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The Domain of a Point Set Surface
Nina Amenta and Yong J. Kil
University of California at Davis
Introduction
x (x)
x
(x)
Motivation
MLS
Our Line Integral
Understanding MLS
MLS
Amenta, Kil, SIGGRAPH 2004
e(x,a)
n(x)
Energy Field of MLS
),(),,(),( 2i
iiMLS pxxapaaxe
a
Amenta, Kil, SIGGRAPH 2004
Gaussian Weight
a
Vector Field of MLS
),(argmin)( a axexn MLSMLS
a
nMLS(x)
Amenta, Kil, SIGGRAPH 2004
Extremal Surface
Amenta, Kil, SIGGRAPH 2004
Energy on
An Energy and Vector Field (not MLS)
en
Circular plot
x
n(x)a
||e(x,a)||
MLS Vector Field
MLS Best Fitting Plane
MLS Corner Example
Ideal Stream Lines
MLS Circular Plot
MLS Vector Field
MLS Surface and Vector Field
Optimal Direction via Center of Mass
i
iNi pxp ),(c
c
),() ,,(argmin)( 2a i
iiCOM pxapaxn c
Normalized Gaussian Weight
nCOM
Vector Field and Surface
Estimated Distance Function
i
iNiDIST pxpxdxe ),(),()( 2
x
Estimated Distance Field
High
Low
High
Low
Estimated Distance Field
Estimated Distance Function
Line Integral Intro
Line Integral nI(x)
)),()(),(,
2
axy DISTI xyyeaxe
ax,
),(argmin)( a axexn II
a
x
nI Vector Field
Ideal Stream Lines
nI Stream Lines
Surface and Stream Lines
Overall ViewMLS Center of Mass eDIST & nI
Vector Field
Energy Field
Surface
Conclusion
• Analyze various energy and vector fields.
• nCOM works well except at sharp corners.
• eDIST approximates distance well.
• nI works well, but expensive (Not
recommend for 3D).
Thank you.
Updated paper and slide:http://graphics.cs.ucdavis.edu/~yjkil/pub/domain.html
Defining Surface plugin (to appear):http://www.pointshop3d.com
Estimated Distance and Line Integral
MLS
eDIST nI
eDIST nI
MLS Circular plot example
MLS Energy e(x,a)
Energy + Field
MLS Surface
Surface with maxima
MLS Surface with maxima
