>7:<*pT/*,-OFH*,-;OFC>�;n:[&1AH+Y(pFW>JI7*#6C*,*[Q&76);=>1KRQH*E('K.QW()*[Ug*[QC()*[QL;O+.Mi0j?O&7Tx;=FH*f(HK��d*[?=*[QL;oIvK.*[{w-,_okmFH*r6W>1+R+.&v&1Q'T/&)()*[+?=*<;=>1KRQC-�;OFW*n:[&1?=?O*E:e;�;O&7UC&7+R&7\1M/>@QW(�>@UHUH?=&J�)KRTX>@;O*�AHQHKR0j&1?=T/K�;9M/&10�;O?=K.>1QH\1+.*,-�>1-�KR;�()*<0j&7?OTX-�;=&��H;q;OFW*(H>@;=>H_u`�;tKY-u()K ?y:<AH+R;t;=&o-D;=>@?O;t{�KR;OF�89AC-9;l>w-D*[;t&@0v;=FH*�274 Ug&1K.QL;=-t>1QW(�6HAHK.+Y(#AHU�>�\7&v&v(�-OAH?O0�>1:<*�TV&)()*,+ _

]_^-` bO`�b dgj9k-f�l��#�!� dgj��aj ��j��R��i-f�� D �� f��t�* FHK.+R*�;O?=K.>1QH\1AW+.>1?�TV*E-DF#*,+R*,T/*[QL;=-u>@?=*�:<&1T/T/&1QW+RMnAW-O*,(n0j&1?uT/&v(H*[+.KRQH\3-DAH?O0�>1:[*,-,cE274GI7&1+.AHT/*�TV&)()*,+.-:[>1Qp6C*�:[&1QW-D;O?=AW:<;O*,(BAW-OKRQW\/;O*<;=?=>1FH*,(H?=>1+�*[+.*[T/*[QL;=-,_ ��>1:]FB;O*[;O?]>@FH*E()?=>1+�*[+.*[T/*[QL;oFC>1-q0j&1AW?wI1*,?D;=K.:[*,-,c0j&1AW?o0�>7:<*,-,cd>@QW(�-DKR�'*,()\7*,-,_�� ~ � �9��p�z�z I�>@+.AH*,-n:[>1Q6C*V>1-=-DK.\1QW*,(p;=&y;OFW*�*,(H\1*,-36W>7-D*E('&1Q';=FH*/:]FW>@?O^>1:<;O*,?OKY-9;=K.:,-m&@0�;OFH*�T/>@;O*,?OKY>@+�6g*[K.QH\yT/&)()*[+.*,(|_Z* FH*,Qp0j&1?]:<*,-�>1?O*#>1UHUH+.KR*E(�;=&XI�>@?=KR&7AW-mUC&7KRQL;]-�&@0l;OFW*T/&)()*[+�c�;OFW*m-D;O?=AW:<;OAH?=*�{�K.+.+v(H*<0j&1?=Tp_�}�K.\1AH?=*n�[�W_.�)Xo-DFH&�{w-u;9{q&3-D;=>@;O*,-�&10g>36C*E>�;OK.QH\nFH*,>1?D;�:<&7T/UHA);O*E(0j?=&1T!;=>@\7\1*E(pT/>1\1QH*[;OKY:#?=*,-O&1QW>1QW:<*�K.T/>1\1*,?OM7_mkmFW*f-O*[QW-O&1?o:,>@Qp;]>@\�:[*[?O;=>@K.Q'UW>1?D;]-w&@0�+.KRIvK.QH\X;=K.-=-DAW*-O&y;OFC>�;�;OFH*,M'TX>JMi6g*X-D*,QW-O*,('K.Q�T/&1;OK.&1Q�K.Q�274�_�kmFH*VFH*E>@?O;nT/&)()*[+��H;n;O&B;OFW*/(W>�;=>�K.-nT/*,>1QL;3;=&T/&)()*[+�?O*E>@+�UHFvM)-DKY:[-�>@QW(bFH*E>@?O;#0jAHQW:e;=KR&7Q|_pkmFH*yT/&@;=KR&7Qb&10�;=FH*yUg&1K.QL;=-#&10q;=FH*y�H;O;O*E(hTV&)()*,+�:[>1Q6g*VAC-D*E(';O&pAHQC()*[?]-9;]>@QW(�FH&�{�;=FH*fFW*,>@?O;�K.-n0jAHQC:e;OK.&1QWKRQH\C_�kmFH*X()*[0j&1?=T/>@;OK.&1Q�&@0�>�;O*[;O?]>@FH*E()?=>1+u*,+�^*[T/*,Q7;�&10C;=FH*�T/&)()*[+HKY-l?=*[+Y>�;O*E(r;=&�;OFH*m0j&7?=:[*,-l&7QVKR;�>@QC(r;=FH*w-9;=K��dQH*E-O-�&10C;=FH*m;OKY-=-DAH*m;=FW>�;�KR;�T/&)()*[+Y-[_

+-,/. , � � � ��H6 � I�CE6 �9:�7BSL�IL{: B � J�3�J�Q L� @ G

�o>JIvK.QH\y-OAH?OI7*[M7*,(p()KR�g*,?O*,Q7;3TV&)()*,+.-w0j&1?o274 &76)89*,:<;=-,cC{q*#QH&�{�()KY-O:[AW-O-�;OFH*fTV&L-9;n:<&1T/T/&1QW+RMBAW-D*E(\1*,QH*[?]>@+dUW>1?=>7()K.\1TX-�0j&1?w214s&76)89*,:<;�?O*E:<&1\7QHKR;OK.&1Q|_�kmFHKY-mK.-o>1:e;=AW>@+.+.My()K ?y:[AH+�;EcW6g*,:,>@AW-O*n;OFH*#T/*<;=FH&)(AW-O*,(S()*,UC*,QW(H-XFH*E>JIvKR+.MG&1QP;=FH*>@UHUW+RKY:[>@;OK.&1Q|c�;OFH*;9MLUg*'&@0#(H>@;=>Hcm>@QC( ;=FH*'?=*,�LAHK.?O*,TV*,QL;=-/&@0n;OFW*?=*,:<&7\1QHKR;OK.&1Qi;]>1-�&g_3kmFH*[?=*�>@?=*#TX>@QvMp()KRT/*,QW-DK.&1QC-3>1+R&7QH\X{�FHKY:]F&1QH*f:[>@Q:[+.>7-O-OKR0jMB&7?3:<&7QW-D;O?]>@K.Qp>1Q

�� )�� w�� ¢�R�� ¡ 272

�.� � �� 0 � � �@� �� 2��'� 0�0 � � � �� 0�� 2 �� 2 � 4�� 0 ��

� �� 0�0 � � �� @�� 2 �@�� 3 � � �� 1 0 � � �B� �� @��

�#� �� 1 � 0 ��#3 � ��2,�@� �� 3 ��

}�KR\7AH?=*X�[�W_.� ¡ ��kmFH?=*[*r-OQW>@UC-DFH&1;=-�&10u;=FH*rUHFvM)-OK.:,-9^�6W>1-O*,(BUH?=&):<*,-=-�&10lK.Q � >@;OK.QH\y>XT/*,-OF'&@0�;O?=KY>@QH\7+R*E-;O& �H;n>V:[+R&7AW(B&@0�214�(H>@;=>H_ ��&1AH?O;O*E-DM�&@0��>1QH\��FH*[Q'>1QW(izn*,?=>1?=(i%'*E()KR&7QHK�_ �

¡ 21� �� ! #"$"%"

}�KR\7AH?=*#�[�W_.�)XW�t%'&1;OK.&1QV&@0d;9{�&�6g*,>@;OK.QH\#FH*,>1?D;]-�>1-�:[&1T/UHA);=*,(V0j?=&1T�;=>@\7\1*E(f% Uw`�(H>@;=>W_�kmFH*w-O*[QC-D&7?:[>1Qp;=>1\�+.KRIvK.QH\X;OKY-=-DAH*V>@QW('-O*[QC-D*fK�;]-oT/&@;=KR&7Q'KRQ�214f_gkmFH*fFH*,>1?D;3TV&)()*,+��W;o;O&�;OFH*V(H>�;]>yKY-wT/*,>1QL;;O&pT/&)()*[+�?=*,>1+�UHFvM)-DKY:[-�>@QC(�FH*E>@?O;�0jAHQW:e;=KR&7Q|_XkmFH*/T/&@;OK.&1QbI1*E:e;=&1?]-3-OFH&�{�Qh>@?=*V()KR�d*[?=*[QL;�0j&1?�;OFW*;9{q&VFW*,>@?O;=-,_��&7AH?D;=*,-OMy&@0 �1K.QW>1Fi��>1?�&y>1QW(p4oK.T/K�;=?OKY-w%'*[;=>��H>7-[_ �

�� )�� w�� ¢�R�� ¡ 2 ¡&16H89*,:e;�?=*,:[&1\1QWK�;=KR&7QBUH?=&16W+R*,Ti_�kmFH*E-D*�K.QW:<+.AW()*

� �'� � 2 � �� &� �� 1 �� 1 � ��B� 1 � � �� !� � �!��NàQi:,>1-O*3{q*�{q>1Q7;q;O&/*,QH\1K.QH*[*,?�>-D&7+RA);=KR&7Q;=&p>1Q�K.T/T/*,()KY>�;=*XUH?=>7:e;=K.:,>@+lUH?=&16H+.*[Tpc�&1AW?#UH?O&76H+.*[T TX>JM6g*/-OUg*,:<Kv�C:/*,QH&1AH\7F;=&6C*r-OKRT/UH+.*1_�}W&1?�*[�)>1T/UH+R*7c){�*#TX>JMyFC>JI1*3;O&X\1?]>@6i>/-9;=*[*[+u:<Mv+RK.QW()*,?m0j?O&7T!>389AHTf6H+R*#&10�TX>1QLM&@0o;=FH*[Tp_ }3QZ;OFH*p&@;=FH*[?XFC>@QW(�c�&1AH?XK.QL;O*,?O*E-9;/TX>JMG6C*pK.QSAHQW()*,?=-D;=>1QW()K.QH\�FvAHTX>1QZ&76)89*,:<;?O*E:<&1\7QHKR;OK.&1Q|_bkmFHK.-VK.T/UH+RK.*,-/()*,I1*,+R&7UHT/*[QL;f&10o>�I7*[?=M�\7*[QH*,?=>1+�;=FH*[&7?OMb{�FHKY:]F KY-V:[&1QW-OKY-9;=*[QL;{�K�;=FiTfAH+R;OKR0�>@?=KR&7AW-mUW-OMv:]FW&1+.&1\1KY:[>1+g(W>�;=>w�v>fT�AW:]FiT/&1?=*#()K ?y:[AH+�;3UH?O&76H+.*[Tp_� �#�� 2�� &� �� 0 � �� @� �� 0 � :3A�� b%�>@QvA)0�>1:<;OAH?=*,(�&16)89*E:e;]->@?=*�AW-OAW>@+.+RM#T/&7?O*�?O*,\1AH+Y>@?t;OFW>1Q�QW>@;OAH?]>@+L&1QH*E-[_�%'&1?=*[&�I7*[?Ec<;=FH*[?=*q>1?O*�?OK.\1KY(#KY:<&7QHK.:�UH?=&@;O&1;9MvUC*E-0j&1?#TX>@QvMTX>@QH^�TX>1(H*V&76)89*,:<;=-,c|TX>�&vK.QH\'-D*,I1*[?]>@+&vQH&�{�QbTX>�;=:]FWKRQH\pUW>1?=>7()K.\1TX-�>@UHUH+.KY:[>@6W+R*7_� >�;=AH?]>@+�&16)89*E:e;=-�>1?O*/:<?=*,>@;O*,(6LM'UW?O&):<*E-O-O*,- �j\7*[&7+R&7\1KY:[>@+�cd6HK.&1+.&1\1KY:[>1+ cg*<;]:@_ �h{�FHKY:]F�UH?=&)()AW:[*>p\1?=*,>�;r()*E>@+�&@0mIJ>1?OK.*<;9M�;OFW>@;�TX>JM�6g*�()K ?y:<AH+R;�;=&'TV&)()*,+ _'}WAH?D;=FH*[?=T/&1?=*1ct;OFH*�:[&1QL;O*[�v;r&@0QW>�;=AH?=>1+C&76)89*,:<;=-qTX>JM/6C*n+R*E-O-m:[&1QL;O?]>@K.QH*,(�>@QW(�+R*E-O-qUH?=*,()KY:e;]>@6H+.*w;=FW>@QB;OFW*n:[&1QL;O*[�L;mK.Q�{�FHKY:]FT/>1QvA)0�>1:<;OAH?=*,('&76)89*,:<;=-n>@?=*r0j&7AHQW(�_#}H&7?3*[�H>@T/UH+.*1cg;OFH*VUH?=&16H+.*[T5&10�&16)89*E:e;n?O*E:<&1\7QHKR;OK.&1Q'0j&7?>@A);=&1QH&7TV&7AW-�QW>JIvKR\L>�;=KR&7QfK.Q/&1A);]()&v&1?�*[QvIvK.?O&7QHT/*[QL;=-�-O*[*,T/-�;O&#6g*wT�AW:]F/T/&1?=*�()K ?X:[AH+R;�;OFW>1Q;OFH*qUH?=&16H+.*[Ts&@0C?O*E:<&1\7QHK�[[K.QH\o>@QC(�()*[;O*[?=T/KRQWKRQH\3;OFW*�Ug&7-O*�&10W&16)89*E:e;]-t0j&7?t0�>7:e;=&1?=M�>1A);O&7TX>�;OK.&1Qt_

� / � � 2 �)�� !� �� 0�� 2 �� 0�� 3��h%>1QvMX?O*E:<&1\7QHKR;OK.&1QUH?O&189*,:<;=-nFW>JI1*/()*E>@+R;�&7QH+.M'{�K�;=FbUg&1+.MvFH*,(H?=>Wc�{�FHK.:]FbTX>�&7*,-nT/&v(H*[+.KRQH\pUW>1?D;=K.:[AH+Y>@?=+RM-OKRT/UH+.*1_U�*,:[*[QL;O+.M1cC?O*E-D*E>@?]:]FH*[?]-mFW>JI1*�;=AH?=QH*,(i;=&�{q>1?=(iAW-O*r&@0��LAW>7()?=K.:#-OAH?O0�>1:<*E-[cC{�FHKY:]F'K�;nK.-3:<+Y>@K.TV*E(:[>@QhT/&)()*[+m>@6g&1AH; �7¡�� &10mTX>1QLAH0�>1:e;=AH?=*,(b&16)89*E:e;]-[_kmFH*�T/>@89&1?�:[&1QvI1*,QHK.*[QW:[*XK.-r;OFW>@;�;OFW*TV&)()*,+RK.QH\i>@QW(p;=FH*f-O*[QC-D*E((H>�;]>�>1?O*r?=*,>7()K.+RM'()*E-O:[?OK.6C*E('6vMi;OFH*V-O>1TV*fUH?=KRT/KR;OK.I1*,-,cgUC&L-O-OKR6W+RM{�K�;=Fi-O&1T/* �H;D;=KRQH\X&10uUW>1?=>1T/*<;O*,?=-,_�`�;mKY-mQH&1;�:[+R*E>@?mFH&�{ 6g*,-D;�;O&VT/&)()*[+t-=:<AW+RU);=*,(�cv0j?=*[*[^ 0j&7?OT&16)89*E:e;=-f*[I7*[QG{�FW*[QG;=FH*[MG>1?O*B?OK.\1KY(N&76)89*,:<;=-,_ m -=:<AH+.U);=*,(G&76)89*,:<;,c�-OAW:]F >7-f>b-OUC&7?D;]-f:,>@?Ec;OAH?=6HK.QB6H+Y>1(H*1cH&7?qKY:<*,6C*,?O\Cc)TX>JMyFW>JI1*�TX>@QvM�(HK��d*[?=*[QL;w-DT/&v&@;=FH+.My6H+.*[QW()K.QH\y-OAH?O0�>1:<*n0j*E>�;OAW?O*E-{�FHK.:]Fp>@?=*�QH&@;�*E>1-OKR+.M�-O*[\1T/*,Q7;=*,(BKRQL;=&/-OK.TVUW+R*#UH?=K.TVKR;OK.I1*E-[_

� �'� � 2 � � �� 2�� 2�� 3A�� )&1T/*r&16H89*,:e;3?O*E:<&1\7QHKR;OK.&1Q-O:]FH*,T/*,-q>1-=-DAHT/*3;OFW>@;�&16)89*E:e;=-q;=&f6g*�?O*E:<&7\1QHK�[[*E(y>@?=*3UW?O*E-D*,Q7;=*,(�KRQiK.-O&1+Y>�;=KR&7Q|_lkmFHK.-mTX>JMX&7?T/>JMfQH&@;�6C*3UC&L-O-OKR6W+R*�;=&r*[QW\1K.QH*[*,?�KRQy;OFH*�;]>1-�&V(H&1TX>@K.Q|_l%'AH+R;OK.UH+R*3&16)89*E:e;�*,QvILK.?=&1QHT/*[QL;]-�>@?=*;9MLUWK.:,>@+.+RMyFC>@?]()*[?�6g*,:,>@AW-O*#&16)89*E:e;�0j*E>�;OAW?O*E-�{�KR+.+|6g*r6g&@;OF'TX>7-a&7*,(i>@QW(iK.Q7;=*[?=T/K��)*,(|_qzn+.&16W>1+0j*,>�;=AH?=*#TV*[;OFH&)(H-o{�&7?�&�{�*,+R+|&7QH+.My0j&1?3-DK.QH\1+.*#&16H89*,:e;]-[_qkmFH*�-O*[\7TV*,QL;=>�;=KR&7QBUW?O&76H+R*,T :,>@Qp6g*>1:<AH;O*�KRQpTfAH+�;=KRUW+R*#&76)89*,:<;m*,QvILK.?=&1QHT/*[QL;]-[_�� 2 �@�� 2�� 1 � � 0 �� 2 � � �B� 1 �� *b*�T/K.\1FL;3QW*[*,(';O&�?=*,:[&1\7QHKv[,*r>@Q&76)89*,:<;o0j&7?KRQW-OUg*,:e;=KR&7Q|cH\7?=>7-DUHK.QH\Cc)&1?�&16H89*,:e;o>JI7&1KY(H>@QC:<*1_�}W&1?wK.QW-OUC*E:e;OK.&1QtcH{�*#{q&1AW+.(i+.&L&$&�>�;�;=FH*r-OT/>1+R+()*<;]>@K.+.-�&10m>@;�+.*,>7-9;#UW>1?D;r&10�;=FH*X&16)89*E:e; �vTV&)()*,+RK.QH\'>@QC(�T/*,>7-DAW?O*,TV*,QL;�UW?O*E:<KY-DK.&1QbT�AW-D;r6g*\1&v&)(�_wzn?=>7-DUHK.QH\y>1Q'&16)89*E:e;wFW>7-o()KR�g*,?O*,QL;o?O*E�LAHKR?=*[T/*,Q7;]-[_ � &@;o&7QH+RMp()&v*,-w;OFH*�;=>7-a&B?O*E�7AWKR?=*-D&7TV*�?O&7AH\1FG\7*[&7TV*[;O?=K.:,>@+ &LQW&�{�+R*E()\1*7c�6WA);VKR;/T�AW-D;/>1+.-O&�:[&1QW-OK.(H*[?�6C>@+Y>@QW:[*B>@QC( -D;O?=*[QH\1;OF>@QW(/>1:,:<*E-O-OKR6WKR+.K�;9Mf&@0d;OFW*o&16H89*,:e;�K.QX;=FH*w{q&1?T&v-OUW>7:<*1_ m ?=&16g&@;�?=*,:<&7\1QHK�[[K.QH\n;OFC>�;�>1QX&16)89*E:e;�K.QK�;]-�UC>�;OFBT�AW-D;�6C*�>JI1&7K.(H*,(XTfAW-9;m&1QW+RMXFW>JI7*3>f?O&7AH\1F�K.()*E>�&10|;OFW*�-OK�[[*1c)-OFW>@Ug*1cH>1QW(y+.&):[>@;OK.&1Q&@0t;=FW>�;w&76)89*,:<;,_� �'� ��2�� @� � � �E� 4 � �@� ��h�wAHTX>1QW-�:[>1Q�&7UC*,?=>@;O*��LAHK�;=*m{�*,+R+){�KR;OFV;OFW*�KRTX>@\7*0j?O&7T &1QH+.M�&7QH*m*[M7*1_l%>@QvM�?=*,-O*,>1?=:]FW*[?]-tFW>JI7*q(H*,-OKR\7QH*,(/-OMv-D;O*,TX-�;OFW>@;�AW-O*�&1QH+.M7\@4 KRQL;O*,QW-OK�;9MKRTX>@\7*,-�>1-�KRQHUWA);,_ \14 0j*E>�;=AH?O*E-�0j?O&7T�;=FH*n&16)89*E:e;mKRTX>@\7*3>1?O*3?O*,+.>@;O*,(X;O&f>V214�T/&)()*[+dIvK.>�;OFW*ILK.*[{P;=?=>1QW-90j&7?OTX>@;OK.&1Q�'@AC-DAW>1+R+.Mf;OFH*3T/>@;=:]FHK.QH\#UH?=&):<*E-O-�FC>1-�;=&�()KY-O:[&�I1*,?l;OFHKY-�;=?=>1QW-D0j&1?=T/>@;OK.&1Q>1-m{q*[+.+|>1-q;OFW*#&16)89*E:e;wKY()*[QL;OKR;9M1_�%>�;]:]FHKRQW\VKY-m&@0 ;=*[Qp*,>7-DK.*[?�KR0�214 (H>@;=>VKY-w()K.?O*E:e;O+.M�>JI�>@K.+Y>@6H+.*

¡ 2$X �� ! #"$"%"

>@QW(�;OFHKY-�KY-�;OFW*w?O*E>1-O&1Qf{�FLMfTX>@QvM�:<AW?O?=*[QL;�?O*E-D*E>@?]:]FH*[?]-�>@?=*q{q&1?T&vKRQW\3{�KR;OFX?]>@QH\7*q(W>�;=>W_�kmFW*6C*,+RK.*<0�KY-o;OFW>@;3;=FH*V-OAH?O0�>1:[*f-OFW>@Ug*�&10�&16)89*E:e;]-3>1QW(p;OFW*[K.?nUg&7-OKR;OK.&1QW-n:[>1Q6C*/()K.?O*E:e;=+RM'-O*[QW-O*,(_';OFHKY-oK.Q;=AH?=Q�UH?=&�IvK.()*E-o>B()KR?=*,:<;nK.QW()*[�'KRQL;O&iUg&7-=-DK.6H+.*�&16H89*,:e;nT/&v(H*[+Y-n>1QW(>1+.-O&�?=*,()AC:<*,-o;OFW*>@T/&1AHQL;�&@0l>@Tf6HKR\7AHKR;9MyKRQ':[&1T/UHA);=KRQH\V;=FH*#?O*,\1KY-9;=?=>@;OK.&1Q�;O?]>@QW-D0j&1?=TX>�;OK.&1Qt_� / � � � �� 3A� � 0 � 1 �� 3 � � � � � � � 3 �� 0 �� zn*,&1T/*<;=?OKY:mT/&)()*[+Y-�()*,-=:<?=K.6C*m;=FH*�*<�H>1:<;214 -OFW>1UC*�&@0�>@Q &16)89*E:e;,co{�FHKR+.*�-OMvT�6g&1+.K.:TV&)()*,+.-i()*E-O:[?OK.6C*b>@Q *,Q7;=KR?=*�:[+.>7-O-�&@0#&16H89*,:e;]-[_zn*[&1T/*[;O?=K.:BT/&v(H*[+Y-V>1?O*iFH*E>JILK.+.MNAW-D*E(GK.QZK.QW()AC-9;=?OKY>@+�TX>1:]FWKRQH*iIvK.-OK.&1Q|c�{�FW*[?=*�;=FH*'&16)89*E:e;]-;O&b6C*i?O*E:<&7\1QHK�[[*E(G:<&7TV*�0j?O&7T�>�-OTX>@+.+�UW?O*E-DUg*,:[K �W*E( -O*<;E_P� m 4 (H>@;=>�K.-V6g*,:<&7T/KRQH\bT/&1?=*>JIJ>1KR+Y>@6W+R*X>@QC(h{�KR+.+�AW-OAW>1+R+.M�FW>JI7*y>@+.+�;OFW*yQH*,:[*,-=-O>1?OM�\1*[&7T/*<;O?=KY:X()*<;]>@K.+ _ �vMvT�6g&1+.KY:/TV&)()*,+.->@?=*o?=*,�LAHK.?O*E(XKRQB;=>7-a&)-�{�FH*[?=*3;OFH*,?O*�>@?=*oTX>@QvMy()KR�d*[?=*[QL;qI�>1?OK.*<;=KR*E-�&10t;OFW*3&76)89*,:<;m:[+.>7-O-�;O&V6g*?O*E:<&1\7QHK�[[*,(|_�}H&7?w*<�H>@T/UH+.*1cCKRQpT/*,(HK.:,>@+tK.TX>@\7KRQH\CcH*,>7:]Fp&1?=\7>@QiUH?=&�IvK.()*E-�>/QH*[{s&76)89*,:<;o:<+Y>1-=->@QW('*,I1*,?OMBUC*,?=-O&1QUW?O&�IvKY()*,-w>�AHQHKY�LAH*fI�>1?OKY>�;=KR&7Q|_o%>1QLMi&16H89*,:e;]-oK.Q&7AH?3*,QvILK.?=&1QHT/*[QL;EcW0j&7?*<�H>@T/UH+.*1cH:]FW>1KR?]-,cLFC>JI1*nT/>1QvMyI�>@?=K.>@;OK.&1QW-�>1QW(�?=*,�LAHK.?=*nT/&7?O*3;OFW>1Q'>f\7*[&7TV*[;O?=K.:�>1UHUH?=&7>1:]Ft_� / �+�� 3A� � 0 � � � � � 0 �� 1 ��3A3 �� }36)89*,:<;yTV&)()*,+.-yT/>JM:<&1QL;]>@K.Q>y+Y>@?=\1*r>@T/&7AHQL;3&@0�UW?O*E:<KY-D*�(W>�;=>�{�FHKY:]F'K.-3I1*,?OMp()K ?X:[AH+R;30j&7?3FvAHTX>@QC-�;O&BUH?=&�ILKY()*7_� m 4 (H>@;=>/>@+.&1QW*nTX>JMyQW&@;w6g*#*[QH&7AH\1F�'H-O&1T/*r>7(H()KR;OK.&1QW>1+�&1?=\7>@QWKv[E>�;OK.&1Q�&@0�;OFW>@;o(H>�;]>HcH-OAW:]F>1-�*,TVUWFW>1-OKv[,KRQW\�0j*,>�;=AH?=*,-,c7KY-�&10 ;O*[QXQW*,:<*E-O-=>@?=M1_��o>JIvK.QH\r>r-OMv-D;O*,T�+.*,>1?OQ/&76)89*,:<;�\1*,&1T/*<;=?OMr6vMUH?O*E-D*,QL;OK.QH\�;=FH*#&16H89*,:e;�;=&/K�;]-w-D*,QW-O&1?]-�KY-�>@Q'>@;D;O?]>1:<;OK.I1*nUC&L-O-OK.6HKR+.KR;9M1_

]_^-`�^-à] dg��i ��-� � f�j�D f_�t� �a� dgj9k!f�lah � �a� l#�a� � D f � �U�*E:<&1\7QHKR;OK.&1Qh6vMb>1+RK.\1QHT/*,Q7;f*[T/UH+.&�Mv-#;OFH*�-=>@T/*yUW?OK.QW:<K.UH+.*,-#K.Q 274�&16H89*,:e;f?O*E:<&1\7QHKR;OK.&1Qh>1-rK.Q \@4TX>�;]:]FHKRQW\W_ � �v*[*f��FC>@U);=*[?r�7��0j&1?�6W>7-DKY:#()*{�CQHK�;=KR&7QW-,_ ��kmFH*#TX>@K.QiKY()*E>/K.-o*<�)UH?=*,-=-D*E(�K.Q m +.\1&1?=KR;OFHT�1�C_

43*<;O*,?OT/K.QH*#KR0l>/-O*<;w&@0�KRTX>1\1*#(H>�;]>VUC&7KRQL;=-wT/>@;=:]FH*E-�>/214�&76)89*,:<;mT/&)()*,+ _

�7_�FLMvUg&@;=FH*,-OKv[,*�>y:[&1?=?O*E-DUg&1QW(H*[QW:[*n6g*<;9{q*[*,Q�>y-O*<;n&@0�T/&v(H*[+�UC&7KRQL;=-3>@QW(�>y-D*[;o&@0�K.TX>@\7*�(H>�;]>UC&7KRQL;=-,c\H_�AW-D*n;=FW>�;o:[&1?=?O*E-DUg&1QW(H*[QW:[*o;=&/(H*<;O*,?OT/K.QH*r>f;O?]>@QW-D0j&1?=TX>�;=KR&7Qy0j?=&1T�;=FH*#T/&v(H*[+�;=&f;=FH*r(H>@;=>Hc2W_w>@UHUH+.My;=FH*r;=?=>1QW-D0j&1?=T/>@;OK.&1QB;O&X;=FH*�T/&)()*,+tUg&1K.Q7;]-�;=&yUH?=&v(HAW:<*�>�-D*[;o&@0l;O?]>@QC-90j&7?OT/*,(iT/&)()*[+UC&7KRQL;=-,cH>@QC(�C_w:<&1T/UW>1?O*/;=FH*B;O?]>@QW-D0j&1?=T/*,(hT/&)()*[+qUC&7KRQL;]-r;=&;OFW*i(H>@;=>�UC&7KRQL;=-�;O&�I1*,?OKR0jM�&7?f()KY-OUH?O&�I7*X;OFW*FLMvUg&@;=FH*,-OK.-,_

/ 0�1 � � ��2�3 � ��!qkmFH*r�m>7-DKY: m +RK.\1QWTV*,QL; m +.\1&1?=KR;OFHT*b*#{�KR+.+�+R&v&$&�>�;w6g&@;=FB;=FH*r214oâ214�>@QC(/\14wâ214 :,>1-O*,-,_

4�� 4 � /#0 � 1 3 �� Yt*<;�AW-�>7-O-OAHT/*m;OFC>�;�;=FH*o214 TV&)()*,+.-�>@?=*1c1&7?�:[>1QV6g*o:[&1QvI1*,?D;=*,(�;O&WcL:<&7+R+.*,:<^;OK.&1QC-|&@0H274 T/&)()*[+R^�UC&7KRQL;|0j*E>�;OAW?O*E-[_|`�0);=FH*�(W>�;=>wK.-t?=>1QH\1*�(H>@;=>Wc[;=FH*[Q�:[&1?=?O*E-DUg&1QC()KRQW\m274Z(W>�;=>@^�Ug&1K.QL;0j*,>@;OAH?=*,-l>1?O*q?O*E�LAHKR?=*,(#0j&1?lTX>�;=:]FWKRQH\C_�kmFW*q>1+RK.\1QHT/*,Q7;�UH?=&):<*E()AH?=*��WQW(W-�;OFH*�:<&7?O?=*,-OUg&1QW()*,QW:<*E-�0j?=&1T

�� )�� w�� ¢�R�� ¡ 2v¢

MP2DP2

MP4

DP3

DP4

MODELDATA

MP1DP1

MP3

}�KR\7AH?=*#�[�W_.�J¢)�l��&7?O?=*,-OUC&7QW()*,QW:<*E-u6g*<;9{q*[*,Qy214 TV&)()*,+WUg&1K.QL;=-�>1QW(X214 T/*,-OFy(H>�;]>�UC&7KRQL;=-�;OFW>@;�:[>1Q6g*3AW-O*,(X;O&/:<&1T/UHAH;O*w;=FH*3;O?]>@QW-D0j&1?=TX>�;OK.&1Q/0j?=&1T�;=FH*3T/&)()*,+C;=&r;=FH*n(W>�;=>�KRQ�;OFH*n214o^�274s>@+.KR\7QHT/*[QL;UH?=&):<*,(HAH?O*7_

;OFW?O*,*/:]FW&7-O*[Q�T/&)()*,+�^�UC&7KRQL;n0j*,>@;OAH?=*,-n;=&�;=FH?O*,*X:<&1?=?=*,-OUC&7QW()K.QH\B(H>@;=>@^�Ug&1K.QL;30j*E>�;OAW?O*E-[_VkmFHK.-#:[&1?=?O*[^-OUC&7QW()*[QC:<*o()*[;O*,?OT/K.QH*,-�>r214 ;O?]>@QW-D0j&1?=TX>�;=KR&7QV:[&1QW-OK.-D;OK.QH\r&10|>r214�?O&1;=>@;OK.&1QX>@QW(X>�214 ;=?=>1QW-O+.>@;OK.&1Q{�FH&L-D*q>@UHUH+.KY:[>�;=KR&7Q#;O&3;OFW*�;=FH?O*,*�T/&)()*,+LUg&1K.QL;=-uUH?=&v(HAW:<*E-t;=FH*�;OFH?=*[*q(H>�;]>oUg&1K.QL;=-,_ m Q/>@+.\1&7?OKR;OFWT ;=&()&#;=FHKY-�>@UWUC*E>@?=*,(VKRQB��FC>@U);=*[?w�E2H_�`�0g;=FH*oUg&1K.QL;�:<&7?O?=*,-OUg&1QW()*,QW:<*mKY-�:<&7?O?=*,:<;�>@QW(V;=FH*[?=*�KY-�QH&rQW&1KY-D*7c;OFW*3:<&7?O?=*,:<;�214 ;O?]>@QC-90j&7?OTX>�;=KR&7QX:[>@Q�6C*o0j&1AHQW(y0j?O&7T�;=FH*3;OFH?=*[*wTX>@;=:]FH*E-[_��vK.QW:<*o;OFHKY-�K.-�?=>1?O*,+RMf;OFW*:[>7-D*7c|T/&1?=*/?O&76HAW-D;nUH?=&):<*E()AH?=*,-n;OFC>�;�;9MvUHK.:,>@+.+RM�AW-D*/&7Q�;=FH*X&1?]()*,?n&10�;=*[QN:<&7?O?=*,-OUC&7QW()*,QW:<*E-oFW>JI7*6g*[*[QG(H*[I1*,+R&7UC*E(�_�àQN>1QLMb:[>7-D*7ct&1QC:<*/;OFW*yUC&1;O*,Q7;=K.>1+�;O?]>@QC-90j&7?OTX>�;=KR&7Q�FC>1-�6g*[*[QG:[&1T/UHA);=*,(�c�KR;�K.->@UWUH+RK.*,(�;=&p>1+R+�&@0q;OFH*XT/&)()*[+�UC&7KRQL;=-n;=&'UH?=&v(HAW:<*X>'-O*<;#&@0q;O?]>@QW-D0j&1?=T/*,(�T/&v(H*[+�Ug&1K.QL;=-n;OFC>�;�:[>1Q6g*r()KR?=*,:<;O+.MB:[&1T/UW>@?=*,(�;O&V;=FH*#0jAH+.+t-O*<;w&@0�(H>@;=>VUC&7KRQL;]-[_ m -�K.QB;=FH* \@4�:[>1-O*1cH>/I7*[?=K �g:[>�;=KR&7Q�UH?=&):<*[^()AH?=*3(H*,:<KY()*E-�FH&�{S{q*[+.+W;=FH*3;O?]>@QW-D0j&1?=T/*,(/T/&)()*[+gUC&7KRQL;]-�+.KRQW*oAHUB{�K�;=FX;OFH*�(H>@;=>#Ug&1K.QL;=-q>@QW(X*,K�;=FH*[?()*E:<+Y>@?=*,-�>�TX>�;]:]FG&1?f;O?=KR*E-f>1QH&@;=FH*[?VUg&7-=-DK.6H+.*i:[&1?=?O*E-DUg&1QW(H*[QW:[*1_ m -VKRQ ;OFH*S\@45:[>7-D*7cl;OFH*,?O*i>@?=*K.Q7;=*[+.+RK.\1*,QL;�I�>@?=K.>@;OK.&1QW-�;OFW>@;m-O*[+.*,:<;�;=FH*n:[&1?=?O*E-DUg&1QC()KRQW\rUC&7KRQL;]-�6vMV;OFH*n+.&v:,>@+R^ 0j*E>�;=AH?O*[^ 0j&):[AW-�T/*<;=FH&)(&1?o6LMp-O&1T/*#&@;=FH*[?wUg*[?]:<*,U);OAC>@+t\7?O&7AHUHK.QH\/;O*E:]FHQHKY�LAH*1_m}�KR\7AH?O*��[�W_.�J¢�K.+R+.AW-D;O?]>�;=*,-m;=FH*�214oâ214�:[&1?=?O*[^-OUC&7QW()*[QC:<*,-o;OFC>�;n:[&1T/*�>16C&7A);o0j?=&1T5TX>�;]:]FHKRQW\B>/;=FH?O*,*<â-D*,\1T/*[QL;3274 89AWQW:e;=KR&7Q&@0�>B:]FW>@K.?oT/&)()*[+;O&X>X274sTV*E-DF'(H>@;=>7-D*[;,_

�� i214o^�274 0j*,>@;OAH?=*r>@+.KR\7QHT/*[QL;�7AHQW:e;=KR&7QW-�&@0H+.KRQW*m-O*[\7T/*[QL;=-�>@?=*�:[&1T/T/&1QrK.Q�Ug&1+.MvFH*,()?]>@+v&76)89*,:<;=-,_l��&1QC-DKY()*[?l>o274S:<AHUf&16)89*E:e;lFW>JIL^K.QH\3>n:<Mv+.KRQW(H?OKY:[>1+7UW>1?D;�{�K�;=Ff>3:<Mv+RK.QW()?=KY:[>@+v:[>JIvKR;9Mn0j&1?u;OFH*q+RKY�LAHKY(�>@QC(�>o-O*[T/KY:<K.?=:[AH+Y>@?tFC>@QW()+.*1_�* FW>@;0j*,>@;OAH?=*,-w&@0�;OFH*�:[AHUpT/KR\7F7;w6g*�()*[;O*E:e;O*E(pKRQi;=FH*�214�(H>�;]>X>@QW(iAW-O*,(B0j&1?-�WQW()K.QH\y:<&7?O?=*,-OUg&1QW()*,QW:<*E-K.QiTX>@;=:]FHK.QH\ �

}H*E>�;=AH?O*/*[�L;=?=>7:e;=KR&7QbKY-r>1QbK.T/UC&7?D;]>@QL;rKY-O-OAH*XFH*,?O*7_�`�0q;OFH*�:[+.>7-O-�&10�&16)89*E:e;=-rK.-r-OAW:]Fb;OFC>�;�()KY-9^;OK.QH\7AHK.-OFH*E(GUg&1K.Q7;]-[c�-OAW:]FP>1-V:<&1?=QH*,?=-#Ug&1K.QL;=-,c�Ug*,>�&)-,c�>@QW( UHKR;=-,c�:[>1QG6C*i*,>7-DK.+.M�0j&7AHQW(�c�;OFH*,QG;OFW*>@6g&�I1*3UH?=&v:[*,()AW?O*�-DFW&1AH+Y(y{q&1?T&/{�*,+R+�_�`�0�-OAH?O0�>1:<*E-�>1?O*�-OTV&v&1;OFB>1QW(i()K.-D;OK.QH\7AHK.-OFH*E(yUg&1K.Q7;]-�>@?=*3?]>@?=*&1?nQH&7QH*<�)KY-9;]>@QL;,cd;=FH*[Qh>�6g*<;O;O*,?nT/*[;OFH&)(�0j&1?K�WQW()K.QH\p:<&7?O?=*,-OUC&7QW()*,QW:<*E-oKY-nQH*[*E()*,(�_ �1&7FHQW-O&1Q�>1QW(�w*,6C*,?D;#>�;r�q% ��FW>JI1*�(H*[I1*,+R&7UC*E(>yI7*[?=MB?=&16WAW-9;nT/*<;OFW&v(0j&1?n*<�H>1:<;O+.Mi;OFHKY-oUW?O&76H+R*,Tp_nkmFH*,KR?�214&16H89*,:e;/?=*[UH?=*,-O*[QL;=>@;OK.&1Q :[&1QW-OKY-9;]-�&10f��f>b214 T/*,-OFZT/&)()*[+m&10w;OFH*p&76)89*,:<;/>1QW( \��>b-O*<;/&@0 z � ��xyu(q¢p�z :<&7QW-9;=?OAC:e;O*E(y0j?=&1T�;OFH*#T/*,-OFi;OFW>@;o:]FW>@?]>1:<;O*,?OK�[[*3+R&):[>1+|-DFC>@Ug*30j*E>�;=AH?O*E-m&@0�;OFH*#&76)89*,:<;,_znK.I1*[QB>�T/*,-OF�T/&)()*,+g&10u>V214 &16)89*E:e;Ec7;=FH*#-DAW?D0�>7:<*oQW&1?=T/>1+g:,>@Qy6g*�*,-D;OK.TX>�;O*E(�>@;q*E>1:]FyI7*[?O;O*<�

¡ 2 � �� ! #"$"%"

&@0�;OFH*/T/*,-OF|_rkmFH*,Q;OFW*V?=*[+Y>�;=KR&7QW-OFHKRU�6C*[;9{�*,*[Q�>1QvMi&7?OK.*[QL;=*,(Ug&1K.QL;nK.Q�274wâ-OUW>1:[*f>@QC(�>i-DAH?O0�>1:[*QH&7?OTX>@+�>@;�>�UC>@?O;OKY:<AH+Y>@?/I1*,?D;=*<�Z:,>@QP6C*'?=*[UW?O*E-D*,Q7;=*,( 6LMG;9{�&N()KY-9;]>@QW:[*pUW>@?]>@T/*<;=*[?]-[c S >@QW( �c{�FH*,?O*QS K.-oK�;]-oUg*[?=Ug*[QW()KY:<AW+.>1?3()KY-9;]>@QW:[*#;O&y;OFH*�-OAH?O0�>1:[*rQH&1?=TX>@+�cW>@QC( GK.-oK�;]-o-OKR\7QH*,(pUg*[?=Ug*[QW()KY:eÂH+Y>@?n()K.-D;=>1QW:<*r;O&y;=FH*r;]>@QH\7*[QL;oUH+Y>@QW*f>�;o;OFW>@;3I1*,?D;=*<��_-U�&1;=>�;=KR&7QW>@+�>@QH\7+R*E-o>1?O*#&7TVKR;D;=*,(p0j?=&1T ;=FHK.-()*E-O:[?OK.U);OK.&1Qtc)6C*E:[>@AC-D*n;OFW*[MB>1?O*#>1T�6HK.\1AH&7AW-,_m z � �� xyu(q¢p KY-r>/&vKRQW()^�&10�FHKY-9;=&1\7?=>1T5;OFW>@;#:,>@Qb6C*y:[&1T/UHA);=*,(h>�;r>p-O*[+.*,:e;=*,(�I1*,?D;=*<�&@0q;OFW*T/*,-OF|_ ��>7:]F-DUWKRQ'K.TX>@\1*�{�KR+.+uFC>JI1*r>y-O*<;o&10 � � ~ n�� r ~ ��#q � � �� ~ z AW-O*,(pK.QKR;=-3:<&1QC-9;=?OAW:<;OK.&1Q|_wkmFW*-OKv[,*y&@0m;OFW*�I1&7+RAWTV*X&10w:<&1QL;=?OK.6HA);=KRQH\�UC&7KRQL;=-f()*[Ug*[QC(H-�&7Qh;9{�&-OUHK.Q)^�KRTX>@\7*XUW>@?]>@T/*[;O*[?]-,��'c�;OFW*TX>��)K.T�AHT�()KY-9;]>@QW:[*�0j?=&1T�>3:<&1QL;=?OK.6HA);=KRQH\3UC&7KRQL;u;O&3;OFH*m-D*,+R*E:e;=*,(#I7*[?O;O*<��c�>@QC(�$rcJ;=FH*m>@QH\7+R*�>1+R+.&�{q*,(6g*<;9{q*[*[Qy;OFH*3QH&1?=TX>@+W&10�;OFH*n:<&7Q7;=?OK.6HA);=KRQW\�Ug&1K.Q7;m>@QW(V;=FH*nQH&1?=TX>@+W&10d;OFH*nI1*,?D;=*<��_ m -DUWKRQyK.TX>@\7*wK.-:<&7QW-D;O?=AW:e;=*,(>16C&7A);�>B-DUg*,:[K �C*,(&7?OK.*[QL;=*,(pUg&1K.Q7;��X{�KR;OF�?O*E-DUg*,:<;o;O&p>�-O*<;�&@0�:[&1QL;O?=K.6HA);OK.QH\BUC&7KRQL;=-

� ;OFW>@;wFW>JI1*n6C*,*[Q-O*[+.*,:<;O*,(B6W>7-D*E(�&7Qp-OUg*,:<Kv�W*E(B-OUHK.Q)^�K.TX>@\7*nUC>@?]>@T/*<;=*[?]- $�>1QW(��'_ m Q'>1?O?]>JM/&@0>1:,:<AHTfAH+Y>�;O&7?=-L��S ��3?O*,UH?O*E-D*,QL;=-o;OFH*X-OUHKRQ�KRTX>1\1*/>@QW(�K.-�K.QHKR;OKY>@+.+RM-O*<;�;O&/[[*,?O&C_rkmFH*[Q�0j&1?�*E>1:]FUg&1K.Q7;�� c@K�;]-l()K.-D;=>1QW:<*qUW>1?=>1TV*[;O*,?=-�Sp>@QW( i>1?O*q:<&1T/UHAH;O*,(f{�KR;OF�?=*,-OUg*,:e;�;O&3;OFW*m-O*[+.*,:<;O*E(rT/*,-OFI1*,?D;=*<��vcH>@QC(X;OFW*�>7:[:[AHT�AH+Y>�;=&1?q6HK.QB:<&7?O?=*,-OUg&1QW()K.QH\�;O&f;OFHKY-�SN>@QW(� �KY-qKRQW:[?O*,T/*[QL;O*E(�_ � &@;=*n;OFW>@;;OFW*V-OKv[,*f&10�>B6HKRQbK.Q;OFW*V>7:[:<AWT�AH+Y>�;=&1?�>@?=?=>JMiK.-n&7Q';OFH*/&7?=()*,?3&10�;OFW*fT/*,(HK.>1Q�()KY-9;]>@QW:[*f6g*<;9{q*[*,QI1*,?D;=K.:[*,-qK.QB;=FH*r214 TV*E-DFt_�}uK.\1AW?O*/�[�C_R� � \7KRI7*,-m-O&1T/*�*<�H>@T/UH+.*,-m&10l-OUHK.QBK.TX>@\1*E-[_

β

α

β

α

β

α

β

α

β

α

β

α

2-D points spin-image



3-D surface mesh

}�KR\7AH?=*��[�W_.� � ��H>@T/UH+.*,-�&10H-DUHK.Q#K.T/>1\1*E-[_ � }�KR\7AH?O*�:[&1AH?O;O*E-DM3&@0 m QC()?O*,{ �1&7FHQW-O&1Qn{�K�;=FrUC*,?OT/KY-O-OK.&1Q&@0�`�� o_ U�*,UH?OK.QL;O*E(p0j?O&7T � � ?y:[KR*,Q7;n%'AH+R;OK.UH+R*/%'&)()*,+�U�*E:<&7\1QHKR;OK.&1Q'K.Qh��+.A);D;=*[?=*,(2@^�4?�):[*[QH*E-[c �6vM m _ �w_ �1&7FHQW-O&1Qy>1QW(y%N_)�w*,6C*,?D;Ec n � Tp�p�£w��#qwz � � ~ |�p�� W�{p{n�p(� �p � �� x � r ~ p{n�� z�� uw��£ u ~�~ p(n��!p� � q�� ~ � � � c �7AHQH*X�)V$V � _ :� �WV%V � `��

�vUHK.QK.TX>@\1*E-3>1?O*f:<&1QC-9;=?OAW:<;O*E(>�;�*,>7:]F'I1*[?O;O*[�'&@0�;OFW*fT/*,-OFT/&)()*[+�_#kmFHKY-o\7KRI7*,-3KRQ)0j&7?OTX>@;OK.&1Q&1Q;OFH*f+R&):[>1+�-OFW>1UC*V>�;o*,I1*[?=MiUC&7KRQL;�&@0�;OFW*�T/*,-OF|_3ku&�TX>@;=:]F';9{q&y&16H89*,:e;]-[cC;OFW*�;9{q&�-O*<;=-3&@0�-OUHK.QK.T/>1\1*E-3>1?O*fAW-D*E(�_#kmFH*/-DUHK.Q�K.TX>@\7*f>�;�*,>7:]FUg&1K.Q7;�&@0�;=FH* �W?]-9;n&16)89*E:e;�K.-n:<&7TVUC>@?=*,(p;=&�;=FH*V-OUHK.Q

�� )�� w�� ¢�R�� ¡ 2$VK.T/>1\1*i>�;/*,>1:]F UC&7KRQL;/&@0w;=FH*i-O*,:[&1QW( &16)89*E:e;V6LMG:[&1T/UHA);=KRQW\�;=FH*i:[&1?=?O*,+.>@;OK.&1QG:[&L*&?y:<K.*[QL;V&10w;OFW*UW>1KR?E_fkmFH&L-D*VUg&1K.Q7;#UW>1KR?]-n{�K�;=F�FWKR\7Fb:[&1?=?O*,+.>@;OK.&1QW-o0j&1?=T5;OFH*X274�UC&7KRQL;r:<&7?O?=*,-OUC&7QW()*,QW:<*E-oQH*,*,()*E(0j&1?o&16)89*E:e;oTX>�;]:]FHK.QH\W_mkmFH*#Ug&1K.Q7;n:<&1?=?=*,-OUC&7QW()*[QC:<*,-�>1?O*#\7?O&7AHUg*,(p>@QW(i&7A);O+.KR*,?=-w*[+.KRT/K.QW>�;=*,(pAW-OKRQW\\1*,&1T/*<;=?OKY:�:<&7QW-OK.-D;O*,QW:<M7_�kmFH*,Q|cv>1-�K.Q�>@+.K.\1QHT/*[QL;�K.Qy\1*,QH*[?]>@+�c1>#?=K.\1KY(�;=?=>1QW-D0j&1?=T/>@;OK.&1Q/KY-�:<&7T/UHA);O*E(>@QC(BAC-D*E(i;O&X*[KR;OFW*[?wI7*[?=K�0jM�;OFH*#TX>�;]:]Fp&1?w?=AH+.*#K�;o&7A);,_q}�KR\7AH?O*X�,�W_.�)VV-DFW&�{w-q;OFH*r&7UC*,?=>@;OK.&1Qi&@0l;OFW*-OUHKRQH^�K.TX>@\1*q?=*,:<&7\1QHKR;OK.&1Q�TV*[;OFH&)(f&1QV>n(HK ?y:<AW+�;Ec1:<+.A);D;=*[?=*,(fKRTX>1\1*m:<&1QL;]>@K.QHKRQW\3-OK��f(HK��d*[?=*[QL;�&16)89*E:e;]-;OFC>�;o:<&7?O?=*,-OUg&1QW(y;O&/T/&v(H*[+Y-�KRQ'>/(H>@;=>@6C>1-O*3&10u;9{q*[QL;9My&76)89*,:<;mT/&)()*,+.-,_

� � 4 � / 0 � 1 3 �� m +.KR\7QHT/*[QL;l:,>@Q�>1+.-O&o6g*m>@UHUH+.K.*,(�;=& \14wâ214ZTX>�;=:]FWKRQH\nK.Q�{�FHKY:]F#;OFW*�&76)89*,:<;T/&)()*[+gK.-�;OFH?=*[*[^�(HKRT/*[QC-DK.&1QW>1+ c76HA);q;OFH*n(H>�;]>r:<&7T/*,-�0j?=&1T�> \14 K.TX>@\1*7_uàQ/;=FHKY-�:,>1-O*1c7;OFH*o;O?]>@QW-D0j&1?O^TX>�;=KR&7Q�0j?O&7T T/&)()*,+1Ug&1K.Q7;]-|;=&o(H>@;=>�Ug&1K.QL;=-uK.-tTV&7?O*�:<&1T/UH+.*<��_uàQr>1(H()KR;OK.&1Qr;O&�;=FH*�274 ?=&@;]>�;OK.&1Q#>1QW(214 ;O?]>@QW-O+.>@;OK.&1Q|c1;OFH*,?O*�KY-�>�Ug*[?]-DUg*,:<;OK.I1*�UH?=&@89*E:e;=KR&7Q/:[&1T/Ug&1QH*,Q7;E_�kmFW*�0jAH+.+H;O?]>@QC-90j&7?OTX>�;=KR&7QV:,>@Q/6g**,-D;OK.TX>�;=*,(B0j?O&7Tx>/-D*[;�&@0lUC&7KRQL;w:<&7?O?=*,-OUC&7QW()*,QW:<*E-[c)>/-D*[;�&@0l+RK.QH*r-O*[\1T/*,Q7;w:[&1?=?O*E-DUg&1QW(H*[QW:[*,-,cL>y\@4*[+.+.KRUW-O*V;O&p214�:[KR?]:<+.*fUW+RAW-�-OKRQW\1+.*fUg&1K.QL;#:[&1?=?O*E-DUg&1QC()*[QW:[*1cd&1?#:[&1T�6WKRQW>@;OK.&1QW-3&@0m>@+.+�;OFH?=*[*V;9MvUC*E-n&@00j*,>@;OAH?=*,-,_ukmFWK.-l\7KRI7*,-uAW-�>oI7*[?=M�UC&�{q*[?O0jAH+L;O&v&1+L0j&7?�TX>@;=:]FHK.QH\W_��&1?=?O*E-DUg&1QC()*[QW:[*,-�>@?=*�FvMvUC&1;OFH*E-DK�[[*E(*[KR;OFW*[?q6H+RK.QW()+.MX&1?�;OFW?O&7AH\1Fy?=*[+Y>�;=KR&7QW>@+CTX>�;=:]FWKRQH\ ��-O*[*36C*,+R&�{ ��>@QW(�AW-D*E(/;O&/()*[;O*[?=T/KRQW*3>rUg&@;=*[QL;OKY>@+;O?]>@QC-90j&7?OTX>�;=KR&7Q|_ukmFW*m;O?]>@QW-D0j&1?=TX>�;OK.&1QfK.-�>@UHUH+.K.*,(f;O&�;=FH*w214 T/&)()*,+H0j*,>@;OAH?=*,-�;=&#UH?=&v(HAW:<*!\14 (H>�;]>0j*,>@;OAH?=*,-,_��w*,?O*n>�QH*,{ UH?=&16H+.*[T�:[&1T/*,-�AHU�;OFW>@;m()KY(BQH&@;�>@UHUg*,>1?�K.Q/\14w^ \@4 &7?q274wâ214 >@+.KR\7QHT/*[QL;,_àQZ>1QvM \14 UC*,?=-OUC*E:e;=KRI7*BIvK.*[{�&@0n>�214 &76)89*,:<;,c�-O&1T/*�&10w;OFW*�;=?=>1QW-90j&7?OT/*E(h0j*,>@;OAH?=*,-V>@UHUg*,>1?f&7Q-OAH?D0�>7:<*E-�;OFC>�;n(H&yQH&@;30�>1:[*r;OFW*f:[>1T/*[?]>X>@QW(>1?O*�&v:,:<+.AW()*E(p6LMp&1;OFH*,?3-OAH?D0�>7:<*E-�;OFC>�;n>1?O*f:<+.&7-O*[?�;=&;OFW*fIvK.*[{q*[?E_nkmFvAW-3KRQ�&1?]()*[?3;O&i>1:,:<AH?]>�;=*[+.MBUH?=&)()AW:[*V>B-D*[;n&10�;O?]>@QW-D0j&1?=T/*,(p0j*E>�;OAW?O*E-w;=&B:<&7T/UW>@?=*;O&BKRTX>1\1*#0j*E>�;OAW?O*E-[cd>XFHKY(H()*,Q'0j*,>@;OAH?=*f>1+R\7&1?=K�;=FHT!TfAW-D;36g*f>@UWUH+RK.*,(|_o�wKY(H()*,Q0j*,>@;OAH?=*�>1+R\7&1?=K�;=FHTX->@?=*�?=*[+Y>�;O*E(f;O&r\7?=>1UHFHKY:[-l?=*[QW()*,?OK.QH\r>1+R\7&1?=K�;=FHTX-�>@QW(�cLKR0�>1UHUH+.KR*E(/KRQy-O&@0 ;9{m>@?=*1c7:[>@QX6g*wUH?=&1FWKR6HKR;OK.I1*,+RM-O+R&�{#_u`�0�>1UHUH?=&1UH?=KY>�;O*qT/*,-OF/TV&)()*,+.-�>@QW(f\1?]>@UHFWK.:,-lFW>@?](){m>@?=*�KY-�>JI�>@K.+.>16H+R*7c�;OFW*[QV;OFH*w0jAH+R+W?O*,QW()*[?=K.QH\KY-wUg&7-=-DK.6H+.*1_-}o;OFH*,?O{�KY-D*7cHKR;oK.-3:<&7TVT/&7Qp;O&X*[KR;OFW*[?oK.\1QW&1?=*3;=FH*�FWK.(H(H*[Qp0j*,>@;OAH?=*#UH?=&16H+.*[T &1?oAW-D*r>1Q>@UWUH?O&J�)K.TX>�;O*�>@+.\1&7?OKR;OFWT�;OFW>@;wK.-�QW&@;w\1AC>@?]>@QL;O*,*,(/;=&X6C*r>7:[:<AW?=>@;O*1cv6HAH;oTX>JMy6C*#\7&v&v(B*[QW&1AH\7F�0j&7?I1*,?OKv�C:,>�;OK.&1Qt_kmFH*/k9U�`9�-}KU!�'&76)89*,:<;n?=*,:[&1\7QHK�;=KR&7Q�-OMv-D;O*,T5AW-D*E-nILK.*[{mâ:<+Y>1-=-3TV&)()*,+.-n&10�UC&7+RMvFH*E()?]>@+l&16)89*E:e;]->@QC(��CQW(H-r:[&1?=?O*E-DUg&1QW(H*[QW:[*,-�6g*<;9{q*[*[Qb;=?OK.UH+.*<;=-r&@0mTV&)()*,+�+.KRQW*y-D*,\1T/*[QL;=-#>1QW(�;O?=KRUW+R*[;=-r&109\14�K.Tf^>@\7*r+.KRQH*f-D*,\1T/*[QL;=-,_w%'&)()*,+t;=?OK.UH+.*<;=-3>@?=*r?]>@Q�&7*,(iKRQ�>/;O?]>@K.QHK.QH\yUHFW>7-D*f-D&X;=FW>�;3;O?=KRUW+R*[;=-w{�KR;OF�FHKR\7FUH?=&16W>16HK.+RKR;OK.*,-m&10l()*[;O*E:e;OK.&1Q'>1?O*#-O*[+.*,:e;=*,(2�W?]-9;wK.Qi;OFH*�T/>@;=:]FHK.QH\/UHFW>7-D*r>1QW(B;OFH&L-D*�{�KR;OF'+.&�{ UH?=&16H^>@6WKR+.K�;=KR*E-f>1?O*BQH&@;/:<&7QW-DKY()*,?O*E(N>�;X>@+.+ _hkt?=K.UH+R*[;=-V>@?=*�()*E-O:[?OK.6C*E(G6vMN>I7*,:e;=&1?f&@0wQHK.QH*iUW>@?]>@T/*<;=*[?]-;OFC>�;3()*E-O:[?OK.6g*#;OFH*V>@UHUg*,>1?=>1QW:<*�&10�;=FW>�;3;O?=KRUW+R*[;oKRQp;=FH*�IvK.*[{�:<+Y>1-=-�6g*[K.QH\yTX>�;]:]FH*,(|_m}�K.\1AH?=*y�,�W_�\ �-OFH&�{w-l;OFW*wUW>@?]>@T/*[;O?=Kv[E>�;OK.&1QV&@0|>#+.K.QH*o-O*[\1T/*,Q7;�;O?=KRUH+.*<;E_ m T/&v(H*[+H;=?OK.UH+.*<;�KY-�TX>@;=:]FH*E(V;O&�>1QXKRTX>@\7*;O?=K.UH+R*[;�;OFW>@;wFW>1-�-OK.TVK.+Y>@?�UW>1?=>1TV*[;O*,?=-,_�}3QC:<*#>/TX>�;=:]FiKY-�FvMLUg&@;=FH*,-OK�[[*,(|cv;OFH*#+.KRQW*m89AHQW:e;=KR&7QpUC&7KRQL;=-0j?=&1T!;OFH*�(W>�;=>X;O?=KRUH+.*<;n>@?=*#UW>@K.?O*E(i{�K�;=F';OFH*�FLMvUg&@;=FH*,-OKv[,*,(':[&1?=?O*E-DUg&1QW(HKRQH\X274 I1*,?D;=K.:[*,-m0j?=&1T!;OFW*T/&)()*[+�cW>@QC(B>1QBKR;O*,?=>@;OK.I1*�UC&7KRQL;O^ ;=&@^�UC&7KRQL;w:<&7?O?=*,-OUC&7QW()*,QW:<*[^�6W>7-D*E(X*<�v;=*[?=KR&7?q&7?OK.*[QL;]>�;OK.&1Qi>@+.\1&7?OKR;OFHT

��>7-#\1K.I1*,QhKRQZ��FW>1U);O*,?y�,2 �nK.-�AW-O*,(�;O&�(H*<;O*,?OT/K.QH*/;OFW*X;O?]>@QW-D0j&1?=TX>�;=KR&7Q|_BkmFH*/;=?=>1QW-D0j&1?=T/>@;OK.&1QbK.-;OFW*[QN>@UHUW+RK.*,(�;O&'>i{�KR?=*<0j?]>@T/*VT/&v(H*[+�&@0�;OFH*y274�&16)89*E:e;r>@QC(;=FH*/ILKY-OKR6H+.*/*,()\7*,-#>1?O*/()*<;=*[?=T/KRQH*E(;OFW?O&7AH\1F>XFWK.(H(H*[Q+.KRQW*f()*[;O*,:<;OK.&1Q>1+R\7&1?=K�;=FHTp_w}H&1?3*,>7:]FiUW?O*E()K.:<;O*E('*,()\7*1cW;OFH*V:<+.&7-O*,-D;oKRTX>1\1*r+.KRQW*-O*[\1T/*,Q7;rKY-�(H*<;O*,?OT/K.QH*,(N>1QW(hI1*,?OKv�C:,>�;OK.&1QbKY-rUg*[?O0j&1?=TV*E(b6W>1-O*,(b&1QNFW&�{�-OKRT/K.+.>1?r*,>7:]FhUH?O*E()KY:e;O*E(*,(H\1*XKY-#;O&�K�;]-�:<+.&7-O*,-D;�K.TX>@\1*y-O*[\7T/*[QL;,_p}�KR\7AH?O*��[�W_�\)�X-OFH&�{w-�;=FH*y&1Ug*[?]>�;=KR&7Qh&@0m;OFH*Bk9U�`9�-}KU!�-OMv-D;O*,Tp_

¡ � � �� ! #"$"%"

Scene Recognized Models

intensity image

3-D front view

3-D top view

}�KR\7AH?=*V�,�W_.�)VW��}3Ug*[?]>�;=KR&7QB&10u;=FH*r-DUWKRQ)^�K.T/>1\1*n?O*E:<&7\1QHKR;OK.&1Qp-DM)-D;O*,Ti_ � }�KR\7AH?O*#:[&1AH?O;O*E-DMX&10 m QW()?=*[{�7&1FHQW-O&1Q/{�KR;OFyUg*[?=T/K.-=-OKR&7QV&10�`�� o_%U�*,UH?OK.QL;O*E(V0j?O&7T � � ?y:<K.*[QL;�%'AH+R;OK.UH+.*3%'&)()*,+ U�*E:<&7\1QHKR;OK.&1QXK.Q��+.A);D;=*[?=*,(#2�â4 �):[*[QH*E-[c �w6vM m _ �o_ �7&1FHQW-O&1Q#>1QW(�%N_,�o*[6g*[?O;,c n � �pTp�£��¢q�z � � ~ |�p�� W�{p{n�p(� �p� � � � x � r ~ p{n �H� z�� u�� £ u ~ ~ p(n�� pT � q�� ~ � � � c �7AHQH*/�WV%V � _ :� �WV%V � `��

�� )�� w�� ¢�R�� ¡ �C�

� �

� %� '

� %� '� ' � %X '

X %

}�KR\7AH?=*#�[�W_�\ � �tkmFH*wUC>@?]>@T/*<;=?OK�[,>@;OK.&1QV&@0|>#+.KRQH*w;O?=KRUH+.*<;�KRQ/;=FH*ok9U�`9�-}KU!�/-OM)-9;=*[Tp_�kmFW*o�LAW>@QL;OKR;OK.*,-� % >@QW((� ' >1?O*n;=FH*#()K.-D;=>1QW:<*E-q0j?O&7T�;OFW*#TVKY()Ug&1K.QL;w&@0u+.K.QH* � � ;O&V;OFW*#TVKY()Ug&1K.QL;=-m&@0l+.KRQH*E- � % >@QW( � ' c?=*,-OUC*E:e;OK.I1*,+RM7_ m QH\1+.*,-JX % >@QW( X ' >1?O*�;OFH*y>1QH\1+.*,-o;OFW>@;r+RK.QH*X-O*[\1T/*,Q7;]- � % >1QW( � ' TX>�&7*f{�KR;OFh+.KRQW*-O*[\1T/*,Q7; � � _ m QH\7+R*E- � % >@QC( � ' >@?=*f;=FH*B>1QH\1+.*,-�6g*<;9{q*[*,QN+RK.QH*�-O*[\7T/*[QL; � � >1QW(�;OFH*i:<&1QWQH*,:<;OK.QH\+.KRQH*E-w-OFH&�{�Qy;=& � % >@QW( � ' cH?=*,-OUg*,:e;=KRI7*[+.M1_

}�KR\7AH?=*B�,�W_�\)�1� ��> �3kmFW*f*E()\1*E-3*[�v;O?]>1:e;=*,(�0j?O&7T >�?=*,>1+lKRTX>@\7*1_ �j6 ��kmFH*VTX>�;]:]FH*,(�;O?=KRUW+R*[;�&10�+.KRQW*-O*[\1T/*,Q7;]-�� ;=FHK.:�&V+.KRQH*E- ��>@QW(f;OFW*�KRQHKR;OKY>@+CUC&L-D*�*E-9;=KRTX>@;O*1_ ��:��kmFH*9�CQW>@+HTX>@;=:]FX>@QW(VUg&7-O*1_��&1AH?O;O*E-DM&@0��#>@?=K��AH+.+.K _

�� 4p%>�;]:]FHK.QH\/KRQ'k9U�`9�-}KU!�k9U�`9�-}KU!�VAW-O*,-�;OFH*KV#UW>1?=>1TV*[;O*,?=-�>7-O-O&):<KY>�;=*,(V{�K�;=F�>�;=?OK.UH+.*w&@0|+.KRQW*o-D*,\1T/*[QL;]-�;O&�K.()*,QL;OKR0jMVUg&@;=*[Q)^;OKY>@+CTX>�;=:]FW*,-�6g*<;9{q*[*,Qy>#T/&)()*[+W;O?=KRUH+.*3>1QW(X>@QXK.TX>@\7*m;O?=KRUH+.*1_�zn*,QH*[?]>�;=*o-D*,I1*,?=>1+H()K��d*[?=*[QL;�IvK.*[{w-�&@0>r-OKRQW\1+.*wIvKR*,{ :<+Y>1-=-�&@0t>r274 Ug&1+.MvFH*,()?]>@+C&16)89*E:e;EcL-OAW:]Fy>1-�;OFH*n:]FW>@K.?�&76)89*,:<;�&@0|}�K.\1AH?=*r�[�C_R�7�1_u`9()*[Q)^;OKR0jMy;=FH?=*[*nT/>@89&1?m+.KRQH*#-O*[\7TV*,QL;=-�;OFW>@;w>@UHUg*,>1?qK.Qp>@+.+�M1&1AW?qIvK.*[{w-m>@QC(B:[&1T/UHA);=*3;=FH*�VVUW>@?]>@T/*<;=*[?]--OFH&�{�Q/KRQ�}�K.\1AH?=*r�,�W_�\ � _��w&�{S-DK.T/KR+Y>@?q>@?=*m;OFH*n()KR�g*,?O*,Q7;�UW>@?]>@T/*<;=*[?�I7*,:<;O&1?]-l;=FW>�;�M7&1Ay:[&1T/UHA);=*,( ��&1T/UW>1?O*V;=FH*RViUW>@?]>@T/*<;=*[?]-n&@0q;OFH*E-D*/;=FH?O*,*/+RK.QH*y-O*[\1T/*,Q7;]-n;O&p;=FH&7-O*/&@0�>i:[&1T/UH+.*<;=*[+.M�()KR�g*,?O*,QL;-O*<;�&@0u;OFH?=*[*n+RK.QH*#-O*[\1T/*,Q7;]-[_��o&�{ {�*,+R+|(H&f;=FH*�V�UC>@?]>@T/*<;=*[?]-�()KY-=:<?=KRT/K.QW>�;=*�>1T/&1QH\�;O?=KRUH+.*,-m&10u+.KRQW*-O*[\1T/*,Q7;]- �

¡ �#\ �� ! #"$"%"

� 3A� � � 2 % �� / 0 � 1 �3 �� *�*VFW>JI7*#;=>1+v&7*,(>16C&7A);o;=FH*V>1+RK.\1QWTV*,QL;3&@0q>�214�T/*,-OF�T/&)()*[+;O&X>X274s?=>1QH\1*nKRTX>1\1*#>@QW(i>X214sUg&1+.MvFH*,(H?=>VT/&)()*[+d;=&y>�\14�K.Q7;=*[QW-OKR;9MyKRTX>1\1*1_*b*r:<&7QW-DKY()*,?�FH*[?=*;OFW*�UH?=&16H+.*[T!&@0�:<&7T/UHA);OK.QH\�;OFH*rKY()*,Q7;=K�;9Mp>@QC('UC&L-D*#&10�>V0j?O*,*<^�0j&1?=T 274 &76)89*,:<;w0j?O&7T >X-OK.QH\1+.*7\@4K.Q7;=*[QW-OKR;9MiK.TX>@\7*1_�kmFH*V-O&1+.A);=KR&7Q{�*f{�KR+.+l+R&v&$&p>@;3*,TVUW+R&�M)-n>yIvKR*,{m^�:[+.>7-O-w;9MvUC*V&@0�T/&)()*[+�c�6HA);n;OFW*?=*[UH?=*,-O*[QL;=>@;OK.&1Q/&@0|>#IvK.*[{ :<+Y>1-=-�KY-��LAHKR;O*o(HK��d*[?=*[QL;�0j?=&1T�;OFW*o-D*[;=-�&@0d;O?=KRUW+R*[;=-�&@0�+RK.QH*o-O*[\7T/*[QL;=-�;OFW>@;k9U�`9�-}KU!��AW-O*,(p>@QW(BTX>�;]:]FHKRQW\VKY-�Ug*[?O0j&1?=T/*,(i>�;m;OFH*#+.&�{q*,-D;m+.*[I7*[+�&7QB*E()\1*[^�K.TX>@\1*E-[_kmFH*�>@+.\1&7?OKR;OFHT�(HK.-=:<AW-=-O*,(BFH*[?=*3KY-m6W>7-D*E(y&1QB;OFW*n{q&1?T&/&@0��FH*[Qp>@QW(4�L;=&v:�&vTX>@QtcL{�FW&/:[?O*E>�;=*,(>�-OM)-9;=*[T5;=&i()*[;O*,?OT/K.QH*�;=FH*VUC&L-D*f&@0�274�&76)89*,:<;=-3{�K�;=Fb-OT/&v&@;OF�-DAH?O0�>1:[*,-,_�àQ;OFWK.-�-OMv-D;O*,Tpc|>�214&16H89*,:e;�KY-�T/&)()*[+.*,(V6vMf>#:[&1+.+R*E:e;=KR&7QV&10_\ �% 4 ILK.*[{w- ��:[>1+R+.*,(VT/&)()*[+C>1-OUC*E:e;=- ��*,>7:]FX:<&1QC-9;=?OAW:<;O*E(r0j?=&1T

�WI7*3K.TX>@\1*E-�;=>�&7*[QB6LMX?=&@;]>�;=KRQH\�;OFH*�IvK.*[{�Ug&1K.Q7;�AHUtcH()&�{�Q|cv+R*[0 ;o>@QW(�?OK.\1FL;m&@0u>V:<*,QL;O?]>@+dIvKR*,{�UC&7KRQL;,_àQHUHAH;�0j&1?q:<&7QW-9;=?OAC:e;OK.&1QX&10�&1QH*wT/&)()*,+g>7-DUg*,:<;�&@0|>r:,>@?�KY-�-OFH&�{�QXK.Q�}�KR\7AH?=*#�[�W_�\%\H_ukmFH*n-DK.+.FH&1AH*[;D;=*&@03;OFH*:[*[QL;O?]>@+m*E()\1*,T/>1UZKY-/*<�v;=?=>7:e;O*E(Z>1QW(P-D*,\1T/*[QL;O*E( K.QL;O&N:<AW?OI7*i-O*[\7TV*,QL;=-/{�FH&L-D*iKRQvI�>@?=KY>@QL;0j*,>@;OAH?=*,-�>1?O*#()*,?OK.I1*E(X0j&7?wKRQC()*<�)K.QH\V;O&V;OFHKY-�T/&)()*[+u>1-OUC*E:e;w()AH?=KRQW\X?O*E:<&1\7QHKR;OK.&1Q|_�L;=*[?=*[&@^�+.Kv&7*w:<&1T/UHAH;=>�;=KR&7QW-�>1?O*�Ug*[?O0j&1?=T/*,(/;=&�:<&7T/UHA);O*3UC&7KRQL;]- ��c M7c [ �C&1Qy;OFH*n214 ?=K.T�0j&7?�*E>1:]F

\@4 -OK.+RFH&7AH*<;O;O*mUg&1K.Q7; A|c I �HKRQf;OFH*w:[*[QL;O?]>@+vK.TX>@\1*7_ukmFH*�AWUV>1QW(f(H&�{�QfK.TX>@\1*E-l>@?=*�AW-O*,(�;O&#:[&1T/UHA);=*;OFW*�:<AH?=I�>�;=AH?O*X&10�;=FH*y&76)89*,:<;r?OK.T K.Qh;OFW* � ()K.?=*,:e;=KR&7QN>@QW(b;=FH*X+R*[0 ;V>1QW(b?OK.\1FL;rK.T/>1\1*E-r>@?=*/AW-D*E(;O&h:<&7T/UHA);O*i:<AH?=I�>�;=AH?O*BKRQ ;OFH* � ()K.?O*E:e;OK.&1Qt_ �vK.T/KR+Y>@?=+.M1c�-D;O*,?O*,&@^�+RK�&1*�:[&1T/UHA);]>�;=KR&7QW-f>1?O*BAW-O*,(h;=&:<&7T/UHA);O*w;OFH*o274 +.&):[>�;=KR&7QW-�&10�:[?O*E>1-O*�>@QW(/TX>@?T&�Ug&1K.QL;=-�K.Q/;OFW*3:<*,QL;O?]>@+H*E()\1*,T/>1U|_ukmFvAW-,c7;OFH* \ �% 4T/&)()*[+�>1-OUg*,:e;]-�:<&1QC-DKY-9;n&@0�;=FH*X214�?=KRTpc|:<?=*,>7-D*f>@QW(�T/>1?�&pUg&1K.QL;=-�:<&7?O?=*,-OUC&7QW()K.QH\y;=&�;=FH*/:<*[QL;=?=>1+*,(H\1*iKRTX>@\7*pUH+RAC-V;OFH*i�Z>1QW(GM :[AH?=IJ>@;OAH?=*p>�;X*,>7:]F &@03;OFH*E-D*pUg&1K.QL;=-,_ �3-DK.QH\�;OFHKY-XK.Q)0j&1?=TX>�;OK.&1Qtc>�T/>@;OFH*,TX>�;OKY:[>1+m0j&1?=T�AH+Y>�:,>@QZ;OFH*,QZUW?O&)()AW:[*i>1QZ*E()\1*iTX>@UZ0j&1?X>@QvMN&1;OFH*,?VIvK.*[{�Ug&1K.QL;/K.QZ;OFW>@;IvKR*,{ :[+.>7-O-,cH\7KRI7*[QB;OFH*rIvK.*[{ UW>@?]>@T/*[;O*[?]-,_ m ILK.*[{s:<+Y>1-=-�KY-w()*E-O:[?OK.6C*E(i6LM��;=FH*r-D*[;o&@0�214 UC&7KRQL;=->@QC(�:<AW?OI�>�;=AH?=*,-n()*,-=:<?=KR6g*,(�>@6g&�I1*V>@QW( \ �3>B-O*<;�&@0�K.QvI�>@?=K.>1Q7;30j*,>@;OAH?=*,-3;O&i6g*fAW-O*,(�0j&1?nK.QW()*<�)K.QH\W_kmFH*/214�UC&7KRQL;]-3>1?O*V()*[?=KRI7*,(p0j?=&1T -D;O*,?O*,&@^�+RK�&1*r:[&1?=?O*E-DUg&1QW(H*[QW:[*,-w6g*<;9{q*[*,Q';OFW*V:[*[QL;O?]>@+l>@QW(�>1(J8D>@^:<*,QL;w*,()\7*[TX>@UW-�>7-�()*,-=:<?=K.6C*E(BK.Q��FW>1U);O*,?#�,2H_�kmFW*#KRQvI�>@?=K.>1QL;q0j*E>�;=AH?O*E-w>@?=*#()*[?=K.I1*,(�0j?=&1T�;=FH* \@4*,(H\1*[TX>1UB&10t;OFW*r:<*[QL;=?=>1+�KRTX>@\7*#>1-�()*E-O:[?OK.6C*E(�K.Q��FW>@UH;O*[?#� � _m Q#K.TX>@\7*l;O&w6g*�>@QC>@+.M¢[,*,(nKY-|UH?=&):<*,-=-O*,(3;O&wUW?O&)()AW:[*�K�;]-|*E()\1*�TX>1Ur>@QW(�>w-O*<;t&10H:<AH?=I1*�-O*[\7TV*,QL;=-,_kmFH*�:[AH?=I1*#-D*,\1T/*[QL;]-w>@?=*�AW-D*E(i;O&XK.QW()*[�B;=FH*�(H>@;=>@6C>1-O*n&10�TV&)()*,+|IvKR*,{w-m;O&�UH?O&)()AC:<*#&16H89*,:e;O^�IvK.*[{FvMvUC&1;OFH*E-D*E-[_'kmFH*yTX>@;=:]FHK.QH\�-=:]FH*[T/*/;=*,-D;=-fFLMvUg&@;=FH*,-O*,-#\7*[QH*,?=>@;O*E(�0j?=&1T ;OFW*�K.QW()*<�)K.QH\-=:]FH*[T/*%'*,>7:]F�FvMvUC&1;OFH*E-DKY-mK.QW:<+.AW()*E-m6C&1;OFi&16)89*E:e;�K.(H*[QL;OKR;9M�>@QC(B>1UHUH?=&J�vK.TX>�;=*3Ug&7-O*1_ ��*[?=Kv�C:[>@;OK.&1QiK.-m:[>1?O?=K.*,(&1AH;o6vM2�W;D;OK.QH\�;OFH*7\ �% 4�>1-OUg*,:e;3&@0�*,>7:]F':[>@QC()K.(W>�;O*�TV&)()*,+t;=&X;OFW*�&16C-D*,?OI7*,(i*,()\7*[TX>@Ut_�àQHK�;=K.>1+R+.M1c;OFW*qUg&7-O*q&@0H;=FH*�&76)89*,:<;�KY-�-O*<;�;O&3;OFH*mUg&7-O*�;=FW>�;l{�&7AH+Y(rFW>JI7*�UH?=&)()AW:<*E(#;=FH*�:<*[QL;=?=>1+L>7-DUg*,:<;u;=FW>�;�FW>7-6g*[*[QXFvMvUg&@;OFW*,-OKv[,*,(f;O&#TX>�;]:]F|_lkmFH*�UH?=&@89*,:<;O*E(f*E()\1*�K.TX>@\7*q&10d;OFW>@;�TV&)()*,+C>7-DUg*,:<;�K.-�:[&1T/UW>1?O*E(r;=&;OFW*#&16W-O*[?=I1*E(y*,(H\1*�TX>@U|_�àQiT/&7-D;o:[>7-D*E-[cv;=FH*[My{�K.+.+|QH&@;o>1+RK.\1Qi{q*[+.+�^�*[QH&7AH\1Ft_lkmFvAW-�;OFH*#TX>�;]:]FHK.QH\{�K.+R+HUW?O&):<*,*,(V6vM�?=*{�WQWKRQH\�Ug&7-O*�UW>@?]>@T/*[;O*[?]-��hKRQ/&1?]()*,?l;O&r()K.T/KRQHKY-OF/;OFH*!\14 ()KY-9;]>@QW:[*�6C*[;9{�*,*[QV;OFW*UH?=&@89*E:e;O*E(T/&)()*[+�*,()\7*[TX>@Ub>@QW(�;OFH*X&76W-O*[?=I1*,(*,()\7*[TX>@U|_/}�KR\7AH?=*B�,�W_�\@2BKR+.+RAC-9;=?=>@;O*,-3;=FH*XTX>�;=:]FH^K.QH\�-D;O*[Ut_kmFH*y*,(H\1*[TX>1Uh(H*[?=KRI7*,(b0j?=&1T ;OFH*yK.QHUHAH;fK.T/>1\1*XKY-�-OFH&�{�QNK.Q ��>��<c�>@QW(N>'T/&)()*,+�Ug&7-O*FvMvUC&1;OFH*E-DK�[[*E(�0j?=&1Tx;OFH*#K.QW()*[�)KRQH\y-D;O*,UpK.-w-OFH&�{�QpK.Q ��6 �e_O�v*[I7*[?]>@+�KR;O*,?=>@;OK.&1QW-m&10lT/&)()*,+|6C&7AHQW(H>1?OM\1*,QH*[?]>�;=KR&7QB>1?O*#-OFH&�{�QBK.Q ��: �<cC>1QW(y;=FH* �W?]-9;w>7:[:<*,U);=>16H+.*nTX>@;=:]FpK.-�-OFH&�{�QiKRQ�� ( �e_

]_^-`�^-`�� dg��i ��-�� f�l �� j �!��l dgj9k-fHlahm -fK.QG;9{q&@â()KRT/*,QW-DK.&1QC>@+�TX>@;=:]FHK.QH\Wc�?=*[+Y>�;=KR&7QW>@+�T/&v(H*[+Y-f:,>@QG6g*BAC-D*E(NKRQP214!&16)89*E:e;V?O*E:<&1\7QHKR;OK.&1Q;O&�TV&�I7*�>J{m>JMX0j?O&7Tx;=FH*�\7*[&7TV*[;O?=K.:#>1QW(i;O&�{m>@?](B;OFH*V-DMvTf6C&7+RKY:@_ m +R\7&1?=K�;=FHT!� ¡ -DAWTVTX>1?OK�[[*E-�;OFW*

�� )�� w�� ¢�R�� ¡ �L2

}�KR\7AH?=*V�,�W_�\%\H�l}�K.I1*�K.QHUHA);oK.TX>@\7*,-mAW-O*,(�0j&1?o:[&1QW-D;O?=AW:<;OK.QH\/&1QH*�T/&)()*[+t>7-DUg*,:<;w&@0l>X:[>@?E_��&1AH?O;O*E-DM&@0 �7KRQH+.&1QW\X��FH*,Q|_

6W>7-DKY:V?O*,+.>@;OK.&1QW>1+l(HK.-D;=>1QW:<*XTX>�;]:]FHK.QH\i;O*,:]FWQHK.�LAH*V;=FW>�;r{m>1-#()*E-O:[?OK.6g*,(�KRQ ��FW>1U);O*,?y�1�7ct-DK.T/UH+.K �W*E(;O&/-OKRQH\7+R*3?O*,+.>@;OK.&1QW-,_lkmFH*3*[�H>1:e;qT/&v(H*[+Y-q>1QW(yT/*[;OFH&)(H-qAW-O*,(B()*[Ug*[QW(�&1QB{�FH*<;=FH*[?�;OFH*nK.T/>1\1*�(H>�;]>KY-�214�&7?!\@4f_

4�� 0 �@�� 0 �� 0 � kmFH?O*,*<â()K.TV*,QW-OKR&7QW>@+g?O*,+.>@;OK.&1QW>1+CT/&)()*,+.-�>1?O*n:<&1T/Ug&7-O*,(�&@0�274 UH?OK.T/K�^;OK.I1*E-u>1QW(�274S-DUW>@;OKY>@+L?O*,+.>@;OK.&1QW-OFHK.UW-,_u��?=K.TVKR;OK.I1*E-|TX>JM�6C*mI7&1+.AHT/*,-,cJ-OAH?O0�>1:[*�UW>@;=:]FH*E-[cJ&1?�+.KRQH*�~�:[AH?OI7*0j*,>@;OAH?=*,-fK.QZ214 -OUW>1:[*1_Nzn*[QH*,?=>1+RK�[[*E(G:<Mv+.KRQW(H*[?]-�>@?=*B:[&1T/T/&1QH+.MhAW-O*,(G>7-�I7&1+.AHT/*<;O?=KY:yUH?=KRT/KR;OK.I1*E->@+.&1QW\n{�KR;OFy-O&1T/*9&vK.QW(/&@0�214 :[&1QHQW*,:e;=KR&7Q/?O*,+.>@;OK.&1QW-OFHK.U|_�� p � ��z�� nOq$p � x�p ~ n�� z cL>1?O*�I7&1+.AHT/*<;O^?=K.:fUH?=KRT/KR;OK.I1*,-nFvMvUC&1;OFH*E-DK�[[*E(;=&B6g*/AW-O*,(�KRQbFvAHTX>@QbILKY-OKR&7Q|c�FW>JI1*V>@+Y-D&i6g*[*[QbAW-O*,(�KRQh214�&76)89*,:<;?=*,:<&7\1QHKR;OK.&1Qt_�àQW()AC-9;=?OKY>@+u&16)89*E:e;=-wT/>JMB6C*f?O*,UH?=*,-O*[QL;O*E(�6vMB;OFH*,KR?3UH+.>1QW>@?w>1QW(':<Mv+.KRQC()?OKY:[>1+t-OAH?D0�>7:<*E->@QC(i;OFH*�-OAH?O0�>1:[*�>1(J8D>7:<*,QW:<MB?O*,+.>@;OK.&1QW-OFHK.U|_�kmFH?O*,*<â()K.TV*,QW-OKR&7QW>@+�+.KRQW*f>@QC(':<AH?=I1*r-O*[\7TV*,QL;=-w:,>@Q'6g*AW-O*,(h{�KR;OF (HK��d*[?=*[QL;7&vK.QW(H-�&@0o-OUW>�;=K.>1+�?O*,+.>@;OK.&1QW-OFHK.UW-,c�-OAW:]F >7-r:<&7QHQH*,:<;OK.&1QW-,clUW>@?]>@+.+.*[+�UW>1KR?]-,c�>1QW(:<&7+R+.K.QH*,>1?qUC>@K.?=-,_kmFH* z ~ �� wz�� svu ~ p{z�� uw��£ � s � � z T/&)()*,+.-m{q*[?=*#()*,-OKR\7QH*,(�;O&y(H*,-=:<?=KR6g*�I1*[?=MX?=&1AH\7FBT/&)()*[+Y-m&@0�214&16H89*,:e;]-m>@QW(B>@?=*3K.QL;O*[QC()*,(�0j&1?�;OFH*#()*E-O:[?OK.U);=KR&7QB>@QC(y?=*,:<&7\1QHKR;OK.&1Q�&@0�:[&1T/UH+.*<�yTX>@QH^�TX>1(H*o&16H89*,:e;]-[c{�FHKY:]FX>@?=*�TX>1(H*�AHU/&@0CTX>1QLM�UW>@?O;=-,_�kmFW*qUC>@?O;=-�:[>1Q/FW>JI1* � >�;�&7?�:<AH?=I1*E(f-OAH?O0�>1:<*E-[c7>@QW(�;OFH*,M�*[�vKY-D;K.Q>f+Y>@?=\1*�I�>@?=K.*<;9M1_�àQW-9;=*,>7(p&@0�;O?=MLK.QH\V;O&B()*,-=:<?=KR6g*#*,>7:]FBUC>@?O;wUH?O*E:<KY-D*,+RM7cW>1-mK.Qp;OFW*r-DAH?O0�>1:[*��v*,()\7*��I1*,?D;=*<�iTV&)()*,+.-,cC0j&1?o?=&1AW\1FpTX>�;=:]FWKRQH\�*,>1:]F'UC>@?O;o:[>@Q'6g*f:[+.>7-O-OKv�W*,('>7-o> z ~ �� cd> � svu ~ p cC&7?3> � s ��<_

�L;=K.:�&)-m>@?=*w+.&1QH\Cc7;=FHK.Q�UW>1?D;]-�;=FW>�;mFW>JI1*3&1QH+.M/&1QH*�-OKR\7QHK �g:[>@QL;m()KRT/*,QW-DK.&1Qt_l��+.>@;O*E-�>1?O* � >�;=K.-OF|cv{�K.(H*

¡ �7� �� ! #"$"%"

�.� �� B�� 1 � �

� � � 3A� � 0 ��

�� 1 � � � � � � '� � �� 0��

}�KR\7AH?=*B�,�W_�\@2H�w%�>�;=:]FWKRQH\i*,(H\1*[TX>1UW-nAW-DK.QH\b�1��\y-=:[>1+R* � ' ��> �o&76W-O*[?=I1*,(p*E()\1*,TX>@U�' ��6 �o;OFH*/T/&)()*[+*,(H\1*[TX>1U�' ��:��u*[I1&7+RAH;OK.&1Q�&10C:<&7QvI1*[?=\1*,QW:<*�KRQ�;OFH*�>1+RK.\1QHT/*,Q7;�>1+R\7&1?=K�;=FHT4'��( �H�H;O;O*E(�*E()\1*,T/>1Uf-OFH&�{�Q-OAHUC*,?OK.T/UC&L-D*E(�&7Qi;OFH*#&7?OK.\1K.QW>@+dK.TX>@\1*7_�� H>1TVUW+R*#:<&7AH?O;O*,-OMX&@0 �7KRQH+.&1QW\y��FW*[Q|_ �

�� )�� w�� ¢�R�� ¡ � ¡

�� àQy*E>1:]Fy:[>7-D*o6C*,+R&�{S*<�)UH+Y>@K.QXFH&�{STX>@QvMV&16)89*E:e;�T/&)()*,+.-q>@QW(/FW&�{PTX>1QLMVT/&)()*[+d>1-OUC*E:e;]-�{q&1AH+Y(X6g*QH*,*,()*E(i0j&1?�;=FH*�>@UWUH+RKY:[>@;OK.&1Q|_ m +Y-O&WcH*[�vUW+.>1KRQ'{�FW>@;3>1:,:<AH?]>1:[My&@0lUg&7-O*rT/KR\7F7;w6g*rQH*,*,()*E(�_ ��> �màQ'>:[>1?O{m>1-OF|cC;OFH*/>@AH;O&1TX>@;OKY:rTX>1:]FHK.QH*,?OMpQH*,*,(H-o;O&i?O*E-D*[;3KR;=-O*[+R0q>7:[:<&7?=(HKRQH\y;O&y;=FH*VTV&)()*,+l&@0�:,>@?3;OFW>@;FW>7-�*,Q7;=*[?=*,(�_ �j6 ��àQi>rUW>1?�&vK.QH\r\7>1?=>1\1*7c1>rT/&1QWK�;=&1?=KRQH\f>@QW(XK.QvI1*,Q7;=&1?=Mf-OM)-9;=*[T�QH*[*E(H-�;O&f?O*E:<&1\7QHK�[[**,>7:]Ff:,>@?�T/&)()*[+v;=FW>�;�*[QL;=*[?]-�>@QW(f*<�)KR;=-�>@QC(�?=*,:[&1?](#;OFW*�;=KRT/*�&10W;OFW*�*[I1*,QL;,_ ��: � m :[&1T/UHA);=*[?�IvK.-OK.&1Q-OMv-D;O*,TxQH*,*,(H-q;=&y-O:,>@Qp>@Qp>@A);=&1T/&16WKR+.*#\1?]>JI1*,M7>@?](V;O&/?=*,:[&1?](�FH&�{�TX>@QvMy{�?=*,:�&)-m>@?=*nUW?O*E-D*,Q7;w>1QW({�FW>@;-&LK.QW(�;OFH*,MB>1?O*7_

�� %>%&1*�>f:[AH?OI�>@;OAH?=*3T/&)()*,+d>7-DUg*,:<;�&@0�-O&1T/*n&16)89*E:e;�>@QW(B-DFW&�{ ;OFW>@;�K�;w:[>1Q�\7*[QH*,?=>@;O*�-DK.+RFW&1AH*[;D;O*E-q&@0;OFC>�;�&16)89*E:e;mAHQW()*,?w-DTX>1+R+d?=&@;=>@;OK.&1QW-,_l}H&1?m*[�)>1T/UH+R*7cH:<&7QW-DKY()*,?q>�;O&7?OAW-q&10uTX>�89&7?�&7A);=-OK.(H*�(HK.>1TV*[;O*,?� � >@QW(�T/KRQH&7?�()K.>1T/*<;O*,?m&@0��7_lkmFW*nT/&)()*,+d>7-DUg*,:<;qKY-m:<*,Q7;=*[?=*,(B>�;q;OFH*�IvKR*,{ Ug*[?=UC*,QW()KY:<AH+Y>@?q;O&f;OFW*:<K.?]:<+.*n&10u;=FH*#TX>�89&7?m(HK.>1TV*[;O*,?,_�43*{�WQW*�>/-D*[;w&@0�274�Ug&1K.Q7;]-w>@+.&1QW\�;=FH*#T/&v(H*[+t-OKR+.FH&7AH*<;O;O*�;O&7\1*[;OFH*,?{�KR;OF/;OFW*[K.? � >1QW( � :[AH?OI�>@;OAH?=*,-,_�kmFW*[Qy-OFH&�{ FH&�{Z;OFWK.-�-DK.+RFW&1AH*[;D;O*3:]FW>@QH\7*,-�AWQW()*[?�-DTX>@+.+H?=&@;]>�;OK.&1QC-6vM�:<?=*,>@;OK.QH\X-DMvQL;OFW*<;OKY:nKRTX>1\1*,-,_

43*<;O*,?OT/K.QH*#KR0u;9{q&/?O*,+.>@;OK.&1QW>1+d(H*,-=:<?=KRU);=KR&7QW-�>@?=*�-DK.T/KR+Y>@?�*,QH&1AH\7F�;=&XTX>�;=:]Ft_��K.-�>X-O*<;�&@0lT/&)()*[+|UC>@?O;=-,_�SKY-w>/-D*[;m&10�Ug&7-=-OKR6H+.*�+.>16C*,+.-�0j&1?m;OFW*#UW>@?O;=-,_�� K.-o>f?=*[+Y>�;=KR&7QB&�I7*[?q;OFW*#UW>@?O;=-,_��K.-w>V?=*[+Y>�;=KR&7QB&�I7*[?�;OFH*#+Y>@6g*[+Y-[_}�KRQC(i>/TX>1UHUHK.QH\��p0j?=&1T � ;O& 7Z;OFC>�;wT/KRQWKRT/K�[[*,-�;OFH*#*,?O?=&1?m\1K.I1*,QB6vM�� T�� 8(ZT ; �D �4T ;�� _ � ( T �tAW-OKRQH\b>@QNK.QL;O*[?=UH?=*<;]>�;OK.&1Qh;=?O*,*1c�()KY-O:[?O*[;O*y&7?�UH?=&16C>@6HK.+RKY-D;OKY:X?O*,+.>@�H>�;OK.&1Qtcu&7?&@;=FH*[?�T/*[;OFH&)(H-w(H*,-=:<?=KR6g*,(BKRQ��FW>1U);O*,?#�1�7_

/#0�1 � �� 2 3 � !mkmFH*#�q>7-DKY: U�*[+Y>�;=KR&7QW>@+|43KY-9;]>@QW:[*�%�>�;=:]FWKRQH\Xku*,:]FHQWK.�LAH*

¡ �¢X �� ! #"$"%"

Plates

Sticks

Blobs

}uK.\1AW?O*/�[�C_ \@�W��v*[I7*[?]>@+d*<�H>1TVUW+R*E-m*,>1:]Fi&@0�-D;OKY:�&v-,c)UH+Y>�;=*,-,cH>@QW(B6H+.&16W-,_

UW>1?D;]-�{�KR;OFX;9{q&rQH*E>@?=+RM � >�;m-DAH?O0�>1:[*,-�:[&1QHQW*,:e;=*,(X6vM/>�;OFWKRQB*,()\7*w6C*[;9{�*,*[Q/;=FH*[Tp_��+Y>�;=*,-�FC>JI1*�;9{q&-OKR\7QHK �g:[>@QL;�()K.TV*,QW-OKR&7QW-[_��q+.&16W-m>1?O*nUW>@?O;=-�;=FW>�;wFW>JI7*n>1+R+g;=FH?O*,*#-DK.\1QHKv�C:,>@QL;m(HKRT/*[QC-DK.&1QW-,_ m +.+d;OFW?O*,*&vKRQC(H-�&@0qUW>@?O;=-�>@?=*VQH*,>1? �):<&1QvI7*<��cg-O&'>B-D;OKY:�&�:,>@QHQH&1;n6g*[QC(�I7*[?=M'T�AW:]Ftcd;OFH*y-OAH?O0�>1:<*E-n&@0q>BUH+Y>�;=*:[>1QHQH&1;�0j&1+Y(XI1*,?OMfT�AW:]FtcL>1QW(y>#6H+.&16B:[>@QX6g*o6WAHT/ULM7c76WA);q:,>@QHQH&1;�FW>JI7*�+.>1?O\7*w:<&7QW:[>JIvKR;OK.*,-,_�}�K.\1AH?=*�[�C_ \@�V-OFH&�{w-m-O*[I1*,?=>1+d*<�H>@T/UH+.*,-m&10l-D;OKY:�&)-[c)UH+Y>�;=*,-,cH>@QW(B6H+.&16W-,_

m -D;OKY:�&v- �LUW+.>@;O*,- �v>1QW(¢�v6H+R&76W-VT/&v(H*[+3(H*,-=:<?=KR6g*,-XFW&�{�;OFW*�-9;=K.:�&)-,cmUH+.>@;O*E-[c�>@QC(S6H+R&76W-y>1?O*pUHA);;O&7\1*[;OFH*,?l;O&�0j&1?=T�>1Q/&16)89*E:e;,_lkmFH*E-D*w()*E-O:[?OK.U);=KR&7QW-�>@?=*�>@+Y-D&�?=&1AH\7F�'@;=FH*[MV:[>1QHQH&@;�-OUg*,:<KR0jMr;=FH*wUHFvM)-D^KY:[>@+�Ug&1K.QL;=-�{�FW*[?=*3;9{q&VUW>@?O;=-�89&7KRQ|_ m -D;OKY:�&yFW>7-q;9{�&/+.&1\7K.:,>@+d*[QW(iUg&1K.QL;=-,cH>f+.&1\7K.:,>@+�-O*<;w&@0�KRQL;=*[?=KR&7?Ug&1K.Q7;]-[cH>1QW(p>V+R&7\1KY:[>@+�:[*[QL;O*,?q&10�TX>7-O-�;OFC>�;o:[>1QB6g*r-OUC*E:<Kv�W*,(i>1-�:[&1QHQH*E:e;=KR&7QBUg&1K.QL;=-,_ m UW+.>@;O*#FW>7->#-O*<;�&10d*E()\1*�Ug&1K.QL;=-,cL>#-O*<;�&@0�-DAH?O0�>1:[*�UC&7KRQL;]-[cv>@QW(/>r:[*[QL;O*,?�&@0dTX>1-=-[_ m 6H+.&16XFC>1-�>#-O*<;�&10|-DAH?O0�>1:[*Ug&1K.Q7;]-u>1QW(#>o:[*[QL;O*,?t&10HT/>7-O-,_}3QW+RM3;OFHKY-uTVK.QHK.TX>@+LKRQ)0j&7?OTX>@;OK.&1Q�:,>@Q#6g*�AW-O*,(#K.Q#;=FH*�&76)89*,:<;uT/&)()*[+Y-[_kmFH*�?=*[+Y>�;=KR&7QW>@+1TV&)()*,+10j&7?u>w-D;OKY:�&)- �vUH+Y>�;O*E- �)>@QW(#�L6H+.&16W-gT/&)()*[+LKY-t>�\7&L&)(�*[�)>1T/UH+R*�&@0H>m0�>@K.?=+RM�()*<^;=>1KR+.*,(X-OMvT�6g&1+.K.:m&76)89*,:<;�T/&v(H*[+H;=FW>�;�FW>1-�6g*[*,QXAW-O*,(X-OAW:[:[*,-=-90jAH+.+.M�K.Qy-DMvT�6g&1+.KY:m&16)89*E:e;�?=*,:<&7\1QHKR;OK.&1Qt_`�;w:<&7QW-DKY-D;=-�&@0��WI7*3?=*[+Y>�;=KR&7QW-,_�kmFH*�AHQC>@?=My�)`9%�ZY��Z� m U�k-�y?O*,+.>@;OK.&1QyKY-�>f+RKY-9;m&@0t;OFH*�UW>1?D;]-�&10t;OFW*&16H89*,:e;E_ ��>7:]F�UW>1?D;�FW>7-�-D*,I1*[?]>@+�()*E-O:[?OK.U);=KRI7*�>@;D;=?OK.6HA);=*,-mK.QW:<+.AW()K.QH\XKR;=-q;9MvUC* � -9;=K.:�&dcHUW+.>@;O*�&1?�6H+.&16 �>@QC(pT/>JMi>@+Y-D&/K.QW:<+.AW()*�QLAWTV*,?OKY:#K.Q)0j&1?=TX>�;=KR&7QiUg*[?O;=>1KRQWKRQH\/;=&X;OFW*�-DK�[[*r>1QW(C~�&1?w-OFW>@Ug*r&@0�;OFW*rUW>@?O;,_kmFH*w�9} � � �q�qk-�W~%� �o�� }KUlk-�n?O*,+.>@;OK.&1Q�:[&1QL;=>1KRQC-u-O&1T/*q&@0);OFW*qT/&L-9;lKRT/Ug&1?O;=>1Q7;�KRQH0j&1?=T/>@;OK.&1Qr&7Q;OFW*3-D;O?=AW:e;=AH?O*o&@0�;OFW*o&16H89*,:e;E_l`�;q:<&7QW-OK.-D;=-�&@0�X�^�;OAWUH+R*E-�&10�;OFH*o0j&1?=T � � � � % �� LT��J� �� <_kmFH*#:<&7T/UC&7QH*[QL;=- � � >@QC( � % >@?=*n-OK.TVUW+R*#UW>1?D;]-[c�� 3��O}KU�k-��KY-q;O?=AH*�K�0 � � -OAHUHUg&1?O;=- � % >@QW(�0�>@+Y-O*&@;=FH*[?={�KY-D*7cH>@QW(i�K}-* (H*,-=:<?=KR6g*,-q;=FH*r:<&7QHQH*,:<;OK.&1QB;9MvUC*#&10 � � >@QW( � % _kmFH*�&@;=FH*[?m0j&7AH?m?O*,+.>@;OK.&1QW-q*[�vUW?O*E-O-�:[&1QW-D;O?]>@K.QL;=-,_�kmFH*#k9U�`9� Y�� 9} � �)k9U m ` � k�?=*[+Y>�;OK.&1QiFW>7-�w�L;OAHUW+R*E-w&@0�;=FH*r0j&7?OT � � � � % �� ' ��$� � �m{�FW*[?=*f-OKRT/UH+.*�UW>1?D; � % ;O&7AW:]FH*,-o6C&1;OF � � >@QW( � ' cg>1QW(

� m % �'KY-�;O?=AH*�KR0 � � >@QC( � ' ;O&1AC:]F � % &1Qn;OFH*q-O>1T/*�*[QW(��&1?u-OAH?O0�>1:[*��g&@0 � % >1QW(n0�>@+Y-D*�&@;OFW*[?={�K.-O*1_tkmFW*

�� )�� w�� ¢�R�� ¡ �)¢

6

5

1

4

3

2

1 Stick 2 Stick 3 Stick 4 Stick 5 Plate 6 Plate

PART# TYPE SP1 SP2 SUPPORTS HOW

SP1 SP2 SP1 SP2

1 2 1 5 1 3 2 5 1 4 3 5 2 3 4 5 2 4 5 6 3 4

CONNECTS-SUPPORTSSIMPLE-PARTS

PARALLEL PERPENDICULAR

1 5 True end-edge2 5 True end-edge3 5 True end-edge4 5 True end-edge

TRIPLES

SP1 SP2 SP3 SAME

1 5 2 True

5 6 True edge-edge 2 5 3 True

1 5 3 True1 5 4 True1 5 6 False

2 5 4 True2 5 6 False3 5 4 True3 5 6 False4 5 6 False

}�KR\7AH?=*��[�C_ \ ¡ �mkmFH*r0jAW+R+l?=*[+Y>�;OK.&1QC>@+u-D;O?=AW:<;OAH?=*�&10�;OFH*/-9;=K.:�&)- �LUH+Y>�;=*,- �v>1QW(¢�L6W+R&76W-mT/&v(H*[+�&@0�>�:]FC>@K.?&16H89*,:e;E_

¡ � � �� ! #"$"%"

� m U m Y�Y��ZYS?=*[+Y>�;=KR&7Qb>1QW(�;OFH*y� �ZUw� � � 43Ò� �!Y m U�?=*[+Y>�;OK.&1QbFW>JI7*VUC>@K.?=-�&10�;=FH*/0j&1?=T � � � � % �{�FH*,?O*i-DK.T/UH+R*BUW>@?O;=- � � >1QW( � % >1?O*�UW>@?]>@+.+R*,+ ��&1?VUC*,?OUg*[QW(HK.:[AH+.>1? �rKRQ ;OFH*BT/&v(H*[+�_b}�K.\1AH?=*��,�W_�\ ¡K.+R+.AW-D;O?]>�;O*E-n;OFH*B-9;=K.:�&)- �LUH+Y>�;=*,- �v>@QC(¢�L6H+.&16C-wT/&)()*[+�&@0q>pUW?O&1;O&@;9MvUg*X:]FW>@K.?#&16)89*E:e;E_ m +.+�:]FW>1KR?]-�{�K�;=F-OKRT/K.+.>1?�?O*,+.>@;OK.&1QW-m-OFH&1AH+Y(iTX>�;=:]FB;OFWK.-�T/&)()*,+ cH?=*[\L>@?]()+.*,-=-�&10t;OFW*#*<�H>1:<;�-OFW>1UC*E-�&@0u;OFH*#UW>1?D;]-[_�� L;OKY:�&)- �vUH+Y>�;O*E- �)>@QW(#�L6H+.&16W-�T/&)()*[+Y-43?=>J{�>UWK.:<;OAH?=*�&10o>-DK.T/UH+.*�Ug&1+.MLFW*,()?]>@+m()*,-�&b&16)89*E:e;V>1QW(G:[&1QW-D;O?=AW:e;V>'0jAH+.+m?O*,+.>@;OK.&1QW>1+�-9;=K.:�&)- �UH+Y>�;=*,- �v>@QC(¢�L6H+.&16C-�T/&)()*,+d0j&1?m;OFW*#&16)89*E:e;,_

� � � � �� 0 �� 0 �@� �� 0 �� 0 � * FH*[QB;OFH*#(H>@;=>V:<&7QW-DKY-D;=-q&@0�\14sKRTX>1\1*,-,cvIvKR*,{�:<+Y>1-=-�TV&)(v^*[+Y-�:[>1QB6g*�AW-O*,(BKRQW-D;O*E>1(B&@0u0jAH+R+u214s&16H89*,:e;�T/&)()*[+Y-,_�kt?]>@K.QHK.QH\V(W>�;=>V()*,?OK.I1*E(�*,K�;=FH*[?w-OMvQ7;=FH*<;=K.:,>@+.+RM&1?o0j?O&7T >�-D*[;o&@0�?=*,>@+uKRTX>1\1*,-w&@0�;OFW*�&16H89*,:e;n:[>@Q'6g*�AC-D*E(pKRQ';=FH*f:[&1QW-D;O?=AW:<;OK.&1Qp&@0�;=FH*,-O*rT/&)()*[+Y-[_43*[Ug*[QW()K.QH\y&7Qi;OFH*�:[+.>7-O-m&10�&76)89*,:<;=-,cW>X-O*<;o&10�AW-O*<0jAW+�\@4�0j*,>�;=AH?=*,-w>1?O*�*<�v;=?=>7:e;O*E(B0j?O&7TxK.T/>1\1*E-m&@0;OFW*�&16H89*,:e;E_kmFH*y0j*E>�;=AH?O*E-r*[�L;=?=>7:e;=*,(b0j?=&1T *,>1:]Fb;=?=>1KRQHK.QH\K.TX>@\7*�>@?=*XAW-O*,(h;=&UH?=&v(HAW:<*�>?O*,+.>@^;OK.&1QC>@+|()*E-O:[?OK.U);OK.&1Qp&10u;=FW>�;wIvK.*[{ &10u;=FH*#&16H89*,:e;E_�kmFH*#?=*[+Y>�;=KR&7QW>@+�()*E-O:[?OK.U);OK.&1QC-�>@?=*3;=FH*[Q':[+RAW-D;O*,?O*E(;O&0j&1?=T ;=FH*�IvK.*[{mâ:<+Y>1-=-D*E-�&@0m;OFH*B&16)89*E:e;E_ ��>1:]FhIvKR*,{�:<+Y>1-=-#K.-�?O*,UH?=*,-O*[QL;O*E(�6vMh>:<&7T�6HK.QH*E(h?O*[^+Y>�;OK.&1QC>@+�(H*,-=:<?=KRU);=KR&7QN;OFC>�;fK.QW:[+RAW(H*,-V>@+.+�;=FH*y0j*E>�;OAW?O*E-r;=FW>�;VFW>JI1*y6g*[*,Q ()*[;O*,:<;O*E(GK.Q >@+.+�IvK.*[{w-�&@0;OFC>�;/ILK.*[{!:<+Y>1-=-[_hkmFH*p:<&1Tf6HK.QH*,(N?=*[+Y>�;=KR&7QW>@+q()*,-=:<?=K.U);OK.&1QZK.-�;OFH*i?=*[+Y>�;OK.&1QC>@+qTV&)()*,+�&10w;OFW*BIvK.*[{:<+Y>1-=-,_�k�MvUHK.:,>@+.+RM7c7>1QX&16)89*E:e;�{�K.+R+gFW>JI7*�&1Q/;OFW*o&1?]()*,?�&@0��WI7*wIvKR*,{S:[+.>7-O-O*,-,c1*E>1:]F/{�KR;OFyKR;=-�&�{�Q/?O*,+.>@^;OK.&1QC>@+|()*E-O:[?OK.U);OK.&1Qt_lkmFW*#ILK.*[{mâ:<+Y>1-=-�TV&)()*,+.-�:,>@Qi6C*#AC-D*E(y0j&7?m0jAH+R+t?O*,+.>@;OK.&1QW>1+gTX>@;=:]FHK.QH\Wc){�FWK.:]FiK.-*<�)Ug*[QW-OK.I1*#{�FH*,Qp;OFH*,?O*r>1?O*�TX>@QvMB(HK��d*[?=*[QL;oT/&)()*[+Y-�K.Qp;OFH*r(W>�;=>16W>1-O*#&1?m0j&7?w?=*[+Y>�;OK.&1QC>@+�K.QW()*<�)K.QH\Wc>1-tKRQL;=?O&)()AW:[*,(�K.QV��FW>1U);O*,?��1�7_t}H&7?t&7AH?|*<�H>1TVUW+R*�FW*[?=*1cJ{�*�;=>�&7*�;OFW*�?=*[+Y>�;OK.&1QC>@[email protected]()*[�vK.QH\o>1UHUH?=&7>7:]F|_kmFH*�Uw`�}�&76)89*,:<;�?O*E:<&7\1QHKR;OK.&1QN-OMv-D;O*,T ?=*,:[&1\1QWKv[,*,-#214x&16)89*E:e;]-rK.QNT�AH+R;OKR^�&76)89*,:<;f-=:<*[QW*,-�0j?=&1T

\@4�K.TX>@\1*E-[_�àTX>@\7*,-n>@?=*r;]>�&1*,QK.Q�UW>1KR?]-[cd{�KR;OF�;OFH*X:[>1T/*[?]>��H�)*,(0j&1?3;OFH*/UW>1KR?E_ }3QH*�K.TX>@\1*VFW>7-;OFW*r+RK.\1FL;o-O&1AH?]:<*#>@;�;OFH*r+.*<0 ;o>1QW(i;OFW*#&@;OFW*[?wFW>7-m;OFW*#+RK.\1FL;o-O&1AH?]:<*#>�;�;=FH*r?=KR\7FL;,_�kmFH*r;9{�&/K.T/>1\1*E->@?=*�AW-O*,(/;=&�()*[;O*[?=T/KRQW*o{�FHKY:]FX?O*,\1K.&1QW-�>@?=*o-DFC>1()&�{w-�>1QW(/FHK.\1FH+.K.\1FL;=-,c7-O&#;OFC>�;q>rFHKR\7F)â�7AC>@+.K�;9MV*,()\7*K.T/>1\1*V&@0|89AC-9;�;OFW*V&76)89*,:<;=-�:[>1Q�6g*/&16);]>@K.QH*,(�_VkmFH*V*,()\7*fK.TX>@\1*VKY-3AC-D*E(;=&B&76);=>1KRQb-9;=?=>1KR\7F7;O^�+.K.QH*>@QC(V:[KR?]:<AW+.>1?Dâ>@?]:�-O*[\7T/*[QL;=-l0j?=&1T�{�FHKY:]Ff;=FH*w?=*,:[&1\1QWK�;=KR&7Q�0j*E>�;OAW?O*E-�>@?=*w:<&7QW-9;=?OAC:e;O*E(�_l}uK.\1AW?O*#�,�W_�\�X-OFH&�{w-#>'-O>1T/UH+R*/+.*<0 ;f>1QW(b?OK.\1FL;rK.TX>@\1*/UW>1KR?r>1QW(�;OFH*�*<�v;O?]>1:<;O*,(�*,(H\1*XK.T/>1\1*/&16H;=>@K.QH*E(�_B}�K.\1AH?=*�[�C_ \L¢r-OFH&�{w-�;OFW*r-9;=?=>1KR\7F7;�+.KRQW*,-�>@QC(i:[KR?]:<AW+.>1?m>1?=:,-q*<�v;O?]>1:<;O*,(�0j?=&1T�;=FH*#*,()\7*�KRTX>@\7*1_U�`�} &16H89*,:e;]-�:[>1QXFW>JI1*�UW+.>1QW>@?Ec7:[ML+.K.QW()?=K.:,>@+�cL>1QW(V;OFH?=*,>7()*,(X-OAH?O0�>1:[*,-,_ukmFHKY-�+.*,>7(H-l;=&�>#QvAHT�6g*[?&@0�AW-D*[0jAH+�FHK.\1F)^�+.*[I1*,+t0j*E>�;=AH?O*E-[_rkmFW*f;=*[Q�0j*,>�;=AH?=*,-n*[T/UH+.&�M1*E('6vM U�`�}�>@?=*1�3*[+.+RK.UW-O*,-,c|:<&L>��)K.>1+u>1?=:,-

� ;9{q&Wcl;=FH?=*[*1c�>1QW(NTfAH+�;=KRUW+R* �ec�UW>1?=>1+R+.*[+�UW>@K.?]-r&@0w+.K.QH*i-O*[\7T/*[QL;=- �j6g&@;OFP:<+.&7-O*�>@QC(h0�>@? �ecl;=?OK.UH+.*,-f&@0+.KRQH*r-O*[\7T/*[QL;=- � ��â-DFC>@Ug*,(p>@QW(��Câ-OFW>@Ug*,( �<c�Y�^.89AHQW:<;OK.&1QW-,c �3^R89AHQC:e;OK.&1QC-[cW>1QW( �w^.89AHQW:<;OK.&1QW-,_�}�K.\1AH?=*�[�C_ \ � -OFH&�{w-V-D&7TV*p&10w;OFH*i0j*E>�;OAW?O*E-X:<&1QC-9;=?OAW:<;O*E(N0j?=&1T ;OFW*i+.K.QH*'-D*,\1T/*[QL;=-/>1QW(Z>1?=:,-�&10n}�K.\1AH?=*�[�C_ \L¢v_�kmFH*3+.K.QH*w0j*E>�;OAW?O*E-�K.QW:<+.AW()*o;9{�& Y�^.89AHQW:<;OK.&1QW-q>@QW(�>rUW>1KR?q&@0|UW>1?=>1+R+.*[+C+RK.QH*E-[_�kmFH*n>@?]:w:<+.AW-D;O*[?-OFH&�{w-m;OFW?O*,*�:<&L>��)K.>1+t>@?]:[-,_ � &@;=*r;=FW>�;oQW&@;o*,I1*[?=M�+.K.QH*f-O*[\7TV*,QL;o&1?o>1?=:#-O*[\7T/*[QL;o6g*,:<&7T/*,-o>yUW>@?O;&@0g;OFW*O�WQW>@+H0j*,>�;=AH?=*,-lAW-O*,(VK.QVTX>@;=:]FHK.QH\W_l}�KR\7AH?=*n�,�W_�\�V3KR+.+.AW-9;=?=>@;O*E-�;OFH*�*,Q7;=KR?=*�-D*[;�&@0_U�`�} 0j*,>�;=AH?=*,-,_àQ�>7(H()KR;OK.&1Q';=&y;OFW*f+Y>@6g*[+.*,(p0j*E>�;=AH?O*E-[c�U�`�}�AW-O*,-3+Y>@6g*[+.*,('6HK.QW>1?OMp?=*[+Y>�;OK.&1QC-w&�I1*,?�;OFW*�0j*E>�;OAW?O*E-;O&X?=*,:[&1\7QHKv[,*�&16)89*E:e;=-,_�kmFH*#?=*[+Y>�;=KR&7QW-OFHKRUC-m*[T/UH+.&�M1*,(B6vM2U�`�}�>@?=*1��-OFW>1?OK.QH\/&1QH*#>1?=:1cW-DFC>@?=KRQH\V&1QW*+.KRQH*7cu-OFW>@?=K.QH\y;9{q&p+RK.QH*,-,ct:[&7>��)KY>@+.K�;9M7cdUH?O&J�)K.T/K�;9M>@;�*[�v;O?=*[TX>@+�Ug&1K.QL;=-,ct>@QW(�*[QC:<+.&7-O*,-e~J*[QC:<+.&7-O*,(v^�6vM1c>1-�-OFH&�{�QiKRQh�,�W_ 2 � _

�� )�� w�� ¢�R�� ¡ �¢V

}�KR\7AH?=*��,�W_�\�XH�BkmFH*p+R*[0 ;�>@QW( ?OK.\1FL;/KRTX>@\7*,-V&@0�>@QZKRQW(HAW-9;=?OKY>@+�&76)89*,:<;/>1QW( ;OFH*p*,(H\1*,-V*[�L;=?=>7:e;=*,(;OFW?O&7AH\1F>1QKRTX>1\1*rUH?=&):<*E-O-OKRQW\�-9;=*[U';=FW>�;n?O*,T/&�I1*,-o-DFW>7()&�{w-o>1QW('T/&7-D;3FWKR\7FH+RK.\1FL;]-[_n��&7AH?O;O*,-OMi&@0%>1AH?O&y��&7-D;=>W_

2

4

5

6

7

8

9

2

3

5

6

7

8

9

}�KR\7AH?=*r�[�C_ \L¢v�ukmFW*3-D;O?]>@K.\1FL;�+.KRQH*n-D*,\1T/*[QL;]-�>1QW(X:<K.?=:[AH+Y>@?�>1?=:,-�*[�L;=?=>7:e;=*,(V0j?=&1T�;OFH*3*,()\7*oK.TX>@\1*o&@0}�KR\7AH?=*V�,�W_�\�XW_��&7AH?D;=*,-OMy&@0l%>@AW?O&��&7-D;=>W_

4

57

89

1

1

1

}�KR\7AH?=*V�,�W_�\ � �lkmFW*#+RK.QH*�0j*,>@;OAH?=*,-,cH>@?]:30j*,>@;OAH?=*,-�>1QW(i*[+.+RK.UW-O*�0j*,>�;=AH?=*,-�:<&7QW-D;O?=AW:e;=*,(�0j?O&7T�;OFW*#+RK.QH*,->@QC(B>1?=:,-m&@0�}�K.\1AH?=*/�[�C_ \L¢v_��&1AH?O;O*E-DMy&10�%>1AH?=&y��&L-9;]>H_

¡1¡ � �� ! #"$"%"

� >�� +R+.KRUC-D*E- �j6 �w��&L>��)K.>1+.-Dâ2

d >= 40 pixels

� : �w��&7>@�)K.>1+.-D^�TfAH+R;OK ��( �m��>1?=>1+R+.*[+R^ 0�>1?

d < 40 pixels

�j*��m��>1?=>1+R+.*[+Râ:<+.&7-O* � 0 � ��^�;O?=KRUH+.*

�j\ � �g^ ;=?OK.UH+.* ��F �OY�^.89AHQW:<;OK.&1Q

�jK ��o^.89AHQW:<;OK.&1Q � 8 � �w^.89AHQW:e;=KR&7Q}�KR\7AH?=*V�,�W_�\�VW��}W*,>�;=AH?=*,-mAW-O*,(iK.Q�;=FH*�U�`�}�-DM)-D;O*[Tp_��&1AW?D;=*,-OMy&@0l%>@AH?=&��&7-D;=>W_

�� )�� w�� ¢�R�� ¡1¡ �

��> �9�vFW>@?=*�&1QH*#>1?=: ��6 �9�vFW>1?O*�&1QW*n+.K.QH*

� : �9�vFW>1?O*n;9{q&/+RK.QH*,- � ( �w��&7>@�vKY>@+

��*��w��+.&7-O*�>@;w*<�v;O?=*[TX>1+gUg&1K.QL;=- � 0 ��q&1AHQW(HKRQH\/6g&J�B*,QW:<+.&7-O*,-e~KY-m*[QC:<+.&7-O*,(B6LM�6C&7AHQW()K.QH\X6g&J�}�KR\7AH?O*/�,�W_ 2 � �U�*,+.>@;OK.&1QW-m6g*<;9{q*[*,Qp-=>@T/UH+.*�UW>@K.?]-�&10u0j*E>�;=AH?O*E-[_��&7AH?D;=*,-OMy&@0l%>@AW?O&��&7-D;=>W_

¡1¡ \ �� ! #"$"%"

1: coaxials-multi2: ellipse3: parallel lines

FEATURES:

MODEL-VIEW

12

3

RELATIONS:a: enclosesb: coaxial

21

3 3

1

2

a a a b

3

2

nodes: features

PARTIAL GRAPH

arcs: relations

a 2

3

1

ab

a

2-GRAPHS

}�KR\7AH?=*f�,�W_ 2H�1��)>1TVUW+R*n\1?]>@UHFi>@QW(B:<&7?O?=*,-OUC&7QW()K.QH\ \�^�\7?=>1UHFW-�0j&1?q;OFW* � FH*<�)QvA);]��&76)89*,:<;,_��&1AH?O;O*E-DM&@0�%>1AH?O&y��&7-D;=>W_

kmFH*#-D;O?=AW:e;=AH?=>1+|()*,-=:<?=K.U);OK.&1Qi&@0l*,>7:]F�T/&)()*[+R^�IvK.*[{ K.-�>V\7?=>1UHFi-D;O?=AW:<;OAH?=*�{�FH&7-O*�QH&)()*,-�>1?O*n;OFW*0j*,>@;OAH?=*f;9MLUg*,-#>1QW({�FW&7-O*f*E()\1*E-3>1?O*f;OFH*/?=*[+Y>�;=KR&7QW-DFWKRU';9MvUg*,-,_f}W&1?nAW-D*/K.Q;=FH*/?O*,+.>@;OK.&1QW>1+uK.QW()*[�L^K.QH\yUH?=&):<*,(HAH?O*7cH;=FH*�\7?=>1UHFpK.-n()*,:[&1T/Ug&7-O*,(iKRQL;=&B>y-O*<;o&10Z\J^�\1?]>@UHFW- �j\1?]>@UWFW-�&@0l;9{q&yQH&)()*E- �<cC*E>1:]FFW>JIvK.QH\/;9{�&XQW&v(H*,-o>1QW(p>X?=*[+Y>�;OK.&1QC-DFHK.Up6C*[;9{�*,*[Qp;=FH*[Tp_�}�KR\7AH?O*X�,�W_ 2H�#-OFH&�{w-�&1QW*rT/&v(H*[+R^�IvK.*[{ &@0>iFH*<�)QvA);r&76)89*,:<;,cu>pUC>@?O;OKY>@+l0jAH+.+�^�\1?]>@UWFb-D;O?=AW:e;=AH?=*V?=*[UW?O*E-D*,Q7;=KRQW\B;=FH?=*[*/&@0mK�;]-�0j*,>@;OAH?=*,-#>1QW(�;OFH*,KR??=*[+Y>�;OK.&1QC-DFHK.UW-,cH>@QW(�;OFW* \J^�\1?]>@UHFi()*,:[&1T/UC&L-DKR;OK.&1Qt_U�*,+.>@;OK.&1QW>1+7K.QW()*[�vK.QH\nKRQV>oUW?O&):<*E()AH?=*�;=FW>�;�TX>�;]:]FH*,-l>@Q�AHQ�&vQH&�{�Q�K.TX>@\7*�;=&n>oUC&1;O*[QL;=K.>1+R+.Mr+Y>@?=\1*(H>@;=>@6C>1-O*�&@0�&16)89*E:e;O^�IvK.*[{ST/&v(H*[+Y-[cLUH?=&v(HAW:<K.QH\r>r-OTX>@+.+C-O*<;�&10|FLMvUg&@;=FH*,-O*,-�>7-�;=&r{�FHKY:]FX&16)89*E:e;=-�>@?=*UH?=*,-O*[QL;�KRQB;OFW*#KRTX>@\7*1_�kmFH*,?O*nK.-o>@Q�&1�C^�+.KRQH*#UW?O*,UH?O&):[*,-=-DK.QH\�UWFW>1-O*n;O&X-D*[;�AHU�;=FH*r(H>@;=>/-9;=?OAC:e;OAW?O*E->@QC(>@Q'&7Q)^�+.K.QH*�TX>�;]:]FHK.QH\yUHFW>7-D*7_3kmFH*f&@�g^�+.K.QH*�UHFC>1-O*�:<&7QW-9;=?OAC:e;=-3>yFW>7-DFp;]>@6H+.*r;=FW>�;�KY-wAW-O*,('6vM;OFW*i&7Q)^�+RK.QH*�UWFW>1-O*1_GkmFH*iK.QW()KY:<*,-V;=&�;=FH*iFW>1-OFG;]>@6H+.*i>1?O*B�@^�;OAHUW+R*E-f?=*[UW?O*E-D*,Q7;=KRQW\ \J^�\1?]>@UHFC-r&@0n>T/&)()*[+R^�IvK.*[{�&@0o>1QN&16)89*E:e;E_�kmFH*B:[&1T/Ug&1QH*,Q7;]-r&10�;OFH*B�@^�;OAHUH+.*�>1?O*X;=FH*y;9MvUg*,-f&@0m;OFW*y;9{q&QH&)()*,->@QC(p;OFH*f;9MvUC*E-n&@0�;OFW*�;9{q&�?=*[+Y>�;=KR&7QW-DFWKRUW-,_�}H&1?n*<�H>1TVUW+R*7cC;=FH*��1^ ;=AHUH+.* ��*[+.+RK.UW-O*1cg0�>@?nUW>1?=>1+R+.*[+�UW>@K.?Ec*[QC:<+.&7-O*,(v^�6vM1c@*,QW:<+.&7-O*,- ��T/*,>@QC-�;OFC>�;�;=FH* \J^�\1?]>@UWFf?=*[UH?=*,-O*[QL;]-�>@QX*[+.+.KRUW-O*m0j*,>@;OAH?=*o>1QW(X>n0�>@?�UC>@?]>@+.+R*,+UW>1KR?m0j*E>�;OAW?O*7c){�FH*[?=*n;OFH*#*,+R+.KRUC-D*#KY-�*[QC:<+.&7-O*,(B6LMy;OFH*#UW>1?=>1+R+.*[+dUW>1KR?�&10�+.K.QH*r-D*,\1T/*[QL;]-�>@QW(�;OFH*#UC>@?O^>@+.+.*[+|UW>1KR?w;OFvAW-�*,QW:<+.&7-O*,-m;=FH*r*,+R+.KRUC-D*7_ �vK.QW:<*�TV&L-9;w&10l;OFH* Uw`�}�?=*[+Y>�;=KR&7QW-�>@?=*r-DMvT/T/*<;=?OKY:@c);=FH*#;9{q&?=*[+Y>�;OK.&1QC-DFHK.UW-�>1?O*�&10 ;O*,QX;OFH*3-O>1TV*7_�}W&1?�KRQW-D;=>1QW:<*7c@;=FH*o�1^ ;=AHUH+.* �j*,+R+.KRUC-D*7cL:[&7>��)KY>@+W>1?=:�:[+RAC-9;=*[?Ec7-OFW>@?=*>@QB>@?]:@c -DFW>1?O*�>1Q�>@?]: ��(H*,-=:<?=KR6g*,-q>#?=*[+Y>�;OK.&1QC-DFHK.UX{�FH*,?O*n>@QX*[+.+.KRUW-O*3>1QW(y>r:[&7>@�vKY>@+g>@?]:w:<+.AW-D;O*,?�-OFW>@?=*>@QZ>@?]:�-O*[\1T/*,Q7;E_bkmFW*B-OMLTf6C&7+RKY:�:[&1T/Ug&1QH*,Q7;]-�&10w;OFW*B�1^ ;=AHUH+.*,-V>@?=*�:<&7QLI7*[?O;O*E(b;O&bQLAWT�6g*[?]-r0j&7?FW>7-DFHK.QH\C_�kmFH*/UH?=*[UH?=&):<*,-=-OKRQH\i-9;]>@\7*�\1&v*E-o;=FH?=&1AH\7F�*,>7:]F�T/&)()*[+R^�ILK.*[{�KRQ�;OFH*X(H>@;=>16W>1-O*1cd*[QC:<&)()*,-*,>7:]Fy&@0�K�;]-9\J^�\1?]>@UHFW-�;O&VUH?=&v(HAW:<*�>��1^ ;=AHUH+.*3K.QW()*[��cH>@QW(B-9;=&1?=*,-�;OFH*nQW>@T/*�&@0t;OFH*nT/&v(H*[+R^�IvK.*[{ >1QW(>1-=-O&v:[K.>@;O*E(yK.Q)0j&1?=TX>�;OK.&1QiK.Qp>V+.K.-D;wK.QB;=FH*r-O*[+.*,:e;=*,(B6HK.Qi&10u;=FH*#FW>7-DFB;=>16H+R*7_

�� )�� w�� ¢�R�� ¡1¡ 2

M1 M 5 M 23 M 81, , ,

81M

1M 5M M 23 81M

clusterarc

coaxial

ellipse

anshare

arcfunction

hash

(1,2,9,9)(1,2,9,9)

List of Models2-graph

retrieved list of models

each modelvote for

, , ,1M 5M M 23

+1 +1+1 +1

accumulators

}�KR\7AH?=*V�,�W_ 2$\H��&1;OK.QH\X-O:]FH*,T/*�0j&1?�?=*[+Y>�;OK.&1QC>@+dKRQC()*<�)K.QH\W_��&7AH?D;=*,-OMX&@0�%>@AW?O&y��&7-D;=>W_

}3QW:[*#;OFH*VFW>7-DF)^�;=>16H+.*rK.-�:[&1QW-D;O?=AW:e;=*,(�cgKR;nKY-oAC-D*E('KRQ�&1Q)^�+.KRQH*�?O*E:<&1\7QHKR;OK.&1Q|_ m +Y-D&BAW-D*E('KY-3>B-D*[;&@0t>7:[:[AHT�AH+Y>�;=&1?]-�0j&1?�I1&@;=KRQW\WcL&1QH*�0j&7?�*E>1:]F/UC&L-O-OK.6H+R*3T/&v(H*[+R^�IvK.*[{SKRQy;OFH*n(H>�;]>@6W>7-D*7_�* FH*,Q�>r-=:<*[QW*KY-r>@QW>1+RM#[,*,(�cuK�;]-#0j*,>@;OAH?=*,-�>@?=*V*[�v;O?]>1:e;=*,(h>@QC(b>p?=*[+Y>�;=KR&7QW>@+�()*,-=:<?=KRUH;OK.&1QbKRQh;=FH*X0j&1?=T &10w>'-D*[;r&@0\J^�\1?]>@UWFW-�K.-�:<&1QC-9;=?OAW:<;O*E(�_ikmFW*[Q|c�*,>7:]F \�^�\7?=>1UHFbKRQh;=FH*�()*E-O:[?OK.U);OK.&1QhKY-r*,QW:<&)()*E(�;=&UH?=&)()AW:<*y>1QK.QW()*<�{�KR;OF�{�FHKY:]F;O&i>1:,:<*,-=-o;OFH*VFW>1-OF';]>@6H+.*1_#kmFH*V+RKY-D;�>7-O-O&):<KY>�;O*E(p{�K�;=F�;=FH*/-D*,+R*E:e;O*E('6HK.Q�KY-n?O*[^;O?=K.*[I1*E(_')KR;�:[&1QW-OKY-9;]-�&10�>1+R+�T/&)()*[+R^�ILK.*[{w-�;=FW>�;�FW>JI7*o;=FHK.-mUC>@?O;OKY:<AH+Y>@?-\J^�\1?]>@UWF|_ m I7&@;O*nKY-q;OFH*,Qp:,>1-D;0j&1?�*E>1:]FiT/&v(H*[+R^�IvK.*[{ K.Qi;OFH*#+.KY-9;E_�kmFHK.-mKY-�Ug*[?O0j&1?=T/*,(�0j&1?w>@+.+d;OFW* \J^�\1?]>@UHFW-�&@0�;OFW*#KRTX>@\7*1_ m ;�;OFW**[QC(h&@0m;OFH*�UH?O&):[*,()AH?=*1cu;OFW*yT/&v(H*[+R^�IvK.*[{w-#{�KR;OFN;=FH*yFHK.\1FW*,-D;�I1&1;O*,-�>@?=*y-D*,+R*E:e;O*E(h>1-rFvMvUg&@;OFW*,-O*,-,_}�KR\7AH?=*X�[�W_ 2$\fK.+R+.AW-D;O?]>�;=*,-m;=FH*r&1QH^�+.KRQW*r?O*E:<&7\1QHKR;OK.&1QiUH?=&v:[*,-=-[_qkmFH*7\�^�\7?=>1UHFi-OFH&�{�QpK.Qp;OFH*��C\1AH?=*#K.-:<&7QvI1*[?O;O*E(i;O&�;OFH*VQvAHT/*[?=K.:��@^�;OAHUH+.* �D�1c�\)c VHc V��w{�FHK.:]F�-D*,+R*E:e;=-n>y6WKRQ�KRQ�;OFH*VFW>1-OF';]>@6H+.*1_�kmFW>�;�6HK.QKY-3>7:[:<*E-O-O*,(B;=&�?=*<;O?=K.*[I1*f>X+RKY-D;3&@0�0j&7AH?oT/&)()*,+.-,� � c � c % ' c�>1QW( �� _3kmFW*f>1:,:<AHTfAH+Y>�;O&7?=-w&@0*,>7:]FB&10t;=FH*,-O*#T/&v(H*[+R^�IvK.*[{w-�>@?=*�KRQC:<?=*[T/*[QL;O*E(�_

m 0 ;=*[?�FLMvUg&@;=FH*,-O*,-�>@?=*w\1*,QH*[?]>�;=*,(�c7I1*[?=Kv�C:[>@;OK.&1Q/T�AW-D;�6g*oUg*[?O0j&1?=T/*,(�_�kmFH*w?=*[+Y>�;=KR&7QW>@+WKRQW(H*<�)KRQW\-D;O*[UfUH?=&�ILKY()*E-t:<&7?O?=*,-OUg&1QW()*,QW:<*E-�0j?=&1To\@4PK.TX>@\1*�0j*,>@;OAH?=*,-t;O& \@4PT/&v(H*[+L0j*,>@;OAH?=*,-uKRQV>wT/&)()*[+R^�ILK.*[{#_kmFH*E-D* \@4 T/&v(H*[+C0j*,>�;=AH?=*,-q>@?=*w+RK.Q�&7*,(y{�KR;OF�;OFH*o0jAH+.+|214�TV&)()*,+g0j*,>�;=AH?=*,-�&10|;OFW*3FvMvUC&1;OFH*E-DK�[[*E(X&16H^89*,:<;,_�kmFW* U�`�} -OMv-D;O*,T UC*,?D0j&7?OTX-yI7*[?=K �g:[>�;=KR&7QS6LMPAW-OKRQW\ :<&7?O?=*,-OUC&7QW()K.QH\ \@4oâ214 Ug&1K.QL;BUW>1KR?]-,c\@4oâ2145+.KRQH*'-O*[\7TV*,QL;/UC>@K.?=-,c�>1QW( \145*[+.+RK.UW-O*<â214 :[KR?]:<+.*pUW>@K.?=-f;=&h:[&1T/UHA);=*'>@QP*,-D;OK.T/>@;O*p&@0n;OFW*;O?]>@QC-90j&7?OTX>�;=KR&7Qp0j?O&7T5;OFH*X274�T/&)()*,+�&10�;OFW*fFvMvUC&1;OFH*E-DK�[[*E(&76)89*,:<;3;=&�;=FH*fK.TX>@\7*1_�Y|K.QH*/>@QW(�>@?]:-O*[\1T/*,Q7;]-�>@?=*VUW?O&189*,:e;=*,(;O&p;OFW*VK.TX>@\7*VUW+.>1QH*X>@QW(b>p()K.-D;=>1QW:<*/KY-#:<&7TVUWA);O*E(�;=FW>�;r()*[;O*,?OT/K.QH*,-#KR0;OFW*wI1*,?OKv�C:[>@;OK.&1QVK.-�-DAW:,:<*E-O-D0jAH+H&7?�K�0d;OFW*�FLMvUg&@;=FH*,-OK.-�K.-�K.QW:[&1?=?O*E:e;,_l}�KR\7AH?=*,-m�[�C_ 272�>@QW(i�[�C_ 21�n-OFH&�{P>-=>@T/UH+.*q?=AHQV&@0g;OFH*-Uw`�} -OMv-D;O*,Tp_�}�K.\1AH?=*��[�W_ 212n-OFH&�{w-u;OFH*�*E()\1*mK.T/>1\1*q0j?=&1T�>nT�AW+�;=K�^�&16)89*E:e;�-=:<*[QW*>@QC(�;OFH*q+.KRQH*�0j*,>@;OAH?=*,-,c@:<K.?=:[AH+Y>@?u>1?=:�0j*,>�;=AH?=*,-�>@QW(#*,+R+.K.UW-D*E-u(H*<;O*E:e;=*,(�_l}�KR\7AH?O*3�[�C_ 21�w-DFH&�{w-u>@QrK.QW:[&1?O^

¡1¡ � �� ! #"$"%"

}�KR\7AH?=*y�[�C_ 272H� m ;O*E-9;nKRTX>1\1*f>1QW(pKR;=-3+RK.QH*f0j*,>�;=AH?=*,-,cg:[KR?]:<AH+Y>@?3>@?]:�0j*,>@;OAH?=*,-,cg>1QW('*,+R+.KRUC-D*�0j*,>�;=AH?=*,-,_��&1AW?D;=*,-OMy&@0l%>@AH?=&��&7-D;=>W_

?=*,:e;wFvMvUg&@;OFW*,-OK.-mUH?=&)()AW:[*,(B6LM�;OFH*r-OM)-9;=*[TpcH{�FHKY:]Fp{q>7-q?OAH+.*,(i&7A);w6vMX;OFH*�I1*[?=Kv�C:[>@;OK.&1Q�UW?O&):<*E()AH?=*>@QC(r;=FH?O*,*q:[&1?=?O*E:e;lFvMLUg&@;=FH*,-O*,-,c�{�FHKY:]Ff{q*[?=*�:[&1?=?O*E:e;=+RM#I7*[?=K �W*E(�_ukmFW*OUw`�}PUC&L-D*m*E-9;=KRTX>�;=KR&7Q�UH?=&):<*[^()AH?=*m{q>7-�\1K.I1*[QfKRQ��FW>1U);O*,?m�,2H_�}�KR\7AH?O*��,�W_ 2 ¡ -OFH&�{w-l>n6H+.&v:�&r(HK.>1\1?]>@T�&@0C;OFH*�{�FW&1+.* U�`�} -DM)-D;O*,Ti_

�� /U�*[+Y>�;=KR&7QW>@+�K.QW()*[�)KRQH\*b?OKR;O*i>UH?=&1\7?=>1T ;OFW>@;VK.T/UH+.*[T/*[QL;=-f?=*[+Y>�;OK.&1QC>@+�K.QW()*[�vK.QH\�0j&1?�&76)89*,:<;fTX>�;]:]FHK.QH\W_�kmFW*�UH?=&1\7?=>1T-OFH&1AH+Y(hAW-O*y>'-9;=&1?=*,(b+.KR6H?]>@?=M�&10q&76)89*,:<;�T/&)()*[+Y-[c�*,>7:]Fh?O*,UH?O*E-D*,QL;O*,(b6vM�>'-O*<;f&@0!\J^�\1?]>@UHFC-[_�kmFW*K.QHUHA);3;O&/;OFW*�?=*,:<&7\1QHKR;OK.&1QiUHFW>7-D*�K.-w>y?O*,UH?O*E-D*,QL;=>�;=KR&7QB&10�>/T�AH+R;OKR^�&76)89*,:<;oK.T/>1\1*7cC>@+Y-O&VK.Q';=*[?=T/-w&@0>/-D*[;�&@0\�^�\7?=>1UHFW-,_�kmFW*nUW?O&7\1?]>@T�-DFW&1AH+Y(�?=*<;=AH?=Qi>V+.K.-D;�&@0u*E>1:]FiT/&v(H*[+�K.QB;=FH*#(H>�;]>@6W>7-D*3;OFC>�;wFW>7->�;�+.*,>7-9; ¡ �� &10uKR;=-!\�^�\7?=>1UHFW-�KRQi;OFW*#KRTX>@\7*1_

]_^-`�^-`�b dg��i ��-��-� � � �� j �!�l dgj9k-fHlahzn*[&7T/*<;O?=KY:3T/&)()*,+.-�\7KRI7*3UW?O*E:<KY-D*#()*(�WQHKR;OK.&1QW-�&10l-OUg*,:<Kv�C:n&16H89*,:e;]-('C>X� m 4�T/&)()*[+t(H*,-=:<?=KR6g*,-�>/-OKRQ)^\1+.*V&16)89*E:e;3{�KR;OFh>@+.+�:<?=K�;=K.:,>@+�UC&7KRQL;]-n>1QW(�(HKRT/*[QC-DK.&1QW-n-OUC*,+R+.*,(�&1A);E_�U�*[+Y>�;=KR&7QW>@+�T/&)()*[+Y-�>@?=*�T/&1?=*\1*,QH*[?]>@+)K.Q/;OFC>�;�;=FH*[M/()*E-O:[?OK.6C*w>#:[+.>7-O-�&@0�&16)89*E:e;]-[c76HA);�*E>1:]F/*[+.*[T/*,Q7;�&10d;OFW>@;�:<+Y>1-=-�T�AC-9;�FC>JI1*m;OFW*-=>@T/*w?=*[+Y>�;OK.&1QC>@+W-D;O?=AW:e;=AH?=*1_l}H&1?�*<�H>@T/UH+.*1cv>r:]FW>1KR?�T/K.\1FL;�6g*3()*E-O:[?OK.6g*,(X>1-�FW>JIvKRQW\r>#6W>1:�&dcL>#-D*E>�;,c>@QC(y0j&7AH?�+R*,\7-m>�;O;=>7:]FH*,(�AHQW()*,?OQH*E>�;=Fi>1QW(B>@;m;OFH*r:[&1?=QH*[?]-�&10t;=FH*r-D*E>�;E_ m QH&@;=FH*[?w:]FC>@K.?�;=FW>�;�FW>7-m>Ug*,()*E-9;]>@+C>1QW(V6W>1-O*�K.QW-9;=*,>7(/&@0d0j&1AH?�+R*,\7-�{q&1AH+Y(VQH&@;�T/>@;=:]F/;=FHK.-�()*,-=:<?=K.U);OK.&1Q|_lkmFH*m0jAHQC:e;OK.&1QH^�6W>7-D*E(>@UWUH?O&L>1:]F/;=&�&16H89*,:e;m?=*,:<&7\1QHKR;OK.&1Q/;]>�&7*,-�;OFHKY-m>�-D;O*[U�0jAH?O;OFH*,?,_l`�;�>�;D;=*[T/U);]-�;=&V(H*{�WQH*�:<+Y>1-=-O*,-�&10t&16H^89*,:<;=-�;OFH?=&1AW\1FX;=FH*[K.?�0jAWQW:e;=KR&7Q|_�kmFvAW-�>f:]FW>@K.?�KY-�-O&1T/*[;OFHK.QH\r;=FW>�;m>rFvAHTX>@Q�{�&7AH+.(�-DKR;�&7Q�>@QW(yT/>JMFW>JI7*3TX>@QvM�(HK��d*[?=*[QL;w?=*[+Y>�;OK.&1QC>@+�-9;=?OAC:e;OAW?O*E-[c){�FHKY:]F'>@+.+|-O>@;OKY-90jMB>V-O*<;w&10u0jAWQW:e;=KR&7QW>@+|:[&1QW-D;O?]>@K.QL;=-,_

�� )�� w�� ¢�R�� ¡1¡7¡

}�KR\7AH?=*X�[�W_ 2@�C� m Q'K.QW:[&1?=?O*E:e;wFvMvUC&1;OFH*E-DKY- �jAWUHUC*,?o+.*<0 ; �w>@QC(i;OFH?=*[*�:[&1?=?O*E:e;�FvMvUC&1;OFH*E-D*E-[_w��&1AH?O;O*E-DM&@0�%>1AH?O&y��&7-D;=>W_

}HAWQW:e;=KR&7Q)^�6C>1-O*,(y&76)89*,:<;�?O*E:<&1\7QHKR;OK.&1Q�{m>1-qUHK.&1QW*[*[?=*,(B6vM2�L;]>@?T&y>@QW(i�q&�{�M1*[?mK.Q�;=FH*[K.?oz U �o}l}-OMv-D;O*,Tp_�z U �3}l} :<&7QL;=>@K.QW-q;=FH?O*,*�+R*,I1*[+Y-m&@0�&vQH&�{�+R*E()\1*7��7_m;OFH*r:,>�;O*,\1&7?OM/FHK.*[?]>@?]:]FvMX&@0�>1+R+t&16)89*E:e;=-mK.Qi;OFH*�&vQH&�{�+.*,(H\1*n6W>1-O*\H_m;OFH*r()*(�WQHKR;OK.&1Qp&@0�*,>7:]Fi:,>�;O*,\1&7?OMXK.Q�;=*[?=TX-�&@0u0jAHQW:e;=KR&7QW>@+tUH?O&7UC*,?D;=KR*E-2W_m;OFH*�&vQH&�{�+.*,()\7*3UW?OK.T/K�;=KRI7*,-mAHUg&1Qp{�FHKY:]F�;=FH*�0jAHQW:<;OK.&1QW>1+t()*(�WQHKR;OK.&1QW-w>1?O*n6W>7-D*E(

�8 �� 0 �� 1 � � ��3 � �� >1:]F�&vQH&�{�+.*,(H\1*oUW?OK.T/K�;=KRI7*nKY-�>fUW>@?]>@T/*<;=?OK�[[*E(yUH?=&):<*E()AH?=*o;=FW>�;�K.TfÛH+.*[T/*[QL;]-�>o6W>7-DKY:q:<&1QC:<*[UH;l>16C&7A);�\7*[&7TV*[;O?=M1c�UHFvM)-OK.:,-u&7?�:,>@AW-=>�;=KR&7Q|_ m &vQH&�{�+.*,()\7*�UH?=K.TVKR;OK.I1*�;=>%&1*E->VUC&7?D;=KR&7Qp&@0�>V274 -OFW>@Ug*r()*,-=:<?=K.U);OK.&1Qp>1-mK.QHUHA);n>@QW(i?=*<;OAW?OQW-�>VI�>@+.AH*�;=FW>�;wK.QW()KY:[>@;O*,-wFH&�{ {q*[+.+|KR;-=>�;OKY-a�W*,-�-OUg*,:<Kv�C:�?=*,�LAHK.?=*[T/*[QL;=-,_ukmFW*o-DKR�/z U �3}�} &vQH&�{�+.*,()\7*�UH?OK.T/K�;=KRI7*,-�(H*{�WQH*w;OFH*o:[&1QW:[*[U);]-�&@09�� ?O*,+.>@;OK.I1*n&1?=KR*,Q7;]>�;=KR&7Q� ()KRT/*,QW-DK.&1QC-� UH?O&J�)K.T/K�;9M� -9;]>@6HK.+RKR;9M� :<+.*,>@?]>@QC:<*� *[QW:[+R&L-DAH?=*

¡1¡ X �� ! #"$"%"

using a singlecamera and two different light sources

Acquire image pair

Remove shadows and highlights

Extract primitive featuresand combine to produce high-level features

and construct a set of 2-graphs representing the imageCompute relationships among high-level features

from the pairand produce a combined image

obtain an edge image

pose estimation to verify or disprove the hypothesesUse 3D mesh models of the objects and

and vote for potential object modelsUse the 2-graphs to index the hash-table

Apply the Cannyedge operator to

}�KR\7AH?=*V�,�W_ 2 ¡ ��}�+.&�{�()KY>@\7?=>1T�&@0�;OFH*�U�`�}�&16)89*E:e;�?=*,:<&7\1QHKR;OK.&1Qi-DM)-D;O*,Ti_

�� )�� w�� ¢�R�� ¡1¡ ¢kmFH* n�p(svu ~ ��¤wp � n��p{� ~ u ~ � � � UH?OK.T/K�;=KRI7*�K.-mAW-O*,(�;O&X()*[;O*,?OT/K.QH*�FH&�{ {q*[+.+d;OFH*#?=*[+Y>�;=KRI7*o&1?=K.*[QL;=>@;OK.&1Q&@0�;9{q&/-OAH?O0�>1:[*,-�-=>�;OKY-a�W*,-�-O&1T/*r()*E-DK.?O*E(�?=*[+Y>�;=KR&7QW-OFHKRUt_�}H&1?o*<�H>@T/UH+.*1c);=FH*�;O&7U'-DAH?O0�>1:[*�&@0�;OFH*�-O*,>@;&@0�>X:]FW>1KR?3-DFH&7AH+Y(B6g*�>1UHUH?=&J�vK.TX>�;=*[+.MyUC*,?OUg*[QC()K.:[AH+Y>@?w;=&/;OFH*V>1(J8D>7:<*,Q7;o-OAH?O0�>1:[*#&@0�;OFH*f6W>1:�&d_�kmFW*

£w��xyp(��z�� z UH?=KRT/KR;OK.I1*pUg*[?O0j&1?=T/-X(HKRT/*[QC-DK.&1QW-V;=*,-D;=-V0j&7?y-DKR�GUC&L-O-OK.6H+R*'()K.T/*[QW-OK.&1QZ;9MLUg*,-,�p{�K.();OF|c()*,U);OF|cmFH*,KR\7FL;,cm>@?=*,>Hc�:<&1QL;=KR\7AH&1AW- -DAW?D0�>7:<*1cq>@QW(ZI1&7+RAWTV*7_ àQZT/&L-9;y&76)89*,:<;=-V;OFW*()KRT/*,QW-DK.&1QC-/&@0&1QW*XUW>@?O;r&@0q;OFH*X&76)89*,:<;�:<&7QW-9;=?=>1KRQ�;OFW*�()K.TV*,QW-OKR&7QW-#&@0q;OFW*X&@;OFW*[?rUW>1?D;]-[_BkmFH* � n � ¥$��x7� ~ & UH?OK.T/K�^;OK.I1*f:]FH*,:�&)-m0j&7?3�LAW>@+.KR;=>�;=KRI7*�-OUW>�;=K.>1+t?=*[+Y>�;OK.&1QC-DFHK.UW-�6g*<;9{q*[*,Q'*[+.*[T/*[QL;]-w&@0�>1Q'&16)89*E:e;�6 -3-DFW>1UC*7_w}H&7?*<�H>1TVUW+R*7cd;OFH*VFW>@QC()+R*V&@0q>�UHKR;=:]FW*[?�T�AW-D;�6C*X-OK�;=AW>�;=*,(�>16C&�I7*r;=FH*V>JI7*[?]>@\7*r:<*[QL;=*[?�&@0�TX>7-O-3&@0�>1Q&16H89*,:e;m;=&XT/>%&1*�KR;w*,>1-OM/;O&X+.KR0 ;,_kmFH*#-D;=>@6WKR+.K�;9M�UH?OK.T/K�;=KRI7*#:]FH*,:�&)-�;OFW>@;o>V\1K.I1*[Qp-OFW>@Ug*�K.-�-D;=>16H+R*�{�FH*,QBUW+.>7:<*,(i&7Qi>/-OAHUHUg&1?O;OK.QH\UH+Y>@QH*�KRQV>o\7KRI7*[Q#&7?OK.*[QL;=>@;OK.&1Q�>1QW(#{�KR;OFV>oUg&7-=-DK.6H+.*�0j&7?=:[*�>@UWUH+RK.*,(|_�kmFH* {s�pTu�n�uw�� p UH?OK.T/K�;=KRI7*�:]FH*E:�&)-{�FH*[;OFH*,?�>r-OUC*E:<Kv�W*,(/I7&1+.AHT/*w&@0|-OUW>1:[*�6C*[;9{�*,*[QyUC>@?O;=-�&10g;=FH*o&76)89*,:<;�KY-�:<+.*,>1?�&@0�&76W-9;=?OAC:e;OK.&1QC-[_l}H&7?*<�H>1TVUW+R*7c3>Z?O*E:e;=>1QH\1AW+.>1?�I1&7+RAWTV*b>@6g&�I1*�;OFH*h-D*E>�;pT�AW-D;p6C*h:<+.*,>1?�0j&7?p> UC*,?=-O&1Q ;O&S-DKR;p&1Q KR;,_}�KRQC>@+.+RM7cW;=FH* p(� (s � z�rtn�p UH?=KRT/KR;OK.I1*#;=*,-D;=-�0j&7?o?=*,�LAHK.?O*E(p:<&1QC:[>JIvK�;=KR*E-�&@0l;=FH*r&16H89*,:e;E_ m {�K.QH*�\7&16H+.*<;Ec0j&1?�K.QW-D;=>1QW:<*7c)T�AW-D;wFW>JI1*#>/:<&7QW:[>JIvKR;9M/;O&/FH&7+.(B;OFW*#{�KRQH*7_

�5� � � �� 0 � �G� � � � � � kmFH*�()*{�WQWK�;=KR&7QV&10g>30jAHQW:<;OK.&1QW>1+)&16)89*E:e;�:<+Y>1-=-l-DUg*,:[K �C*,-�;OFW*m0jAHQW:e;=KR&7QW>@+UH?=&1Ug*[?O;OK.*,-XKR;�TfAW-9;BFW>JI1*pK.QS;O*[?=TX-y&103;=FH*��QH&�{�+.*,()\7*��?=KRT/KR;OK.I1*E-[_ kmFH*�z U �o}l}�0jAHQW:e;=KR&7QW>@+:[>@;O*,\1&1?=K.*,-l;=FW>�;mFW>JI1*o6C*,*[Q�AC-D*E(X0j&1?q&16H89*,:e;]-�K.QX;=FH*n:[+.>7-O-O*,- ��rtn�� ~ rtn�p c £�� za|�p�z cW>1QW( |�uw� £ ~ �� s�z >@?=*()*(�WQH*,(i6vMX0j&7AH?�UC&L-O-OK.6H+R*�;=*[T/UH+Y>�;=*,-,�� UH?O&�IvKY()*,-m-D;=>16H+R*�� UH?O&�IvKY()*,-�� -DAW?D0�>7:<*� UH?O&�IvKY()*,-�� :<&7Q7;]>@K.QHT/*[QL;� UH?O&�IvKY()*,-�� FW>@QC()+R*

{�FH*,?O*�� K.-�>VUW>1?=>1TV*[;O*,?q&10u;=FH*�;O*,T/UH+.>@;O*7_�}H&1?�*[�H>@T/UH+.*1cH>/:]FW>@K.?mT�AW-D;wUH?=&�IvK.()*�-D;=>@6W+R*#-OAHUHUg&1?O;>@QC(�>i-DKR;D;]>@6H+.*X-DAW?D0�>7:<*V0j&1?n;OFW*VUg*[?]-O&1Qb{�FH&B{�K.+.+�-DKR;#&1Q�K�;E_ m -O&1AHUb6g&�{�+�TfAW-D;rUH?O&�IvKY()*f-D;=>16H+.*:<&7QL;=>@K.QHT/*[QL;m0j&1?w;OFH*r-O&1AHUiKR;o{�KR+.+t:[&1QL;=>1KRQ|_ m :[AHUpT�AW-D;o:<&7QL;=>@K.Qp>X-DAHKR;=>16H+.*#FW>@QW(H+R*n;OFC>�;o>@+.+.&�{w-KR;�;O&/6C*#UWK.:�&7*,(BAHU'>@QW(2�H;]-m;OFH*r(HKRT/*[QC-DK.&1QW-m&10uKR;=-�6g&)()M1_� 2 � � �@�� 1 � �� 2 � z U �o}l}P\1?=&1AWUW-w>@+.+u:,>�;=*[\1&7?OK.*,-m&10�&16)89*E:e;=-oKRQL;=&�>y:[>@;O*,\1&1?=MX;=?O*,*;OFC>�;o+.K.-D;=-o>@+.+�;OFH*f:[>�;=*[\7&1?=KR*E-�;=FH*r-OMv-D;O*,T!:,>@Q':<AH?=?=*[QL;O+.M�?=*,:[&1\1QWKv[,*1_ m ;w;=FH*�;O&7U'+R*,I1*[+�&10l;OFH*�;=?O*,*>@?=*yI7*[?=M�\1*,QH*[?=KY:y:[>@;O*[\7&1?=KR*E-r-OAW:]FG>1-r0jAH?OQWK�;=AH?O*i>@QW( ()K.-OFH*E-[_ ��>1:]FN-OAW:[:[*[*,(HKRQH\�+R*,I1*[+q\1&v*E-#KRQL;=&T/&1?=*3()*[;=>1KR+ 'L0j&1?�*[�H>@T/UH+.*1cL0jAH?=QHK�;=AH?=*oFW>7-�-OUC*E:<Kv�C:w&76)89*,:<;m:[+.>7-O-O*,-�:]FW>@K.?Ec@;=>16H+.*1cv6C*,QW:]F|cv6g&L&$&)-DFH*,+�09c>@QC(�6g*,(�_ ��I1*[Q�;OFH*E-D*�&76)89*,:<;�:<+Y>1-=-D*E-�:,>@QV6C*w(HKRIvKY()*,(f0jAH?O;OFH*,?)'L:]FW>@K.?]-�:,>@QV6C*w:[&1QvI1*,QL;OK.&1QW>1+L:]FW>1KR?]-,c+.&1AHQH\7*q:]FC>@K.?=-,c�6W>@+Y>@QC-�:]FC>@K.?=-,c@>@QW(fFHK.\1FW:]FC>@K.?=-,c�*<;]:@_l}uK.\1AW?O*n�[�C_ 2$X3-OFH&�{w-�UC&7?D;=KR&7QW-�&@0C;OFH*wz U �o}l}:[>@;O*,\1&1?=My()*(�WQHKR;OK.&1Qi;O?=*[*7_

Uw>@;OFH*,?3;=FW>@Q � ?=*,:[&1\7QHKv[,KRQW\B>@Q�&16)89*E:e;Ec �'z U �o}l} AC-D*E-o;=FH*/0jAHQW:<;OK.&1Q)^�6W>7-D*E(�()*(�WQHKR;OK.&1Qh&@0�>1Q&16H89*,:e;r:,>�;O*,\1&7?OMp;=&i?=*,>7-D&7Q�>16C&7A);r{�FH*<;=FH*[?r>1Q�&76W-O*[?=I1*,(�&16)89*E:e;rK.QW-D;=>@QC:<* �jK.Qh?=>1QH\1*/(H>�;]>��n:[>1Q0jAHQW:<;OK.&1QN>1-#>iT/*[Tf6C*,?#&@0�;OFW>@;�:[>�;=*[\7&1?=M1_/kmFH*[?=*X>@?=*�;9{q&pT/>1KRQh-D;=>@\7*,-n&@0q;OFWK.-n0jAHQC:e;OK.&1QH^�6W>7-D*E(>@QC>@+.Mv-OKY-�UH?=&v:[*,-=-[�g;=FH*�UH?=*<^�UH?=&):<*,-=-OKRQH\�-D;=>1\1*�>@QC(n;OFH*�?O*E:<&1\7QHKR;OK.&1Q�-9;]>@\1*7_ukmFH*�UH?O*,UH?=&v:[*,-=-DK.QH\�-D;=>@\7*KY-�:,>�;O*,\1&7?OMVKRQC()*[Ug*[QW(H*[QL;)'H>1+R+g&16)89*E:e;]-q>1?O*oUH?O&):[*,-=-D*E(XKRQy;OFH*�-O>1T/*oTX>@QHQW*[?E_�àQ�;OFHKY-m-9;]>@\7*�;OFH*�214(H>@;=>wKY-l>@QW>1+RM#[,*,(#>@QC(�>@+.+LUC&1;O*[QL;=K.>1+70jAWQW:e;=KR&7QW>@+v*[+.*[T/*,Q7;]-u>1?O*�*[QvAHT/*[?]>�;=*,(�_�kmFH*q?O*E:<&1\7QHKR;OK.&1Qr-D;=>@\7*

¡1¡%� �� ! #"$"%"

DefinitionsCategory

dishes

handtools

furniture

chair

table

bench

bookcase

bed

cup/glass

plate

bowl

pot/pan

pitcher

hammer

screwdriver

wrench

conventional chairluunge chairbalans chairhighchair

sledge hammerregular hammerclaw hammer

potsauce pan

frying pan

simple benchbench with backbench with arms

single bed

bunk bed

king bed

double bed

box wrench

open end wrench

saucerdinner plateplatter

}�KR\7AH?=*V�,�W_ 2%XW��l&7?D;=KR&7QW-�&10t;=FH*�z U �o}l}P�q>@;O*[\7&1?=My4o*(�WQHKR;OK.&1Q'ku?O*,*1_��&7AH?D;=*,-OMy&@0Y|&7AHK.-O*��L;=>1?�&>@QC(B��*,ILK.Q'�q&�{�M1*[?E_ �

range image segmented range image

}�KR\7AH?=*��[�C_ 2v¢v�XàQHUWA);/(W>�;=>�0j&1?f;OFW*pz U �o}l} -OM)-9;=*[Tp_ ��&7AH?D;=*,-OMh&@0 Yt&1AHKY-D*4�L;=>1?�&N>1QW( ��*,ILK.Q�q&�{�M1*,?,_ �

�� )�� w�� ¢�R�� ¡1¡ V

providessittablesurface

providesstablesupport

Output- Stage OneInitial Function

Verification Interaction

No DeformationFunctionality Confirmed

for Chair

(a) (b)

(c)

providesbacksupport

No DeformationFunctionality Confirmedfor Straight Back Chair

(d)

}�KR\7AH?=*b�,�W_ 2 � �i��?O&):<*E-O-OK.QH\�6vMN;=FH*�z U �o}l}�-OM)-9;=*[Tp_ ��&7AH?O;O*,-OMG&10KY|&7AHKY-D* �L;]>@?T& >@QW(S��*,ILK.Q�q&�{�M1*,?,_ �

¡ X � �� ! #"$"%"

AW-O*,-w;OFH*E-D*r*,+R*,T/*[QL;=-w;O&�:[&1QW-D;O?=AW:e;wK.QW()*[�)*,-�;=FW>�;n>@?=*#AW-D*E(i;O&y?]>@Q�&�&1?]()*,?�;OFH*�&16)89*E:e;3:,>�;O*,\1&7?OK.*,-,_m Q�KRQC()*<�:<&7QW-OK.-D;=-o&@0�>y0jAHQW:e;=KR&7QW>@+�*[+.*[T/*,Q7;nUH+.AW-nK�;]-3>1?O*E>y>@QW(I1&1+.AHT/*1_nkmFH&7-O*f:,>�;=*[\1&7?OK.*,-�;OFW>@;{q&1AH+Y(i6C*fKRT/Ug&7-=-DK.6H+.*�;O&yTX>�;]:]F'6W>1-O*,(i&7Qp;OFH*rK.QW()*[�iK.Q)0j&7?OTX>�;=KR&7Q'>@?=*#UH?OAWQH*,(i0j?=&1Tx;OFH*V-D*E>@?]:]F|_kmFH*B&@;OFW*[?]-f>1?O*y?]>@Q�&b&7?=(H*[?=*,(b0j&1?�0jAH?O;OFH*,?V*,I�>@+.AW>�;=KR&7Q|_�}W&1?V*,>1:]FZ:<+Y>1-=-rFvMvUC&1;OFH*E-DKY-[c�C?=-D;f*E>1:]F&@0mKR;=- &vQH&�{�+.*,()\7*VUW?OK.T/K�;=KRI7*,-�KY-#KRQvI7&%&1*E(';=&iT/*E>1-OAH?O*/FH&�{�{�*,+R+�>i0jAWQW:e;=KR&7QW>@+�*,+R*,T/*[QL;�0j?O&7T ;OFW*(H>@;=>7�H;=-mKR;=-w?O*E�7AWKR?=*[T/*[QL;]-[_ ��>7:]F�&vQH&�{�+.*,()\7*3UH?=K.TVKR;OK.I1*�?=*<;=AH?OQC-�>@Qi*[I�>@+.AW>�;=KR&7QBT/*E>1-OAH?O*7_�kmFW*,-O*>@?=*V;OFH*,QG:<&7T�6HK.QH*,(�;=&p0j&1?=T >/�WQW>1+�>1-=-D&):[K.>@;OK.&1QbTV*E>1-OAH?=*f;=FW>�;�(H*,-=:<?=KR6g*,-#FW&�{�{q*[+.+�;OFH*X{�FW&1+.*-O*<;r&@0q0jAHQW:<;OK.&1QN*,+R*,TV*,QL;=-�0j?=&1T ;OFH*y(H>@;=>pTX>�;]:]FH*,-n;=FH*yFvMvUC&1;OFH*E-DK�[[*E(�&76)89*,:<;�:[>@;O*[\7&1?=M1_y}�K.\1AH?=*�[�C_ 2v¢�-OFH&�{w-�>r;9MLUWK.:,>@+gKRQHUWA);�;=&�;=FH*nz U �3}�} -DM)-D;O*[Tpcv>@QW(�}uK.\1AW?O*f�[�W_ 2 � -DFH&�{w-�>rUg&1?O;OK.&1Qy&10|;OFW*0jAHQW:<;OK.&1QW>1+|?=*,>1-O&1QWKRQH\fKRQi;=FH*r>@QW>1+RM)-OK.-m&10t;=FW>�;o(H>@;=>W_�� p}HAHQC:e;OK.&1QC>@+|&76)89*,:<;m?=*,:[&1\7QHK�;=KR&7Q��&1QC-DKY()*[?l;9{q&�;=>16H+.*,-,�t&1QW*�{�K�;=FV�#+.*[\L-�>�;�;=FH*��r:<&7?OQW*[?]-�>1QW(f;OFH*o&@;OFW*[?�FW>JIvK.QH\r>nUC*E()*,-D;=>1+ _* FW>@;-OKRT/K.+.>1?OKR;OK.*,-#6g*<;9{q*[*,Qh;OFH*E-D*y;9{�&p;]>@6H+.*,-#{q&1AW+.(N>i0jAHQC:e;OK.&1QC>@+�&76)89*,:<;�?=*,:<&7\1QHKR;OK.&1Qh-OMv-D;O*,T AC-D*/;=&:<+Y>1-=-OK�0jMX;=FH*[T!6C&1;OF'>1-q;=FH*r-=>@T/*�&16)89*E:e; �

]_^-`�^-`�^ � f��j�� j � � " ��f�� fàQ/T/&7-D;�274 &16H89*,:e;�?=*,:[&1\1QWK�;=KR&7Qf-=:]FH*[T/*,-,c�;=FH*�T/&v(H*[+HKY-�>�-D*,UW>@?]>�;=*�*,Q7;=K�;9M�0j?O&7T�;OFW*!\@4 K.TX>@\1*E-�&@0;OFW*q&76)89*,:<;,_��w*[?=*q{�*q*<�H>@T/K.QH*�;OFH*qK.(H*,>o;OFW>@;�>1Q�&76)89*,:<;l:,>@Qr6g*m+R*E>@?=QH*,(#6vM#T/*[T/&7?OK�[[K.QH\�>wQvAHT�6g*[?&@0Z\14 K.T/>1\1*E-�&@0�KR;,�m?O*E:<&7\1QHKR;OK.&1QiK.-oUC*,?D0j&7?OT/*E(p6LMiTX>�;]:]FHKRQW\/;OFH*V-D*,QW-D*E(iKRTX>@\7*r&@0�>1Q'AHQ�&vQH&�{�Q&16H89*,:e;3;O&BKRTX>@\7*,-�K.Q�T/*,TV&7?OM7_K}36)89*E:e;3?=*[UW?O*E-D*,Q7;]>�;=KR&7QiKY- &1*[UH;n>�;o;OFH* z�� q��uwssvp(¤�p(s '�TX>�;]:]FHKRQW\yK.-()&7QH*#6vM�()K.?O*E:e;O+.MB:[&1T/UW>1?OK.QH\VKRQL;O*,QW-OK�;9MyK.TX>@\7*,-,_��wK.\1FH*,?�+R*,I1*[+d0j*E>�;=AH?O*E-[cWUC&L-O-OKR6W+RMX0j?=&1T!UW>@?O;=-m*[�v^;O?]>1:<;OK.&1Q|cv>@?=*�QH&1;�AW-O*,(�cv>@QC(/;OFvAW-�UC&L-O-OK.6H+RMf;OK.T/*<â:<&7QW-DAWTVK.QH\�>1QW(X:<&7T/UH+R*[�XUH?O&7\1?]>@T/T/KRQW\3;=FW>�;qK.-()K ?y:<AH+R;�;O&n;O*E-9;�KY-lQH&@;�QH*,*,()*E(�_��v*[I7*[?]>@+vUH?=&16H+.*[TX-�{�K�;=FV;OFHKY-�-DK.\1QC>@+v+R*,I1*,+H>@UHUH?=&7>7:]F�>@?=*m>1(H()?=*,-=-O*,(6g*[+.&�{#_�kmFH*y-OKRT/UH+.K.:[K�;9M�&@0w>@UWUC*E>@?]>@QW:[*<^�6W>1-O*,('?=*,:[&1\7QHK�;=KR&7Q�T/*[;OFH&)(H-#FC>JI1*X>@+.+R&�{q*,(�;OFW*[T ;O&'6g*;O?]>@K.QH*E(B>1QW(B;O*,-D;O*E(�&7Qp+.>1?O\7*n-O*<;]-m&@0lKRTX>@\7*,-m>@QC(i-O&1T/*�K.TVUW?O*E-O-OKRI7*3?=*,-OAH+R;=-mFW>JI7*36g*[*,Qp&16);]>@K.QH*,(�_�l*[?=FW>1UW-[cE;=FH*�T/&7-D;�K.T/UC&7?D;]>@QL;�?O*E-DAH+R;=-�FW>JI7*�6g*[*,Qf&76);=>1KRQW*,(f{�K�;=FfFvAHTX>@Qf0�>1:[*�?=*,:[&1\7QHK�;=KR&7Q|c�{�FHKY:]F{q*n{�K.+.+|AW-O*nFW*[?=*r>1-�>/:<+Y>@?=K�0jMvK.QH\V*<�H>@T/UH+.*1_

m :<&L>@?]-D*�()*,-=:<?=K.U);OK.&1Qi&@0l?O*E:<&7\1QHKR;OK.&1Q)^�6vML^�>1UHUC*E>@?]>@QW:[*�K.-o>1-q0j&1+.+.&�{w-[_� 4oAH?=K.QH\w>q;O?]>@K.QHK.QH\Wc,&1?|+.*,>1?OQHK.QH\Cc[UHFW>7-D*�>�(W>�;=>16W>1-O*l&@0v+.>16C*,+R*E(�KRTX>1\1*,-dKY-|:[?O*E>�;O*E(�_�� 7 � �� >�� {�FH*[?=*�� K.-q;=FH*1^ ;=FB;=?=>1KRQWKRQH\/K.TX>@\1*#>1QW(#7 � KY-�KR;=-m+Y>@6g*[+�_

� m QpAHQ�&vQH&�{�Qi&16)89*E:e;�KY-m?O*E:<&1\7QHK�[[*,(�6vM�:<&7TVUC>@?=KRQH\VKR;=-�K.TX>@\1*�� X;O&/;OFW&7-O*nK.QB;OFH*r(H>@;=>16W>1-O*>@QW(G>7-O-OK.\1QHK.QH\';=FH*�&76)89*,:<;f;=FH*�+Y>@6g*[+ 7 � &10�;OFH*p:<+.&7-O*,-D;r;=?=>1KRQHK.QH\�KRTX>@\7*�� _hkmFH*p:<+.&7-O*,-D;;O?]>@K.QHKRQW\VK.TX>@\7*��:[>@Qp6g*r()*{�CQH*,(p6vMy;=FH*rT/K.QHKRTfAHT ��AW:[+RKY()*,>1Qi(HK.-D;=>1QW:<*�� <(�� %�&1?m6vMy;OFW*#T/>@�)KRTfAHTx()&1;wUH?O&)()AC:e;�� 7cH6g&@;OFp&10u{�FHKY:]Fp{�*,?O*�()*{�CQH*,(iK.Q��FC>@U);=*[? ¡ _kmFH*,?O*#>@?=*1c)&10�:[&1AH?]-D*7cH:<&7TVUW+RKY:[>@;OK.&1QW-qK.Qi*E>1:]Fp-9;=*[Ui;OFC>�;wT�AC-9;�6g*r>1(H()?=*,-=-O*,(�_

� kt?]>@K.QHK.QH\NKRTX>1\1*,-�T�AW-D;�6g*�?=*[UH?=*,-O*[QL;]>�;OK.I1*'&10�;OFH*�KRQW-D;=>1QW:<*E-y&10r&16)89*E:e;=-y;OFW>@;i>1?O*p;=& 6g*?O*E:<&1\7QHK�[[*,(|_|àQ�;=FH*�:[>7-D*q&@0gFLAWT/>1Q�0�>7:<*E- � >@QW(fT/&7-D;�&@;OFW*[?l&16)89*E:e;]- �<c�;O?]>@K.QHK.QH\3TfAW-D;lK.QW:[+RAW(H*:]FW>@QH\7*,-�&10t*<�)UH?=*,-=-OKR&7Q|c1I�>@?=KY>�;OK.&1QXK.Q�+.K.\1FL;OK.QH\Wcv>@QC(y-DTX>1+R+g?O&1;=>@;OK.&1QW-�&@0�;OFW*oFH*E>1(XK.Q/\14�>1QW(214f_� kmFH*w&16H89*,:e;qT�AW-D;�6g*o{q*[+.+�^�0j?]>@T/*,(_'7;OFW*oUg&7-OK�;=KR&7Qy>@QW(y-OK�[[*w&10�>1+R+C0�>1:[*,-�T�AW-D;�6g*o?=&1AH\7FH+RMf;OFW*-O>1TV*7_Z}o;OFH*,?O{�KY-D*7cH>/-D*E>@?]:]F�&@0l-DK�[[*r>1QW(BUC&L-DKR;OK.&1QpUW>1?=>1TV*[;O*,?=-�K.-wQH*[*E()*,(�_

�� )�� w�� ¢�R�� ¡ XW�

� �vKRQC:<*r;=FH*VTV*[;OFH&)(�()&v*,-3QH&@;#-D*,UW>@?]>�;=*r&16H89*,:e;30j?O&7T56W>1:�&v\1?=&1AWQW(�cW6C>1:�&v\1?=&1AHQC(p{�KR+.+u6g*VKRQ)^:<+.AW()*,(BK.QB;=FH*r()*E:<KY-DK.&1QW-�>1QW(B;OFHKY-mT�AC-9;w6g*r:[>1?O*[0jAH+R+.M�:[&1QW-OK.(H*[?=*,(BKRQi;O?]>@K.QHK.QH\W_� ��I1*,Q�KR0C&7AH?lKRTX>@\7*,-l>@?=*m>1-l-DTX>1+R+)>1-m� � � �� c,{�FHKY:]F�KY-�-OA@?y:<K.*[QL;l0j&1?�0�>1:[*q?=*,:[&1\7QHK�;=KR&7Q|cJ;OFW*()KRT/*,QW-DK.&1Q�&@0|;=FH*n-OUW>7:<*o&10u>@+.+gKRTX>@\7*,-�K.-n� � � � � _|`�;�K.-�+RK�&1*,+RMV;=FW>�;q;OFH*�QvAHTf6C*,?�&10|;O?]>@K.QHK.QH\-O>1TVUW+R*E-fKY-XTfAW:]FP-OTX>@+.+R*,?V;OFW>1QZ;=FHKY-('m;=FLAC-[cm-D&7T/*iT/*[;OFH&)(P&@0 £w��xyp{��z�� u�s�� ~ & n�p�£wr� ~ � � �-DFH&7AH+Y(�6g*#AW-O*,(�_

* FHK.+R*�:<&7QL;OK.QLAWKRQH\Cc1;=FH*n?O*E>1()*,?�-DFW&1AH+Y(y:<&7QW-OK.()*,?�;=FH*3:,>1-O*o&10t()K.-=:<?=K.TVK.QW>@;OK.QH\�6g*<;9{q*[*,QX;9{�&f:<+Y>1-=-D*E-&@0�0�>7:<*E-$'�;=FH&7-O*o{�KR;OF�\1+Y>1-=-D*E-�>@QW(/;=FH&7-O*w{�KR;OFH&7A);�;=FH*[T4'v&1?EcL6C*[;9{�*,*[Qy:[>1?=-�{�K�;=Fy?]>1()K.&r>@QL;O*,QHQW>7->@QC(p;OFH&L-D*�{�K�;=FH&1A);n;OFW*[Tp_��q>1Qp;OFH*E-D*V()K��d*[?=*[QC:<*,-36g*f()*[;O*,:<;O*E(�>@T/&7QH\y>@+.+t;=FH*�&1;OFH*,?oI�>@?=KY>�;OK.&1QC-;OFC>�;o>@?=*nKR?=?O*,+R*,I�>@QL; �

*b*nQW&�{ 0j&):<AW-m&7Q�;=FH*#KRT/Ug&1?O;=>1Q7;mUH?=&16H+.*[Tx&@0u?=*,(HAW:<K.QH\f;OFH*#QvAHTf6C*,?q&10�-OKR\7QW>@+d0j*E>�;=AH?O*E-qAW-D*E(;O&�?O*,UH?O*E-D*,QL;�&1AH?�&16)89*E:e;=-,_l}H&1?�0�>1:[*w?O*E:<&7\1QHKR;OK.&1Q|c1K�;qFW>1-�6C*,*[Qy-OFH&�{�Q/;OFW>@;�()K.T/*[QW-OKR&7QW>@+.KR;9MV:,>@QX6g*?=*,()AW:[*,(V0j?=&1T � � � �B� � � ;=&�>1-�+RKR;D;=+R*n>1-�� ¡ M1*[;�-9;=KR+.+C-OAHUHUg&1?O;OK.QH\ Vv¢ � ?O*E:<&7\1QHKR;OK.&1Q/?]>�;O*E-[_��FW>1U);O*,?¡ ()KY-O:[AW-=-D*E(pAW-DK.QH\y()KR�d*[?=*[QL;o6W>7-D*E-m0j&1?�;=FH*�-OUW>1:[*#&@03T � � K.T/>1\1*E-[cW>1QW('-OFH&�{�*E(�FW&�{ >1Q'KRTX>@\7*:<&7AH+Y(B6g*#?=*[UH?=*,-O*[QL;O*E(�>7-w>/-DAHT!&@0lT/*,>@QWKRQH\10jAH+|K.TX>@\1*E-[cH-OAW:]Fp>1-�-D;O*,Ui*E()\1*E-[c)?=K.UHUH+.*1cH*[;=:@_�`�;w{q>7->@+Y-O&�-DFW&�{�QB;=FW>�;nKRTX>1\1*r*,QH*[?=\1Mi{q>7-l89AW-D;3;=FH*f-OAHT &@0�;=FH*f-=�LAW>@?=*,-�&10�;OFH*V:<&v*�?y:[KR*,Q7;]-w{�FH*,Q';OFW*K.T/>1\1*�{m>1-q?O*,UH?=*,-O*[QL;O*E(B>7-�>f+.K.QH*,>1?w:<&1Tf6HK.QW>�;=KR&7QB&10u&1?O;OFW&1QH&7?OTX>@+d6W>7-DKY-mK.T/>1\1*E-[_� �� 3A� 1 � � � � � 2 � � �B� �� 1 �&3A� 1 � �

�vAHUWUC&L-D*o0j&1?�;OFH*nUH?=*,-O*[QL;�;=FW>�;�>�-O*<;m&@0|&7?D;=FH&1QH&7?OTX>1+W6W>7-DKY-�K.TX>@\1*E-��:,>@Qy6g*o0j&7AHQW(�{�K�;=Fy;OFW*0j&1+.+.&�{�KRQH\/UH?=&1Ug*[?O;OK.*,-,_�7_ � � � 9 � 9 % 2 2 2 9 � � {�KR;OF � TfAW:]Fi-OTX>@+.+R*,?m;OFW>1Q � � T � � _\H_wkmFH*w>JI1*,?=>1\1*m�7AC>@+.K�;9Mf&@0�?O*,UH?=*,-O*[QL;OK.QH\n;OFH*3KRTX>1\1*w-O*<;�AW-OKRQW\#;OFHKY-�6C>1-OK.-�KY-�-=>�;=K.-D0�>1:<;O&7?OMrK.Q/;OFW*0j&1+.+R&�{�K.QH\/-D*,QW-D*7_Z}3I1*[?w>1+R+d;=FH* K.TX>@\7*,- ��#KRQi;=FH*�;O?]>@K.QHK.QH\X-D*[;,c){q*#FW>JI1*� �� 9 � D � � % 9�\ D 2 2 2GD � � � 9 � >@QW(�� %� � �� ( �� %�� %� � % � � _

� �� K.-�;OFW*�>1UHUH?=&J�)KRTX>�;=KR&7Qy&@0u&1?=KR\7KRQW>1+CK.TX>@\7* � � AW-OKRQH\X>f+RK.QH*E>@?�:<&7T�6HK.QW>�;=KR&7Q�&10H89AW-D;q;=FH* � 6W>1-OKY-K.T/>1\1*E-[_kmFH*�;=&1Up?O&�{�&@0�}�KR\7AH?=*X�[�W_ 2%VV-OFH&�{w-�-DKR��;=?=>1KRQWKRQH\XK.TX>@\7*,-q0j?=&1Tx&7QH*#&@0�TX>@QvMBKRQW(HKRIvKY()AW>@+Y-�K.Q;OFW*w(H>�;]>@6W>7-D*qTX>1()*�>JI�>@K.+.>16H+.*�6vM#;=FH*9*�*,Kv[,TX>@QHQ/àQW-D;OKR;OA);=*1_�kmFH*mT/K.(W()+R*�?=&�{G&10C;=FH*O�W\1AW?O*m-DFW&�{w-0j&1AW?n6C>1-OK.-�K.TX>@\1*E-w;=FW>�;rFC>JI1*�6g*[*,QN()*[?=KRI7*,(0j&1?�?O*,UH?=*,-O*[QL;OK.QH\y;=FHKY-#-D*[;�&10�0�>7:<*,-)'|;=FH*/+R*[0 ;OT/&7-D;#K.-;OFW*rT/*,>@Q'&10�>@+.+|;O?]>@K.QHK.QH\y-=>@T/UH+.*,-,_qkmFH*�6C&1;D;O&7T!?=&�{ &@0l;OFH*��W\1AH?=*�-OFH&�{w-mFH&�{ ;OFW*r&1?=KR\7KRQC>@+|-OK��0�>1:[*/KRTX>@\7*,-3{�&7AH+Y(�>1UHUC*E>@?n{�FH*[Qb?=*[UH?=*,-O*[QL;O*E(�>7-n>B+.KRQH*E>@?#:<&7T�6HK.QW>@;OK.&1Q�&10t89AW-D;�;OFH*V0j&7AH?#6W>1-OKY-I1*E:e;=&1?]-[_ �v*,I1*[?]>@+�()K��d*[?=*[QL;V?O*E-D*E>@?]:]F�UH?=&@89*E:e;]-rFW>JI7*y-DFH&�{�Qh;=FW>�;VUC*,?OFC>@UW- � � � ¡ &7? � � \ �6W>7-DKY-�K.TX>@\7*,-�>1?O*B-DA@?y:[KR*,Q7;V;O&�?O*,UH?=*,-O*[QL;f>�(W>�;=>16W>1-O*y&10w0�>1:[*�K.T/>1\1*E- �j*7_ \C_b2 � � � 0�>1:[*�K.T/>1\1*E-K.Q&1QH*f&@0��l*,Q7;=+.>1QW(�6 -o-D;OAW(HKR*E- �<c|-D&X;=FW>�;n;OFW*f>JI1*,?=>1\1*r>1UHUH?=&J�vK.TX>�;=KR&7Qi&10 � �� KY-o{�KR;OFHK.Q ¡�� &@0 � � _kmFH*,?O*[0j&1?=*1c@TX>�;]:]FHK.QH\#AW-OKRQH\n;=FH*o>@UWUH?O&J�)K.TX>�;OK.&1Qf{�KR+.+WMvK.*[+Y(/>@+.TV&L-9;l;=FH*o-=>@T/*m?O*E-DAH+R;=-�>1-�TX>�;]:]FHK.QH\AW-OKRQW\�;=FH*'&1?=KR\7KRQC>@+qKRTX>@\7*1_G`�;XKY-/KRT/Ug&1?O;=>1Q7;V;O&h*,TVUWFW>1-OKv[,*�;=FW>�;/0j&7?/;OFH*'(H>@;=>@6C>1-O*�K.+R+.AW-D;O?]>�;O*E(6vMB}�K.\1AH?=*X�[�C_ 2$VHc�� 2 � � �� 1 ��3A� 1 � �B�� 3 ��3A� � � � � 0 � � ��

�� 3 � � �7c1{�FHKY:]Fy*[QC>@6H+.*,-�*�?y:<*,Q7;m:<&7TVUC>@?=K.-O&1Q/{�KR;OF�AWQ�&vQH&�{�QXKRTX>1\1*,-,_l��?=&�ILKY()*E(�;=FW>�;�;OFH*o0j&1AH?6W>7-DKY-mI1*E:e;O&7?=-�>1?O*#-=>JI1*E(yK.QiT/*,TV&7?OM7cW>/:<+.&7-O*#>@UHUH?=&J�)KRTX>@;OK.&1QB;O&V;OFH*�&1?=KR\7KRQW>1+g0�>1:<*#K.TX>@\7*�:,>@Qp6g*?=*[\1*,QH*[?]>�;=*,(B{�FH*[Q'QW*[*,(H*,(�_ � � &@;=*#;OFW>@;w;OFW*��W?]-9;w6W>7-DKY-�I7*,:e;=&1?wKY-�;=FH*rT/*,>1Qp&@0l;OFH*�&1?=KR\7KRQW>1+d0�>1:[*

¡ X¢\ �� ! #"$"%"

}�KR\7AH?=*y�[�C_ 2$VH� � kt&7U?=&�{ �9�vK��p;=?=>1KRQHK.QH\yK.TX>@\7*,-m0j?=&1T &1QH*f&@0�TX>@QvMiKRQW(HKRIvKY()AW>@+Y-3KRQ>y0�>1:<*�KRTX>@\7*(H>@;=>@6C>1-O*%' �jT/KY(H()+.*V?=&�{ ��>JI7*[?]>@\1*�;=?=>1KRQWKRQH\BKRTX>1\1*f>1QW(';=FH?=*[*�T/&L-9;#-DK.\1QWK �C:,>@QL;3*,KR\7*[QvI1*E:e;=&1?]-w()*<^?=KRI7*,(i0j?=&1T ;OFH*V-O:,>�;O;O*[?nTX>�;=?OKR�_' ��6C&1;D;O&7T ?O&�{ ��KRTX>@\7*,-o&@0�;OFW*r;O&7U?=&�{ ?=*[UW?O*E-D*,Q7;=*,('>7-o>y+.K.QH*,>1?:<&7T�6HK.QW>@;OK.&1Qh&@0�&1QW+RM�;OFH*X0j&7AH?rK.TX>@\1*E-#K.Qh;OFH*yT/KY(H()+.*y?=&�{#_��4n>�;]>@6W>7-D*X&10�KRTX>@\7*,-r:[&1AH?O;O*E-DM�&@0��>@*,+|%'&7-O*,-,c)UH?=&):<*,-=-O*,(BKRTX>@\7*,-m:<&7AH?O;O*,-OMy&10�7&1FHQ/*�*,QH\W_ �

-O*<;o>@QC(�QH&1;o>1:<;OAW>1+R+.My&1QW*n&10t;=FH*#&1?O;OFH&7QH&1?=TX>@+�-O*<;,_ �

� � 3A� �� 1 � 2 � � � � � � �&3A� 1 � �

��)KY-9;=*[QW:[*r&@0�;=FH*V6W>1-OK.-3-D*[; � >@+.+.&�{w-w\1?=*,>@;3:<&7T/UH?O*E-O-OK.&1Q'K.QT/*[T/&1?=Mi>1QW(�-OUg*[*,(HAHUK.Q�:<&7TVÛHA);]>�;=KR&7QW-�6C*E:[>1AW-D* � KY-3TfAW:]Fh-DTX>@+.+.*[?3;OFW>1Q �Nc|;OFH*/QvAHT�6g*[?�&10�UHKR�)*[+Y-�KRQ�;OFH*/&7?OK.\1K.QW>@+�K.T/>1\1*7_kmFH*/6W>7-DKY-nKRTX>@\7*,-:9 � >1?O*/:[>1+R+.*,( � n�� {� � uws � x � � ��p{� ~ z &@0�;=FH*X-D*[;#&@0�;=?=>1KRQHK.QH\p-O>1T/UH+R*E-[_ m +.\1&1^?=K�;=FHT �$X�6C*,+R&�{�-�&1*[;=:]FH*E-�?=*,:[&1\7QHK�;=KR&7Q)^�6LMLâ>@UHUg*,>1?=>1QW:<*/AW-OK.QH\�;=FH*,-O*iUH?OK.QW:[KRUW>1+�:<&1T/Ug&1QH*,QL;=-,_N`�;FW>7-w;9{q&yUW>1?D;]-[��>@Q�& � KRQW*r;O?]>@K.QHK.QH\yUHFC>1-O*f>@QC('>@Q&7QH+RK.QH*f?O*E:<&1\7QHKR;OK.&1Q'UHFW>7-D*7_3kmFH* �W?]-9;�-9;=*[UK.Q;OFW*�;O?]>@K.QHKRQW\fUHFC>1-O*nKY-q;O&X:[&1T/UHA);=*�;OFH*�T/*,>1QB&10u;=FH*n;O?]>@K.QHKRQW\VK.TX>@\7*,-m>@QW(BAW-O*n;OFH*,T�;O&/UH?=&)()AW:[*>p-D*[;��&10q()KR�g*,?O*,QW:<*/K.TX>@\1*E-[ct*,>1:]F�6C*,KRQW\B;=FH*y()KR�g*,?O*,QW:<*/&10m>B;O?]>@K.QHK.QH\iKRTX>@\7*V0j?O&7T ;OFH*/T/*,>1QK.T/>1\1*7_y`�0�{�*/;=FHKRQ�&�&@0�*E>1:]Fh()K��d*[?=*[QC:<*XK.T/>1\1*�� w>7-#>pI1*E:e;O&7?#&@0 � *[+.*[T/*[QL;]-[c��6g*,:[&1T/*,-r>1Q>@?=?]>JMf&10 � ?=&�{w-q>@QW( :<&7+RAWTVQC-[_�kmFH*�QH*[�L;�-D;O*[UiKY-q;O&/:<&1T/UHAH;O*n;OFH*#:[&�IJ>1?OKY>@QC:<*wTX>�;=?OKR��&@0;OFW*r;O?]>@K.QHK.QH\XK.T/>1\1*E-[_m�qMi()*(�WQHKR;OK.&1Q|c� � �tKY-�;=FH*�I�>@?=KY>@QW:[*#&@0l;OFH*� � �UHKR�v*,+ cg{�FHK.+R*�� K.-;OFW*n:[&�IJ>1?OKY>@QC:<*w&10�;OFH*� � ��>1QW( � �BUHKR�v*,+.-,cL&�I1*[?q>@+.+g;OFH*3;O?]>@K.QHK.QH\�K.TX>@\1*E-[_��vK.QW:<*n{q*oFW>JI7*3>@+.?=*,>1(HM

�� )�� w�� ¢�R�� ¡ X72:<&7T/UHA);O*E(B;OFH*#T/*,>1Qi>1QW(p()KR�g*,?O*,QW:<*�K.T/>1\1*E-[cv;=FH*r:<&�I�>@?=KY>@QW:[*oTX>�;=?OKR��KY-w()*{�CQH*,(i6vM

�� 9�[�C_ ¡ �kmFH*X-OKv[,*f&10�;OFWK.-#:[&�IJ>1?OKY>@QC:<*�TX>@;O?=K��KY-�I1*,?OM'+Y>@?=\1*7c � � �Nc|{�FW*[?=* ��K.-n;=FH*/QvAHT�6g*[?�&@0qUHKR�v*,+.-K.QZ>@Q KRTX>@\7*1cl;9MvUHKY:[>1+R+.M \ ¡ X � \ ¡ X'&1?f*[I1*,Q ¡ ��\ � ¡ �W\H_ �v&�;OFH*p:<&7TVUWA);=>@;OK.&1QG&10w*[K.\1*[QvI7*,:e;=&1?]->@QC(X*[K.\1*,QLI�>1+RAH*E-�K.QX;OFW*3QH*[�v;q-D;O*[U�&@0�;OFW*n>1+R\7&1?=K�;=FHT�{q&1AW+.(/6g*3*[�v;O?=*[T/*[+.M�;=KRT/*[^�:[&1QW-OAHT/KRQW\�KR0 � �{q*[?=*�AW-O*,(�()KR?=*,:<;O+.M1_ � �v*[*�� rtxyp(n�� Tu�s �!p� {� � p{z �� 0j&7?3;=FH*/UH?=KRQW:[KRUC>@+l:<&1T/Ug&1QH*,QL;=-�>@+.\1&7?OKR;OFHTp_ �àQW-D;O*E>1(�c){q*r:[>1Qi:[&1T/UHA);=*r>f?=*[+Y>�;=*,(BTX>�;O?=KR� � ;� \1K.I1*[Qi6vM

� ;� � � � � �9�[�C_ X �{�FHKY:]FyKY-�T�AC:]F�-DTX>1+R+.*[? � ��% �e_vkmFH*3*[K.\1*[QvI7*,:e;=&1?]-�>@QW(y*[K.\1*[QvI�>@+.AH*E-�&@0 � ;� >1?O*o?O*,+.>@;O*,(V;=&#;OFW&7-O*&@0 ��h>1-q0j&7+R+.&�{w-[�

� � 9 � � 9 �9�[�C_ ¢ �� ;� 9 ; � � 9 ; �9�[�C_ � �

9 � � � 9 ; �9�[�C_ V �{�FH*,?O*��pKY-m;=FH*rI1*E:e;=&1?�&@0l*[K.\1*,QvIJ>1+RAW*,-m&@0 ��c9�KY-m;OFW*#I1*,:<;O&7?�&@0l*[K.\1*[QvI7*,:e;=&1?]-q&@0 ��cC>1QW( 9 ; K.-;OFW*#I1*,:<;O&7?q&10�*,KR\7*[QvI1*E:e;=&1?]-�&10 � ;� _

kmFH*VT/*<;OFW&v(W-3&10�UH?=KRQC:<K.UW>@+l:<&7TVUg&1QW*[QL;=-�>@QC>@+.Mv-OKY-o()KY-O:[AW-=-D*E(FH*,?O*fFW>JI1*fUH?O&)()AC:<*,(�-D&7T/*�K.TfÛH?=*,-=-DK.I1*p?=*,-OAH+R;=-/K.QS0�>1:<*'?=*,:[&1\7QHK�;=KR&7Q � :<&1QC-DAH+R;y;=FH*'?O*[0j*[?=*[QW:[*,-/6vMZ��K.?=6LMZ>@QW( �vK.?O&�IvKR;=:]F|cmkuAH?�&>@QC(i�l*,QL;O+Y>@QW(�cC>@QW(S�v{q*<;]-w>@QW(4*b*[QW\ �e_O�#&1*,U);OKY:[-wTVK.\1FL;3>1?O\7AH*n;OFW>@;�;OFHKY-wT/*[;OFH&)(pKY-�AHQH+.Kv&7*[+.My;=&{q&1?T&r0j&1?�KRTX>@\7*,-�{�KR;OFB-DK.\1QHKv�C:,>@QL;�FHK.\1F/0j?=*,�LAH*[QC:<MVIJ>1?OKY>�;=KR&7QW-�6g*,:,>@AW-O*o>@AH;O&):<&7?O?=*[+Y>�;=KR&7Q�{�K.+R+d()?=&1U0�>1-D;�{�K�;=Fb-OTX>@+.+l-OFHKR0 ;=-nK.Q�;=FH*fK.TX>@\7*�;=FLAC-n-D;O?=*,-=-OKRQH\�;OFH*V&16H89*,:e;n0j?]>@T/KRQW\B?=*,�LAHK.?O*,T/*[QL;,_r��K.:<;OAH?=*0jAHQW:<;OK.&1QW-�0j&7?�0�>7:<*,-�()&VQH&@;�0�>1:<*o;OFHKY-qUH?=&16H+.*[Tp_��v{�*[;=-m>@QC(y*�*,QH\�FC>JI1*o-OFH&�{�Qy\7&L&)(X?=*,-OAH+R;=-�{�K�;=FTX>@QvM��AHQL;O*[�L;=AH?=*,( �w&16)89*E:e;=-w&@;OFW*[?w;=FW>@Qp0�>7:<*E-w>1-�FC>JI1*r%'AH?]>1-O*r>@QC( � >JM7>1?,c){�FW&y{�*,?O*r>7:e;=AW>@+.+RM>@6W+R*V;O&pK.QL;O*[?=Ug&1+Y>�;O*X274�&16)89*E:e;rUg&7-O*f;=&'>@Qh>1:[:[AH?]>1:<M'&10�;9{q&'()*[\7?O*,*,-nAW-OKRQH\'>B;O?]>@K.QHK.QH\i6W>1-O*/&@0K.T/>1\1*E-q;=>�&7*[QiKRQp-D;O*[UC-�&@0u;O*[Q'()*,\1?=*[*E-[_kuAH?�&B>@QW(i�l*[QL;O+Y>@QC(�\L>JI1*�-D&7+RA);=KR&7QW-q;O&V;9{q&/&@0�;OFH*#UH?=&16W+R*,T/-mQW&@;O*E(p>@6g&�I1*1_�}�K.?=-D;,cv;=FH*[MBAW-D*E(T/&@;=KR&7QG;O*E:]FHQHKY�LAH*,-,c�>7-fK.QS��FC>@U);=*[?yVHc�;O&h-D*,\1T/*[QL;V;OFH*pFH*E>1(N0j?=&1T�>�IvK.(H*[&h-D*E�7AW*[QW:[* ' ;=FHK.-*[QC>@6H+.*,(V;=FH*[T�;=&#0j?=>1T/*�;OFH*o0�>1:[*3>@QC(X>@+Y-D&#;=&rQH&7?OTX>@+.K�[[*wK.TX>@\1*3-DK�[[*7_�v*E:<&7QW()+.M1c7;OFH*,MV?=*[{q*[K.\1FL;=*,(;OFW*wKRTX>1\1*mUHKR�v*,+.-�6vM��W+R;O*,?OK.QH\#{�KR;OFy>�6H?=&7>7(Vz�>1AW-O-OKY>@QV;OFW>@;�()?=&1UHUg*,(V;=FH*�UC*,?OK.UHFH*,?=>1+H6W>7:�&L\7?O&7AHQW(UHKR�)*[+Y-q;O&XQH*E>@?9[[*,?O&V{�FHK.+R*#UW?O*E-D*,?OIvK.QH\�;=FH*#K.TVUg&1?O;=>1QL;�:[*[QL;O*,?m0�>1:[*nK.QL;O*,QW-DKR;OK.*,-,_

¡ X1� �� ! #"$"%"

%�� 1 � 2�� !àQHUHAH;o>V-O*<;�y&@0 +Y>@6g*[+.*,(�;O?]>@K.QHKRQW\VK.TX>@\7*,-�>@QC(�UH?=&)()AW:[*>V6W>1-OKY-�-D*[;��>1QW(p>VI1*,:<;O&7?q&10l:[&v*�?y:<*,Q7;]-q0j&1?�*E>1:]FiKRTX>@\7*1_� � � � � � % 2 2 2 � � � K.-m;=FH*r-O*<;w&@0u;O?]>@K.QHK.QH\/KRTX>@\7*,-,_��jK.QHUHA); �� 9 � 9 % 2 2 2 9 � � K.-q;=FH*r-D*[;w&@0�6W>1-OK.-mI7*,:<;O&1?]-,_ ��&1A);=UHA); �$ �1� � � � � � % 2 2 2 � � � �tKY-m;OFH*#I7*,:<;O&1?m&10�:<&v*&?X:[KR*,QL;=-m0j&7?�KRTX>@\7*��1_ �j&7A);OUHAH; ��7_�� A � � �� <_\H_ �-� � � � � � �4� � �`( � � � A � � c);OFW*r-D*[;m&10l(HK��d*[?=*[QW:[*�KRTX>@\7*,-2W_ � � �s;OFH*r:[&�I�>@?=K.>1QW:<*3T/>@;O?=K��i&16);]>@K.QH*,(�0j?=&1T �3_

�C_ �o-O*;OFW*�UH?=KRQC:<K.UW>@+�:<&7TVUg&1QW*[QL;=-�TV*[;OFH&)( ;O&Z:[&1T/UHA);=*�*,KR\7*[QvI1*E:e;O&7?=-X>1QW( *,KR\7*[QvI�>@+.AH*,-�&@0� � _ ��-O*[*�;=*<�v; �

¡ _3��&1QW-D;O?=AW:e;V;OFW*iI7*,:<;O&1? � >7-V;OFH*p6W>7-DKY-/-D*[;/6vM -O*[+.*,:<;OK.QH\�;OFH*'T/&7-D;y-DK.\1QWK �C:,>@QL; � *[K.\1*[QHÎ1*,:<;O&7?=-)'n-D;=>1?D;i0j?=&1T�;OFH*b+Y>@?=\1*,-D;B*,KR\7*[QvI�>@+.AH*�>1QW( :[&1QL;OK.QvAH*�K.Q�()*E:<?=*,>7-DK.QH\ &7?=(H*[?�&10r;OFW**[K.\1*[QvI�>@+.AH*E-�;=&X-D*,+R*E:e;�;OFW*r:<&1?=?=*,-OUC&7QW()K.QH\f*,KR\7*[QvI1*E:e;=&1?]-[_

XW_-U�*[UH?=*,-O*[QL;G*E>1:]F�;O?]>@K.QHK.QH\ K.T/>1\1* �� 6vM�>�+.KRQH*E>@? :[&1Tf6HKRQC>�;OK.&1Q�&10';OFH* 6C>1-OK.- I1*,:<;O&7?=-,�� 9 � D � � % 9 % D 2 2 2 D � � � 9 �

% 0 �� B� 1 � � � � 2�� !àQHUHAH;�;OFH*r-O*<;w&10u6W>7-DKY-mI1*E:e;O&7?=-��c);OFH*r(W>�;=>16W>1-O*�&@0l:<&v*�?y:<K.*[QL;o-O*<;]- ��$ � � c>@QC(B>V;=*,-D;wKRTX>@\7* � � _ }3AH;OUHA);�;=FH*r:<+Y>1-=-m+Y>@6g*[+|&10 � � _�7_3��&1T/UHA);=*nI7*,:<;O&1?�&10�:[&L*&?y:<K.*[QL;=- $ � � � � � � � % 2 2 2 � �� |0j&1?�� '\H_w}uK.QW(B;OFW*��iQH*,>1?O*E-9;�QH*,KR\7FL6g&1?]-q&@0lI1*E:e;O&7? $ � K.Qi;OFH*r-O*<;�� $ � � '2W_w4o*E:<KY()*�;OFH*r:[+.>7-O-q&10 � � 0j?O&7T�;OFW*#+.>16C*,+.-m&10t;OFW*��pQH*,>1?O*E-9;�QH*,KR\7Fv6C&7?=-

�jUg&7-=-DK.6H+.My?O*D89*,:<;wKRQp:[>7-D*�QH*,KR\7FL6g&1?]-m>@?=*n0�>@?�&1?�K.QW:[&1QW-OK.-D;O*,QL;mK.Qp+.>16C*,+.- ��'

/ 0�1 � � ��2�3 � � ! U�*E:<&1\7QHKR;OK.&1Q)^�6vM7^ m UWUC*E>@?]>@QW:[*oAW-OKRQW\y>V�m>7-DKY-q&@0��?=KRQW:[KRUC>@+t��&1T/Ug&1QH*,Q7;]-[_

�� )�� w�� ¢�R�� ¡ X ¡�� }36);]>@K.Q�>P-D*[;i&10�� 0�>1:[*�K.TX>@\1*E-B>1QW( � � +Y>@QW(W-O:,>@Ug*,-i-DAW:]F ;OFW>@;>@+.+nK.TX>@\7*,-BFW>JI1*�;OFH*N-=>@T/*()K.T/*[QW-OKR&7QW- T � � _��&1T/UHA);=*w;=FH* ��AC:<+.K.()*E>@Qy()KY-D;=>@QC:<*o6g*<;9{q*[*,Qy>@+.+WUW>1KR?]-�&10�KRTX>@\7*,-�>@QW(X()KY-OUH+.>JM;OFW*3()KY-9;]>@QW:[*,-�KRQ�>7\ � � \ � AHUHUg*[?�;=?OKY>@QW\1AH+Y>@?�TX>@;O?=K��_�4o&r;OFH*o0�>1:<*E-�:[+RAW-D;O*,?�:[+R&L-D*�;=&1\7*<;OFW*[? � kmFW*+Y>@QW(H-=:[>1UC*E- � * FC>�;mK.-q;=FH*�?=>@;OK.&�&@0t;OFH*#:<+.&7-O*,-D;q;O&f0�>@?O;OFH*E-9;�()KY-9;]>@QW:[* � `9-�;OFW* ��AW:<+.KY()*,>1Q�()KY-9;]>@QW:[*UH?=&1T/KY-DK.QH\V0j&1?�?=*<;=?OK.*[I�>@+g0j?=&1Tx>1QpKRTX>@\7*#(H>�;]>@6W>7-D* � ��)UH+.>1KRQt_

�� Y|*[; � � 6g*�>@QNK.TX>@\1*�&@0w>@QNAHQ�&LQW&�{�QN&16)89*E:e;f>1QW(h+R*[;�� 7 � � 6g*B>-O*<;f&@0�+.>16C*,+R*E(;O?]>@K.QHK.QH\VKRTX>@\7*,-,_ m -O-OAHT/*3;OFW>@;�>1+R+dK.TX>@\1*E-�>1?O*3QH&1?=TX>@+.Kv[,*,(B-D&�;OFW>@;"�� $�%� ��7_��>�� vFH&�{ ;OFW>@;�� ( � � �%�HK.-�T/K.QHK.TVK�[[*E(p{�FH*[Q � � �� KY-�TX>��)KRT/K�[[*E(�_ ��6 ��)UH+Y>@K.Qi{�FLM�;OFH*�?O*E-DAH+R;wKY-�QH&@;�;=?OAW*{�KR;OFH&7A);�;OFH*r>7-O-OAHT/U);=KR&7Q�;=FW>�;o>1+R+�K.TX>@\1*E-mFW>JI1*nAHQHKR;3-OKv[,*1_

� �B� � � �� 3 �� @� �� -�� 5�� 2+��*� � 3,� �

kmFH*�T/*<;=FH&)(H-�&10gUH?=K.QHKRUC>@+W:[&1T/UC&7QH*[QL;]-�>@QW>1+RM)-OK.-�>1+R+.&�{Z>#-OAH6W-OUW>7:<*m&@0g;O?]>@K.QHK.QH\#UW>�;O;O*,?OQW-�;O&#6g*?=*[UH?=*,-O*[QL;O*E(XK.Qi>V:<&7TVUC>1:e;�0j&1?=Tp_lkmFW*n6C>1-OK.-�;OFW>@;�6C*E-9;�?=*[UH?=*,-O*[QL;=-�;OFH*n;=?=>1KRQHK.QH\/(H>�;]>Hc):<&7T/UHA);O*E(>1-�>@6g&�I1*1cuFW>1-�6C*,*[QG:,>@+.+R*E(�;=FH*B-O*<;r&10 x � z ~ pT¥ � n�p{zTz��¤wp �{p�u ~ rtn�p�z �� z�� _'kmFH*�{�&7?�&�&@0��1&7FHQ*b*[QH\iFW>1-�()*,T/&1QW-D;O?]>�;=*,(p;=FW>�;#{�FHK.+R*f;OFW*fT/&7-D;�*<�)UH?=*,-=-DK.I1*�0j*,>�;=AH?=*,- n�p � n�p{z{p(� ~�;=FH*X-DAH6C-DUW>7:<*f&@0;O?]>@K.QHK.QH\nKRTX>@\7*,-u&1U);=KRTX>1+R+.M1c�;=FH*[M�QH*[*E(rQH&1;l?=*[UW?O*E-D*,Q7;�{�*,+R+v;=FH* £w� �!p(n�p(� �p{z � p ~�� p�p(�R��x�u)q$p{z K.Q/()K�0 ^0j*[?=*[QL;�:<+Y>1-=-D*E-[_�*b*[QH\/K.Q7;=?O&)()AC:<*,(y;OFH*nAW-O*3&10t;=FH* x � z ~ £w� z( {n��x �� u ~ ��#q!�{p�u ~ rtn�p{z �� z�� c){�FHKY:]F:[>1Q'6C*V()*[?=K.I1*,(i0j?=&1T ()KY-=:<?=KRT/K.QW>@QL;3>1QW>@+.M)-DKY-[_�%4n}l-30j&v:[AW-w&7QK.T/>1\1*rI�>1?OKY>@QW:[*�;OFW>@;n:,>@Q()KR�g*,?D^*[QL;=K.>@;O*r&76)89*,:<;=-�K.Q()KR�g*,?O*,Q7;�:<+Y>1-=-D*E-[_q}�KR\7AH?O*��[�W_ � � :[&1QL;O?]>1-D;=-�% ��}l-w{�KR;OF%4n}l-[_wkmFH*�&1?=KR\7KRQW>1+(H>@;=>�:[&v&1?]()KRQC>�;O*E-�>1?O* � � � �� % �<_ � � K.-�;OFH*#()K.?=*,:e;=KR&7Qy&@0uT/>@�)KRTfAHT�IJ>1?OKY>@QC:<*3>1QW( � % KY-�&7?D;=FH&1\7&1QW>1+;O& � � ');=FLAC-[cW:[&v&1?]()KRQC>�;O*E- � � �� % >@?=*#% ��}l-,_�kmFH*#&1?=K.\1K.QW>@+�:<+Y>1-=-O*,-m&@0�I1*E:e;O&7?=-�>1?O*�?=*[UH?=*,-O*[QL;=*,(y6vM;OFW*X*[+.+RK.UW-O*,-�{�KR;OFhTX>�89&1?#>1QW(�T/K.QH&1?r>@�)*,-�>@+.KR\7QH*,(�{�KR;OF � � �� % _ ��U�*,:,>@+.+l;OFW>@;#>1Qb>1+R\7&1?=K�;=FHT 0j&7?�WQW(HKRQH\i;=FH*,-O*X>��)*,-nK.Q�;=FH*�\@4�:,>1-O*f{m>1- �W?]-9;#UH?=*,-O*[QL;=*,(K.QG��FW>@U);=*[?r2W_ � kmFH?O*E-DFW&1+Y(H-n&1Q�*,K�;=FH*[?� � &1? � % (H&fQH&1;q()KY-=:<?=KRT/K.QW>�;=*3{q*[+.+C6g*<;9{q*[*,Qy;=FH*o;9{q&f:[+.>7-O-O*,-,_u%�43}G>@�)*,- � � � % cH:[&1T/UHA);=*,(/0j?=&1T()KY-O:[?OK.T/KRQC>@QL;q>1QW>@+.M)-DKY-[cv>@+.+.&�{ UC*,?D0j*E:e;�-D*,UW>@?]>�;=KR&7QX&@0|;=FH*o;=?=>1KRQWKRQH\V-O>1T/UH+R*E-�6C>1-O*,(y&7Q�>�;OFH?=*,-OFH&1+Y(&1Q6� � _

m -O*,:<&7QW(VKRT/UH?=&�I1*,T/*[QL;�TX>1()*�6vM *b*[QW\�>@QW(VFHKY-�:[&1+.+R*E>@\7AH*,-�;=&�;OFH* � *[K.\1*,QW-DUC>1:<*m?=*,:[&1\1QWK�;=KR&7Q)^6vML^�>1UHUC*E>@?]>@QW:[*,�y>1UHUH?=&7>7:]FK.-3;=FH*y()*[I7*[+.&1UHT/*,Q7;�&@0q>i-O*,>1?=:]F;O?=*[*/:<&1QC-9;=?OAW:<;OK.&1Q�UH?O&):[*,()AH?=*f;OFW>@;UH?=&�IvK.()*E- � � � � % � �q-D*E>@?]:]FX;OK.T/*n0j&1?O�WQW(HKRQH\V;=FH*�QH*,>1?O*E-9;mQH*[K.\1Fv6g&1?]-�K.Qp>V(W>�;=>16W>1-O*o&10 �G;O?]>@K.QHK.QH\-=>@T/UH+.*,-,_HU�*E:[>@+.+L;OFW>@;�()*,:[K.-OKR&7Q�;=?O*,*,-u0j&1?l&76)89*,:<;l:[+.>7-O-OK �g:[>�;=KR&7Qr{q*[?=*�K.QL;O?=&v(HAW:<*E(rK.QX��FW>1U);O*,?l�W_ m ;*,>7:]FX()*,:[K.-OKR&7QfUg&1K.QL;�K.Q/;OFH*�;=?O*,*1c1>1QXAHQ�&vQH&�{�Q/K.T/>1\1*mKY-�UH?=&@89*,:<;O*E(f&7QL;O&�;OFW*wT/&7-D;�()K.-=:<?=K.TVK.QW>@;OK.QH\-OAH6W-OUW>1:[*nQW*[*,(H*,(B;O&XTX>�&7*#>V(H*,:<KY-OKR&7QB&7Qi{�FWK.:]Fp6H?]>@QW:]Fi&1?�6W?=>1QW:]FH*,-�;=&/;=>�&7*�QH*<�v;,_�kmFH*r%4n}�-AW-O*,(i>�;w()KR�g*,?O*,QL;wQH&)()*,-mK.Q�;=FH*r()*E:<KY-DK.&1Q�;O?=*[*�I�>@?=My{�K�;=F�;=FH*�;O?]>@K.QHK.QH\/-O>1TVUW+R*E-q0j?O&7T�{�FHKY:]F�;=FH*[M{q*[?=*r()*[?=KRI7*,('>1QW('>@?=*�;OAHQW*,(p;=&X;OFH*fUW>@?O;OKY:<AW+.>1?o-DUW+RKR;D;=KRQH\B()*,:[K.-OKR&7QW-�;=FW>�;�>@?=*#QH*[*E()*,(|_�`�;oK.-36g*,-D;0j&1?r;OFH*BKRQL;O*,?O*E-9;=*,(b?=*,>1(H*[?#;=&:<&1QC-DAH+R;r;=FH*y?=*<0j*[?=*[QC:<*,-#;O&&76);=>1KRQhT/&1?=*y()*<;]>@K.+.-�&1Qh;=FHK.-�?O*E:<*,Q7;=+RM()*,I1*[+.&1Ug*,(�;OFW*[&1?=M1_

¡ X$X �� ! #"$"%"

1Y

2Y

X1

X2

1Z

2Z

----- -

------- -- --

--- ---- - - --

---- -- -

----

--- -

-

-

-

--

--

- -- -

- - - - - --

--

--

--

--

----

-

-----

-

+++ ++ + +++++++++++

---

--

-

--

- --

--

-- -

---

--

which separatesMDF value

MDF vector

MEF vector

No MEF value canseparate the twoclasses

the classes

}�KR\7AH?=*i�,�W_ � � ��kmFW*XTV&L-9;r*[�)UH?O*E-O-OK.I1*V0j*,>@;OAH?=*,-#()*[;O*,?OT/K.QH*,(b6vM;=FH*X*[K.\1QH*,I1*E:e;O&7?=-n&10�;=FH*�-=:[>�;O;O*,?TX>�;=?OKR�B?=*[UH?=*,-O*[QL;�;=FH*�(H>@;=>/{q*[+.+ cC6HA);oTX>JM�QW&@;w?=*[UH?=*,-O*[QL;�;OFW*�()KR�g*,?O*,QW:<*E-�6C*[;9{�*,*[Q:[+.>7-O-O*,-m{q*[+.+ _43K.-=:<?=KRT/K.QW>@QL;�>1QW>@+.M)-DKY-X:[>1QP6g*'AW-O*,(Z;O& �CQW( -DAW6W-DUC>1:<*E-V;OFW>@;�*[T/UHFC>1-OKv[,*p(HK��d*[?=*[QW:[*,-X6g*<;9{q*[*,Q:<+Y>1-=-O*,-,_ � }�KR\7AH?O*#:[&1QL;O?=KR6WA);O*E(�6vM �C_ �v{q*<;]-�>@QW( �C_t*�*,QH\W_ �

�� > � }36);]>@K.Q�>y-O*<;n&@0�2 � � FvAHTX>@Q'0�>7:<*�K.TX>@\7*,-w>1QW(p;O?=*,>@;3*E>1:]F'&1QW*�>1-3>�-OKRQH\7+R*�I1*,:<;O&7?o&@0 T � �:<&v&7?=()K.QW>@;O*,-,_ ��6 �o��&1T/UHAH;O*#;=FH*�-=:[>�;O;O*,?wTX>�;O?=KR�i>@QC(BT/*E>@QpKRTX>1\1*�0j?=&1T�;=FH*,-O*�2 � � -O>1T/UH+R*E-[_ ��:��}H?=&1T ;OFW*B?=*,-OAH+R;=-rK.Q ��6 ��:[&1T/UHA);=*X;OFW*BT +Y>@?=\1*,-D;r*[K.\1*,QvIJ>1+RAW*,-r&10�;OFH*i-O:,>�;O;O*[?fTX>�;O?=KR�h>1QW(h;OFW*:<&7?O?=*,-OUg&1QW()K.QH\rT�*,KR\7*[QvI1*E:e;O&7?=-�-D&�;OFW>@;OV ¡�� &@0�;=FH*3*,QH*[?=\1MVK.Qy;OFW*n-=:[>@;D;O*,?�TX>�;=K��yKY-�?O*,UH?O*E-D*,QL;O*,(|_��( �K�)*[+.*,:e; ¡ &10�;OFW*V&7?OK.\1K.QW>1+|0�>1:[*,-n>�;�?=>1QW()&7T/'�?=*[UW?O*E-D*,Q7;n*,>7:]F�>1-n>�+.K.QH*,>1?n:[&1T�6WKRQW>@;OK.&1Q&10�;OFW*T56C*E-9;n*[K.\1*,QLI7*,:<;O&1?]-q0j?=&1T ��:��e_ ��*��34oKY-DUW+.>JMi*,>7:]F'&@0l;OFH* ¡ >@UWUH?O&J�)K.TX>�;OK.&1QC-w()*[?=K.I1*,(pK.Q � ( �w>1QW(:<&7T/UW>@?=*o;=FH*[Tx;O&/;=FH*#&1?=KR\7KRQC>@+dKRTX>1\1*1_

�� )�� w�� ¢�R�� ¡ Xv¢+-,/.�� CE6-<�6-3�6 B �96-G

%'*E-DFiT/&v(H*[+Y-�:<&1T/*n0j?=&1Tx:[&1T/UHA);=*[?�\1?]>@UWFHK.:,-[cv{�FH*,?O*n;=FH*[M�>1?O*nAW-OAW>@+.+.M�:[>1+R+.*,(BUC&7+RMv\7&1Q�T/*E-DFH*E-[_kmFH*r}W&1+.*[M p ~ uws 9 \1?]>@UWFHK.:,-q;O*[�L;wKY-w>/\7&L&)(B?O*[0j*[?=*[QW:[*�0j&1?m;=FHK.-3-DAW6)89*,:<;,_�kmFH*r-OAH?O0�>1:[*<^�*,()\7*<^�I1*[?O;O*[�?=*[UH?=*,-O*[QL;=>@;OK.&1Qf{q>7-�KRQL;=?O&)()AW:[*,(fKRQ/;=FH* �oà�)`�} � �/-OMv-D;O*,T�>@; �wQHK.I1*,?=-OK�;9M�&@0�%>1-=-O>7:]FvAW-D*[;D;]-uK.Q/;OFW*�)Vv¢ � -[_�kmFH*3-D;O?=AW:e;=AH?=*3-OFH&�{�QXKRQy;OFHKY-�;=*<�v;�:<&1T/*E-�0j?=&1T�;OFH*3T/&1?=*o?=*,:<*,QL;�{�&7?�&V&@0��q>1T/UW- �D�)V%V¢\ �<_zn*[QW*[?]>@+.Kv[,*,( :[Mv+RK.QW()*,?VT/&)()*,+.-/{q*[?=*R�W?]-D;/UW?O&7UC&L-D*E(N6vM �qKRQ)0j&7?=(Z>@QW( A);OK.+.Kv[,*,(Z6LM � *[I�>@;OKY>�>1QW(�qKRQH0j&1?](�D�)VL¢7¢ ��{�FH&/{�&7?�&7*,(X{�KR;OFp?]>@QH\7*n(W>�;=>W_�kmFH*�T/&1?=*3?=*,:[*[QL;w>@?O;OKY:<+.*n6vM�Uw&1Tx>1QW(B%*,()K.&1QHK()KY-O:[AW-=-D*E-�;OFW*f:<&7T/UHA);=>@;OK.&1Q&10�:<Mv+RK.QW()*,?=-o0j?=&1TE\@4�(H>�;]>H_K}n:<;O?=*[*,-o{�*,?O*#&7?OK.\1K.QW>1+R+.MBUW?O&7UC&L-D*E(B6vM�wAWQ7;=*[? �D�)Vv¢ � �m>1QW(p()*[I7*[+.&1Ug*,(B0jAH?O;OFH*,?w6vM �L>1:�&vK.QW-�>@QW('k�>@QWKRT/&@;=& �9�WV � � �e_�kmFW*[MB>1?O*r(HK.-=:<AW-=-O*,(K.Qb()*[;=>1KR+�K.Q �H>@T/*<;�6 -n6g&L&$& �9�WV%V � �e_�}3AH?#()K.-=:<AC-O-OKR&7Q�&10�-DAWUC*,?=�LAW>7()?OKY:[-�:[&1T/*,-nT/&7-D;O+.Mp0j?O&7T ;OFW*{q&1?T&i&10qznAHU);]>Hct�q&7\1&1QWK c�>@QC(��m>�8D:,-DM��9�WV � V��ec�>1QW(';=FH*/+R*[0 ;nI7*<;O?=KY:<+.*fK.+R+.AW-D;O?]>�;=KR&7QW-3>1?O*f0j?=&1T5;OFW*T/&1?=*3?=*,:[*[QL;�{�&7?�&X&10��>1?�&dcv%'*<;]>��H>1-,cH>@QW( m �)*,+ �9�)V$V%X �ecv{�FHKY:]FBKY-�>@+Y-D&X()KY-=:<AW-=-D*E(yK.Qi;OFH*#-O*,:e;=KR&7Q&1Qp()*[0j&1?=T/>16H+.*nT/&)()*,+.-,_kmFH*�K.Q7;=?O&)()AC:e;OK.&1QB&@0u;OFH*#IvK.*[{mâ:<+Y>1-=-�:[&1QW:[*[U);�KY-m\1*[QW*[?]>@+.+RMX:<?=*,(HK�;=*,(�;O&X��&v*[QW()*,?OK.Q�&y>1QW(��>1Q43&L&7?OQ �D�)Vv¢wV��<_��q>1T/UW- �D�)V$V$\ �<c7��AH+R+.K �9�)V$V%X �ec7>1QW(B��&L-9;]> �9�WV%V ¡ �lAW-O*,(XIvK.*[{mâ:<+Y>1-=-�T/&)()*[+Y-�;=&�?=*,:<^&1\7QHK�[[*f;OFH?=*[*[^�()K.T/*[QW-OK.&1QW>1+�&16)89*E:e;=-,_/%>�;]:]FHKRQW\i6vM�>1+RK.\1QWTV*,QL;�{m>1-nK.QL;O?=&v(HAW:<*E(�6vM�Yt&�{�* �9�WV � ¢ �>@QC(�;=FH&1?=&1AW\1FH+.My>@QW>1+RM#[,*,(B6LMi�wAHQL;=*[QH+.&):]FH*[?w>1QW( �w+.+RTX>@QWQ �D�)V$V � �<_�kmFH*r214oâ214�>@+.K.\1QHT/*[QL;w()KY-9^:<AC-O-O*,(VFH*,?O*o:[&1T/*,-�0j?O&7T�;=FH*w{q&1?T&r&@0 �7&1FHQW-O&1QX>1QW(/�w*[6g*[?O; �D�)V$V � �<c@{�FHK.+R*w;OFH* \14wâ214�()KY-O:[AW-O-OK.&1Q:<&7T/*,-�0j?O&7T�;OFH*�{q&1?T&/&@0u��AH+R+.K �9�WV%V$X��e_lkmFH*n;O?=*,>@;OT/*[QL;m&@0t?=*,:[&1\7QHK�;=KR&7Q)^�6LMLâ>@+.KR\7QHT/*[QL;�&10u-DT/&v&@;=F&16H89*,:e;]-�{q>7-t;]>�&7*[Qr0j?=&1Ts;=FH*m{�&7?�&�&10 �7KRQ)^ Y|&7QH\��FW*[Q �9�)V$V%X �ec�>@QW(fKY-u?=*[+Y>�;=*,(r;O&3;OFH*m&1?=K.\1K.QW>@+L{�&7?�&&@0��m>1-O?OKu>@QW( �w+.+.T/>1Q��9�)V �%� �e_�%�>�;=:]FWKRQH\X-D;OKY:�&)-9^�UH+Y>�;O*E-9â>@QC(v^�6W+R&76W-qTV&)()*,+.-w{q>7-w()*,-=:<?=K.6C*E(BK.Qp;OFW*{q&1?T&V&10�vFC>@UHK.?O& p ~ uws 9 �9�WV � ��e_�U�*,+.>@;OK.&1QW>1+CTX>�;]:]FHK.QH\fK.Qi\1*[QW*[?]>@+g{q>7-q(HK.-=:<AW-=-O*,(yK.QS�vFW>@UWKR?=&f>1QW(�o>1?=>1+RKY:�& �D�)V � �1c|�WV �L¡ �e_OU�*,+.>@;OK.&1QW>1+|KRQC()*<�)K.QH\�:[>1Qp6C*�0j&1AHQW(pK.Qp;OFW*r{�&7?�&B&@0��&7-D;=> �D�)V$V ¡ �<_9}3AW?()KY-O:[AW-=-DK.&1Qr&7Q#0jAHQW:<;OK.&1QW>1+v&16)89*E:e;u?=*,:[&1\7QHK�;=KR&7Qr:<&7TV*E-|0j?=&1T ;=FH*�{q&1?T&n&@0 �L;]>@?T&n>1QW(��q&�{�M7*[? �D�)V%V$X��<_��K.?O6vMh>@QW( �vKR?=&�IvK.:]F �9�)V$V � �r>@UWUH?O&L>1:]FH*E(b;OFH*iUH?=&16H+.*[T &10w0�>1:[*�K.TX>@\1*p:<&7T/UH?O*E-O-OK.&1Q|cl{�FHKY:]FkuAH?�&>1QW(��l*,QL;O+Y>@QW( �D�)V$VH��;OFH*,Q�>7()&1U);=*,(0j&1?nTV&7?O*V*�?y:[KR*,Q7;�?=*,:<&7\1QHKR;OK.&1Q�&@0�0�>7:<*,-,_��v{q*<;=-�>1QW(

*b*[QH\ �9�)V$V%X ��()*[I7*[+.&1Ug*,(>�\1*,QH*[?]>@+u+R*E>@?=QHKRQW\�-DM)-D;O*,Tic�:,>@+.+R*E(��)�K} ��Y|`9}qcd{�FHK.:]F�KRT/UH?=&�I1*E(pAHUC&7Q;OFW*VUW?OK.QW:<K.UW>1+�:<&1T/Ug&1QH*,QL;=-�>@UHUW?O&L>1:]F6vMAW-OK.QH\i%�43}l-#>@QC(�6vM�:[&1QW-D;O?=AW:e;=KRQW\i>�;O?=*[*[^�-D;O?=AW:e;=AH?=*,((H>@;=>@6C>1-O*nK.Qp&1?]()*[?q;=&y-D*E>@?]:]Fy0j&1?�QW*,>@?=*,-D;�QH*[K.\1Fv6g&1?]-qKRQ � � % � ;=KRT/*7_�%'AH?]>1-O*#>@QW( � >JML>@? �9�WV%V@��>@+Y-O&wUH?=&v(HAW:<*E(r>@Qr*&?y:<K.*[QL;�-O*,>1?=:]F�T/*<;=FH&)(�>@QC(r-DFW&�{�*E(n;OFW>@;�214Z&16H89*,:e;�UC&L-D*�T/KR\7F7;�6C*�*,-D;OK.TX>�;O*E(;O&f{�K�;=FHK.Q/\��o6vM/KRQL;O*,?OUg&1+Y>�;=KRQW\#;O?]>@K.QHK.QH\rIvKR*,{w-�;]>�&7*[Q�>@;3� � ��K.QL;O*[?=I�>@+Y-('LT/&1?=*[&�I7*[?Ec@{�FHK.+R*n{�&7?�&vK.QH\{�KR;OF�-O*[I7*[?]>@+H&76)89*,:<;=-�&@;OFW*[?�;=FW>@Qy0�>1:<*E-[c7;OFW*[MX>@+Y-D&r0j&1AHQW(X;OFW>@;q>@Q�*[K.\1*[QC-DUW>7:<*�&10t()KRT/*,QW-DK.&1Q/\ � &7?+.*,-=-�{m>1-m-OA@?y:<K.*[QL;q0j&1?m\1&v&)(yUg*[?O0j&1?=TX>@QW:[*1_�kmFH*�:<&�I1*,?=>1\1*w&10t?=*,:<&7\1QHKR;OK.&1QH^�6vML^�>1UHUg*,>@?]>@QC:<*�K.Q�;=FHK.-:]FW>1U);O*,?�()?=*[{�FH*,>JIvK.+RM'0j?=&1T ;OFW*X{�&7?�&�&@0O*�*,QH\�>@QC(�;=FH*X0j?=*,�LAH*,Q7;=+RM�?O*[0j*[?=*[QW:[*,(b{q&1?T&&@0�ktAW?�&>@QC(B�l*,Q7;=+.>1QW(�_��QW*[?=\1MpT/KRQHK.T/Kv[E>�;=KR&7Qb{m>1-nAW-O*,(�K.Q�;=FH*B¢ � 6 -30j&7?�-OT/&v&@;OFWKRQH\':[&1QL;O&7AH?=-,_/�w&�{q*[I1*,?,cg;=FH*'�)V � ¢UW>1UC*,?#6LM��#>1-=-[c_* KR;�&vK.QG>@QW(bkt*,?�[,&1Ug&1AH+.&7-3K.Qb{�FWK.:]F�;OFH*/;=*[?=T z�� u �%p {m>1-�K.QL;O?=&)()AW:<*E(�ct-O*[*,TV*E(;O&0j?O*E-DFH+.MbKR\7QHK�;=*X;OFW*y?O*E-D*E>@?]:]F�K.QL;O*,?O*E-9;�&10�T/>1QvM�&@;=FH*[?f{�&7?�&7*[?]-[_ m UHUW+RKY:[>@;OK.&1QW-r;O&S�H;O;OK.QH\�>1QW(;O?]>1:�&vK.QH\X-DAW?D0�>7:<*,-�>1QW(pI1&7+RAWTV*E-w�LAHKY:�&L+.MX0j&7+R+.&�{�*E(�_ m T/KRQHK p ~ u�s �9�)V �%� ��UW?O&7UC&L-D*E(i(HMLQC>@T/K.:�UW?O&1^\1?]>@T/T/K.QH\�;=& �H;�>1:<;OK.I1*':<&7QL;O&1AW?=-f;O&hK.TX>@\1*E-[_ }3QH*'&103TX>@QvMG*[�H>@T/UH+.*,-/&@0�KR;yAW-D*pK.QSTV*E()KY:[>@+K.T/>1\1*E-rKY- ��AW* p ~ uws �D�)V$V ¡ �<_�kmFH*B{�&7?�&)-�6LM ��FH*,Q >@QC(G%'*,(HKR&7QHK �9�)V$V ¡ �#>@QW( ��>@?T&gcl%'*[;=>��H>7->@QC( m �)*[+ �9�WV%V%X ��>@?=*#;9{q&X\1&v&)('*<�H>1TVUW+R*E-w&@0�?]>@UHKY()+.Mi(H*[I1*,+R&7UHK.QH\y?=*,-O*,>@?]:]Fp>@QW(>1UHUH+.K.:,>�;=KR&7QW-wK.QUHFvM)-DKY:[-D^�6W>1-O*,(B>@QW(i()*<0j&7?OTX>16H+R*�T/&)()*[+.K.QH\W_�7_ m _ m T/K.QHK c��d_wku*[FW?=>1QHKn>1QW( k�_ *b*[MvT/&1AH;OF �9�)V �%� �ec�� z��¢q £ &w��uwx �� n � q%n�u�x7x ��¢qS� � n

¡ X � �� ! #"$"%"

x7�� x7�%$(��¢q ~ |�p/p{��p{n�q!& � �Ru% ~ ��¤wp4 � � ~ � rtn�z�� ~ |�p � n�p{z(p{�� p � �7|�u�n�£ � ��z ~ nTuw�� ~ z c � �� '�� 3 �'�5�� 9�)V �%� � V ¡ ^ V$VH_

\H_-U#_)�q>7-D?=K�>@QW(/�d_��w+.+.T/>1Q|c � kmFH* m +RK.\1QWTV*,QL;m&10}36)89*E:e;=-m{�KR;OFS�vT/&v&@;=F4�vAW?D0�>7:<*,-,c � n � G9 � �� £�� ~ p(n��R9 � � �)�C9 � � � � x � r ~ p{n �H� z�� cu�)V �%� cLUHU|_�� \�^�� %� _

2W_�è_t�qKR*E()*[?=TX>@Q|c � �oAHTX>@QhàTX>@\1*��oQW()*,?=-D;=>1QW()K.QH\W� Uw*,:<*,QL;7U�*,-O*,>1?=:]Fh>@QC(bkmFW*[&1?=M1c � � � x �� r ~ p{n �H� z�� n�u � |#�� {z�� uw��£��xyu(q¢p n � Tp{z�z��¢q c��&1+�_�2$\Hc � &W_Z�1c }n:<;O&16g*[?Ecm�)V �7¡ c�UHU|_\�V�^D¢�2W_

�C_ }f_uè_��q>@T/UW-,cZY�_�zV_��vFC>@UHK.?O&Cc�>@QW( U#_�%N_��o>1?=>1+RKY:�&dc � àTX>@\1*i��?=*,()KY:e;=KR&7QN0j&1?y��&1T/UHAH;O*[?�oKY-DK.&1Q|c �� |#n�p�p(�a£w��xyp{��z�� u�s�� p� ~ �!p� � q�� ~ � � � � &�z ~ p(x z c m _��L>@K.Q'>@QW(p�l_C}�+.MvQHQ �j*E(H-[_ �ec��+Y-D*,ILK.*[?-�):[KR*,QW:<*#��AH6H+.K.-OFH*[?]-�� c|�WV%V¢\)_

¡ _ �f_C��FH*,QB>@QC(izV_)%'*E()KR&7QHK �9�WV%V ¡ � � p{z{ (n�� ~ � � � � � � � x � s�p�¥�� p� ~ z��n � x � rts ~ � � svp �!uw�#q$p��xyu(q¢p�z � z��¢q uw� ��9u ~ ��¢q� uws�s �� £$p{s cL��&1T/UHA);=*[? �oKY-OKR&7Q�>@QW(�àTX>@\1* �wQW(H*[?]-9;]>@QW()K.QH\Cc��&1+�_XW�1c � &W_�2Hc�� %>JM�WV%V ¡ �92¢\ ¡ â2121�W_

XW_��W_ Y�_1��FH*,QV>1QW(VzV_%�v;O&):�&vT/>1Q|c � 43*<;=*[?=T/KRQHK.QH\#�l&7-O*�&10g274 }36)89*,:<;=-�{�K�;=FX��AW?OI7*,(7�)AH?D0�>7:<*E-[c �� nTuw��z 9 u ~ ~ p(n�� uws &�z�� z2uw��£ � u$ T|t�� p��{� ~ p{s�s�� q¢p(� �p c ��&7+ _h� � � &W_h�1cq�)V$V%XWctUHU|_¡ ¢E^ X$\H_

¢)_w%N_#��_)��&L-9;]>#>@QW(RY�_vzV_t�vFW>1UHK.?O&Cc � �H:<*[QW* m QW>1+RM)-OK.- �o-OKRQW\ m UWUC*E>@?]>@QW:[*<â�q>7-D*E(/%'&)()*[+Y-�>1QW(U�*[+Y>�;=KR&7QW>@+qàQW()*[�vK.QH\Cc � � � � &wx � � z��rtx � � � � x � r ~ p{n �� z�� c � &�I1*,T�6g*[?Ecq�WV%V ¡ c�UHU|_� � 2@^=� �%� _

� _��W_L}H&1+.*[M7c m _vIJ>1Qy43>1Tpct��_L}W*[K.QH*[?Ec �C_v�wAH\7FH*,-,c � � x � r ~ p(n � n�u � |t�� z � n�� (� � s�p�z�uw��£ n�u% (�~ �� p c m (H()KY-O&1Q)^ *�*E-D+.*[M7c�U�*E>1()K.QH\WcH% m c|�WV%V%XW_

VW_ m _�znAHU);=>Wc!Y�_m�q&1\7&1QHK�cw>@QW( U#_q�m>@8D:[-OM1c �� AC>@QL;OKR;=>@;OK.I1*>@QC( � AW>@+.KR;=>�;=KRI7*�%'*E>1-OAH?O*E-X0j&7?;OFH* ��I�>@+.AW>�;=KR&7QN&@0�;=FH*/�vAWUC*,?=�LAW>7()?OKY:y%'&)()*,+ c �� n � Tp�p�£w��#qwz � � ~ |�p �� n �wza| � � � �� ~ p(n � n�p ~ u ~ � � � � �� p{��p�z c��WV � VWcvUHU|_��)X¢\J^]�)X$VH_

� � _��wAHQL;O*,?,c|zV_�%N_.c �� {��p(� ~ � � x � r ~ u ~ � � � uw��£ � u ~ u � ~ n�r� ~ rtn�p{zZ� � n � n�u � |#�� {z ct��Ft_ 4f_�4oKY-9^-D*,?D;]>�;OK.&1Qtcv��?OK.QW:[*<;O&7Q �oQHK.I1*[?]-OK�;9M7cH��?=KRQW:[*<;=&1Q|c � �Cc|�WVL¢ � _�1�7_�4�_H�l_)�wAH;D;O*,QH+.&v:]FW*[?�>@QW(4�d_ �w+.+.T/>1Q|c � Uw*,:<&7\1QHK�[[K.QH\��v&1+.K.(4}36)89*,:<;=-q6vM m +.K.\1QHT/*[QL;m{�K�;=Fi>1QàT/>1\1*7c � �� ~ p(n�� u ~ � � � uws�� rtn�� u�s � � � � x � r ~ p(n �� z�� c ��&1+�_ ¡ c � &W_Z\Hc��)V%V � cvUHU|_��WV ¡ ^ \H�W\)_�W\H_o�3_�Y�_ �L>1:�&vK.QW-n>@QW( �d__Y�_�ku>1QHK.TV&1;O&Cc � }n:e;O^ ;=?O*,*,-o>1QW(�kmFW*[K.? �3-D*VKRQ U�*[UW?O*E-D*,Q7;=KRQW\BkmFH?=*[*[^4oK.T/*[QW-OKR&7QW>@+�}36)89*,:<;=-,c � � � x � r ~ p{n � nTu � |t�� zyuw��£ ��xyu(q¢p n � Tp{z�z��¢q c ��&7+ _f�[�Cct�)V � � cWUHU|_

\��$V@^ \L¢ � _�,2W_ m _ �w_ �7&1FHQC-D&7QZ>@QC( %N_��o*[6g*[?O;,c � � ?y:[KR*,Q7;X%'AH+R;OK.UH+.*'%'&)()*[+-U�*E:<&7\1QHKR;OK.&1QZKRQ ��+RAH;D;O*,?O*E(2�â4 �):<*,QH*,-,c � n � Tp�p�£w��#qwz � � ~ |�p � � � � � �)�{p(n�p(� �p � � � � x � r ~ p(n�� z�� uw��£ u ~�~ p(n��

�!p� � q%�� ~ � � � c��)V%V � cvUW>1\1*,-OXv¢v�<^ XL¢7¢v_�[�C_�%N_@�#>1-=-[c m _�* KR;�&vK.Q|c7>1QW(f4f_1ku*[?T[[&7UC&7AH+R&L- �9�)V � ¢ � � � u �$p{z��! ~ ��¤�p � � � ~ � rtn � � £%p(s�z cL��?O&):1_}uK.?]-9;�àQL;,_��&7Q)09_�&1Q��&1T/UHA);=*[? �3K.-OK.&1Q|c�Yt&1QH&7QW(�c��o� �9�WV � ¢ �a\ ¡ V@^ \%X%VH_� ¡ _�%N_��KR?=6vMh>1QW( Y�_��vK.?O&�IvKY:]F|c � m UHUH+.K.:,>�;=KR&7QZ&10w;OFH*'�#>1?OFvAHQH*,Q)^ Y|&v*[I7*��?=&):<*,(HAH?O*�0j&1?V;OFW*��FW>@?]>1:<;O*[?=K�[,>�;=KR&7Q&@0��wAWT/>1QN}W>1:[*,-,c � �� n�u��z 9 � � u ~�~ p{n�� uws &�z�� z�u�� £ � u$ T|t�� p

�� ~ p(s�s�� q$p(� �p c��&1+�_��W\Hc � &C_q�7c|�)V$V � c7UHUt_w� � 2�^]� �%� _

�� )�� w�� ¢�R�� ¡ X$V�)XW_ �W_ �W_g��&L*,QW()*,?OK.Q�&B>1QW( m _ �C_ ��>@Q43&v&1?=Q|c � kmFH*ràQL;=*[?=QW>@+�Uw*[UH?=*,-O*[QL;=>@;OK.&1Qp&@0 �)&1+.K.( �vFC>@Ug*{�K�;=F4Uw*,-OUC*E:e;�;O& �3K.-OKR&7Q|c � �-� � s � q%�� uws � & � p(n�� p ~ �� z c��&7+ _�2¢\)c��)Vv¢wVWcLUWU|_Z\)�7�<^ \)�)XW_�J¢)_�4�_)zV_$Yt&�{�*7c � kmFW* �oK.*[{�Ug&1K.QL;��&1QC-DKY-9;=*[QW:[MX��&7QW-D;O?]>@K.Q7;Ec � �{� ~ p{n��u ~ � � ��uws�� rtn�� u�s � � � � x �

� r ~ p{n�� z�� c��&7+ _��7c|�)V � ¢vcLUHU|_ ¡ ¢ � ¢�\H_� � _��r_�%'AH?]>1-O*�>@QC( �d_ � >JML>@? �D�)V$V ¡ �<c � ��>1?=>1T/*<;O?=KY: m UHUg*,>1?=>1QW:<* U�*[UH?=*,-O*[QL;]>�;OK.&1Qtc �PK.Q � �

� � � p� ~ �!p � n�p{z(p{� ~ u ~ � � ��z �� x � r ~ p(n �� z�� c �C_v�l&7QW:<*�>@QC(�%N_)�w*,?O6g*[?O;��*,(H- �ec��)UH?OK.QH\7*[?O^��*[?=+.>1\Wcd�)V$V ¡ _

�)VW_9U#_ � *[I�>�;=K.>G>1QW( k�_-}f_��qKRQH0j&1?](�c � 43*,-=:<?=KRUH;OK.&1Q >@QW( U�*,:[&1\1QWK�;=KR&7QP&10f��AH?OI7*,( }36)89*E:e;]-[c � n ~ � � {��u�s �� ~ p(s�s�� q¢p{�� Tp c��&7+ _ � c|�)Vv¢1¢vcLUHU|_m¢1¢E^ V � _

\ � _ �W_��>@?T&dc�4�_�%*<;=>@�H>1-V>@QW( Y�_ m �)*,+ �D�)V$V%X�� u�s &�z�� z � ��Hp�� ~ � p(� ~ n�� {rtsvu�n��Suws�s � �w~ � � ��!uwz{p�£ � � � � s rtx�p ~ n�� p�� n�x�u � s�p � � £%p(s�z u�� £ � �� cC%'*E()K.:,>@+|àTX>1\1* m QC>@+.Mv-OKY-�1&7AH?OQC>@+�c ��&7+ _��7c � &C_�� D�)V$V%X��9UHU|_ ¡ 2@^9¢)�

\)�7_��AH+.+RK�cC�/_g>@QW(SY�_gzV__�vFW>1UHKR?=&Wc � ku?OK.UH+.*<;O^��m>1-O*,(S}36)89*E:e; U�*E:<&7\1QHKR;OK.&1Q �3-DK.QH\2�vMvQL;OFW*<;OKY:r>1QW(U�*,>1+|��?=&16W>16HKR+.KR;9My%'&)()*[+Y-[c �� n � �pTp�£��¢q�z � � � � �� cu�)V$V%XHc ��&7+ _l` ��cWUHU|_q¢ ¡ ^D¢wVH_

\%\H_��r_tU�&1T�>1QW(�zV_)%'*E()KR&7QHK�c � �wK.*[?]>@?]:]FHKY:[>@+g4o*E:<&7TVUg&7-OKR;OK.&1Q�>1QW( m �vKY>@+��vFC>@Ug*n43*,-=:<?=KRUH;OK.&1Q|c �� n�u��z(u% ~ � � ��z � � u ~ ~ p(n�� uws &�z�� zRuw� £ � u% �|#�� p �� ~ p(s�s�� q¢p{�� p c��&1+�_i� ¡ c � &W_p� � c�)V%V72HcLUHU|_ZVv¢�2@^ V � �1_

\@2W_��r_��)>1TV*[;,c � p{z�� q%� u�� £ � uws &�z�� z � � � � u ~ ��uws � u ~ u � ~ n�r� ~ rtn�p�z c m (H(HK.-O&1Q)^ *b*,-O+R*,M1c�U�*E>1()K.QH\Cc% m c|�WV%V � _\��C_9Y�_�zV_ �vFC>@UHK.?O&Cc �C_�4f_�%'&1?=KY>@?O;9M1c Ur_�%N_��3>@?]>@+.K.:�&dc�>1QW(P�l_�zV_�%'AH+.\7>1&1Q�&�>1?,c��7%>�;]:]FHK.QH\kmFH?O*,*<â4oK.T/*[QW-OK.&1QW>1+�}36)89*,:<;=-��o-OKRQH\B>RU�*[+Y>�;=KR&7QW>@+u��>@?]>1()K.\1Tpc � u ~ ~ p(n�� p� � q%�� ~ � � � � ��&7+ _�J¢vc � &W_��Wc��WV � �WcvUHU|_�2 �7¡ ^�� L¡ _\ ¡ _9Y�_|zV_��vFW>@UWKR?=&B>1QW(�U#_|%G_d�3>@?]>@+.K.:�&dc � �v;O?=AW:e;=AH?=>1+�43*,-=:<?=K.U);OK.&1QW-n>@QC(àQH*[�)>7:e;#%>�;]:]FHK.QH\7�Wc

� � � � nTuw��z(u$ ~ � � ��z � � u ~�~ p(n�� u�s &�z�� z7uw��£ � u% �|#��p�� ~ p(s�s�� q$p(� �p � ��&1+�_�� m %`�^�2Wc � &W_¡ c��v*,U);,_��WV � �7cvUHU|_ ¡ � �@^ ¡ �WVH_

\�XW_9Y�_EzV_��vFC>@UHK.?O&CcE>1QW(�U#_J%N_J�o>1?=>1+RKY:�&dcE� m %'*<;=?OKY:�0j&7?��&7T/UW>@?=KRQW\-U�*[+Y>�;=KR&7QW>@+L4o*E-O:[?OK.U);OK.&1QC-O�Wc� � � � nTuw��z(u$ ~ � � ��z � � u ~�~ p(n�� u�s &�z�� z7uw��£ � u% �|#��p�� ~ p(s�s�� q$p(� �p � ��&1+�_�� m %`�^9¢)c � &W_�1c �L>@Q|_m�)V �7¡ cLUWU|_�V � ^ V1�W_

\7¢)_9Y�_%�L;]>@?T&r>@QW(/�/_@�q&�{�M1*,?,c � p{��p{n�� pT ~ �!p� � q%�� ~ � � � � z��¢q � � n�x?u�� £ ��rt� ~ � � � c%*�&7?O+Y(�):<K.*[QL;OKv�C:��AW6H+RKY-OFHKRQW\B��&W_��;=* Y|;=(�c �vKRQW\7>@Ug&1?=*1c��WV%V$XH_

\ � _�4�_��v{q*<;]-�>1QW( �C_$*b*[QW\ � �o-OKRQH\V4oKY-=:<?=KRT/K.QW>@QL;��K.\1*[QH0j*,>�;=AH?=*,-�0j&7?�àTX>1\1* Uw*<;O?=K.*[I�>@+�c � � � � n�u��z 9 u ~ ~ p(n�� uws &�z�� z uw��£ � u% �|#��p(� �� ~ p(s�s�� q¢p{�� Tp c��&7+ _�� c��)V$V%XWcLUWU|_ � 2W�<^ � 2%XW_

\�VW_�%N_CkuAH?T&p>1QW( m _d�l*[QL;=+.>1QW( � ��KR\7*[Q)0�>7:<*,-�0j&1? Uw*,:<&7\1QHKR;OK.&1Qtc � � � rtn�� uws � � � � q%�� ~ ��¤�p � p(rtn � �z{ (��p(� �p c ��&1+�_�2Hc � &C_��1c��WV%VH�7cvUHU|_�¢v�[^ � XH_

2 � _ ��_ ��AH*1c m _1zn&L-DFL;=>7-D6vMr>1QW(7Y�_ m :�&7*[?=TX>@Q �D�)V$V ¡ �<c r ~ � x�u ~ �� p ~ pT ~ � � � � � � � � � � nT£%p(n�z-��|�p�z ~ �!u%£�� q%n�u � |¢z c��'� �� :� � �� 0 ��3,� 1 �� 1 c ��&1+�_��,�Wc � &W_u2Wc��9�WV%V ¡ � ¡ \ ¡ c ¡ 2$XH_

¡ ¢ � �� ! #"$"%"

Documents

WV - Purdue Engineering · x [> } [%& [%& / \ )