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1AT73.01 CAD/CAMCOMPUTER AIDED DESIGN
ERIK L.J. BOHEZASSOCIATE PROFESSOR
DESIGN & MANUFACTURING ENGINEERING
August 2005
2Lesson I: Relation Between Degree n and ShapeLesson II: Any Analytic Function Can Be Written As PolynomialLesson III: Parametric Expression of Curve, Surface and SolidLesson IV: Representations of GeometryLesson V: Identifying Unknown Coefficients in Parametric
Polynomial Equations of a CurveLesson VI: Basic 3D GeometryLesson VII: Perspective and Parallel Projections &
Corresponding Clipping VolumesLesson VIII: CONVEX HULL DEFINITIONLesson IX: BEZIER CURVESLesson X: B-SPLINECURVESLesson XI: NURBSLesson XII: SURFACESLesson XIII: SOLID MODELINGLesson XIV: CAD SYSTEM ARCHITECTURELesson XV: IGES STEPLesson XVI: CAD HARDWARE
3REFERENCE BOOKS:D.F. Rogers, and J.A. Adams: Mathematical Elements for Computer Graphics, 2nd edition, McGraw-Hill, 1990.
G. Farin: Curves and Surfaces for Computer Aided Geometric Design, Academic Press, 1993.
Kunwoo Lee:Principles of CAD/CAM/CAE Systems,Addison-Wesley, 1999
I.D. Faux, and M.J. Pratt: Computational Geometry for Design and Manufacture, Ellis Horwood Limited, 1979.
4REFERENCE BOOKS:V.B. Anand: Computer Graphics and Geometric Modeling for Engineers, John Wiley & Sons, 1993.
W.K. Giloi: An Introduction to Solid Modeling, Computer Science Press, 1998.
M.P. Groover, and E.W. Zimmer: CAD/CAM: Computer-Aided Design and Manufacturing, Prentice Hall, 2000
Zeid: CAD/CAM Theory and Practice, McGraw-Hill, 1991.
5Lesson I: Relation Between Degree n and Shape
6Lesson I: Relation Between Degree n and Shape
7Lesson I: Relation Between Degree n and Shape
8Lesson II: Any Analytic Function Can Be Written As Polynomial
9Lesson III: Parametric Expression of Curve, Surface and Solid
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Lesson III: Parametric Expression of Curve, Surface and Solid
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Lesson III: Parametric Expression of Curve, Surface and Solid
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Lesson IV: Representations of Geometry
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Lesson IV: Representations of Geometry
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Lesson IV: Representations of Geometry
15POLYGON MESH SMOOTH CURVES
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Lesson IV: Representations of Geometry
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Lesson IV: Representations of Geometry
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Conic Sections
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What does a CAD system do with the equations?
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What does a CAD system do with the equations?
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What does a CAD system do with the equations?
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Lesson V: Identifying Unknown Coefficients in Parametric Polynomial Equations of a Curve
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Lesson V: Identifying Unknown Coefficients in Parametric Polynomial Equations of a Curve
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Lesson V: Identifying Unknown Coefficients in Parametric Polynomial Equations of a Curve
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Lesson VI: Basic 3D GeometryCoordinate System
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Lesson VI: Basic 3D GeometryParametric Line & Plane Equation
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Lesson VI: Basic 3D GeometryDot and Cross Vector Product
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VECTOR CROSS PRODUCT
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Lesson VI: Basic 3D Geometry3D Transformations, Scaling, Translation, Rotation
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Lesson VI: Basic 3D Geometry3D Transformations, Scaling, Translation, Rotation
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Lesson VII: Perspective and Parallel Projections &Corresponding Clipping Volumes
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Lesson VIII: CONVEX HULL DEFINITIONDefinition of POINTS & VECTORS
VECTOR = DIFFERENCE OF TWO POINTS
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Lesson VIII: CONVEX HULL DEFINITIONDefinition of BARYCENTRIC COMBINATIONS
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OTHER DEFINITION OF CONVEX POLYGON:
-For all possible two points inside the polygon -take two points inside the polygon-connect the two points by a straight line-if all points on this line are inside-then polygon is convex-else it is concave
CONVEX
NON-CONVEX = CONCAVE
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Lesson VIII: CONVEX HULL DEFINITIONDefinition of AFFINE MAPS
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Lesson VIII: CONVEX HULL DEFINITIONDefinition of LINEAR INTERPOLATION
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Lesson IX: BEZIER CURVESCASTELJAU ALGORITHM
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Lesson IX: BEZIER CURVESCASTELJAU ALGORITHM
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Lesson IX: BEZIER CURVESBERNSTEIN POLYNOMIALS
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Lesson X: B-SPLINECURVES
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Lesson X: B-SPLINECURVES
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Lesson X: B-SPLINECURVESB-SPLINE PROPERTIES
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Lesson X: B-SPLINECURVESB-SPLINE CONTROL HANDLES
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Lesson X: B-SPLINECURVESB-SPLINE CONVEX HULL
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Lesson X: B-SPLINECURVESB-SPLINE EMBEDDED LINE
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Lesson X: B-SPLINECURVESRELATION DEGREE/SHAPEMULTIPLE KNOTS
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Lesson X: B-SPLINECURVESKNOT INTERVAL INFLUENCE ON SHAPE
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Lesson X: B-SPLINECURVESDUPLICATE KNOTS
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Lesson X: B-SPLINECURVESUNIFORM B-SPLINES NOT USED IN CAD BECAUSE NO ENDPOINT CONTROL
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B-Spline Properties:- Convex Hull - Local Control- Embedded Straight Line- Conic Section - Degree
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B-spline Control Polygon
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Convex Hull of B-spline : Partial Convex Hull 1
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Convex Hull of B-spline : Partial Convex Hull 2
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Convex Hull of B-spline : Partial Convex Hull 3
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Convex Hull of B-spline : Partial Convex Hull 4
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Convex Hull of B-spline : Partial Convex Hull 5
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Convex Hull of B-spline : Partial Convex Hull 6
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Convex Hull of B-spline : Partial Convex Hull 7
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Convex Hull of B-spline : Partial Convex Hull 8
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Convex Hull of B-spline = Union of Partial Convex Hulls
KNOT VECTOR: (8 Pieces of Curve because we have 8 Convex Hulls){U0 U0 U0 U1 U2 U3 U4 U5 U6 U7 U8 U8 U8}Length of intervals for knotvector:U0U1 = d0d1d2; U1U2 = d1d2d3; U2U3 =d2d3d4; U3U4 = d3d4d5;U5U6 = d5d6d7; U7U8 = d7d8d9
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Convex Hull of B-spline = Union of Partial Convex Hulls
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B-Splines is Inside Convex Hull
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B-Spline Smoothly Embeds Straight Line Segment
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Local Control of B-Spline:-better the lower the degree
B-Spline of Degree n = 2
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B-Spline of Degree n = 3-Less local control-To embed straight line will require more control points in line
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n = 3
n = 2
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B-spline curve-Embedded Straight Line-Circle Approximation
NURBS
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Lesson X: B-SPLINECURVESB-SPLINE PROPERTIES B-SPLINE CANNOT MODEL CONIC SECTIONS
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Lesson XI: NURBSNon Uniform Rational B-spline
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Lesson XII: SURFACES
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Bezier Surfaceof degree 7
b-spline Surfaceof degree 3
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Bezier Surfaceof degree 7
b-spline Surfaceof degree 3
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Bezier Surfaceof degree 7
b-spline Surfaceof degree 3
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Bezier Surfaceof degree 7
b-spline Surfaceof degree 3
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Bezier Surfaceof degree 7
b-spline Surfaceof degree 3
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b-spline surfacedegree 3
b-spline surfacedegree 2
Difference
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Lesson XIII: SOLID MODELING
9Construction Solid Geometry (CSG) Boolean Operatons
9Boundary Representation
9Volume Elements (VOXELS) Octree/Quatree
9Hyperpatch Parametric Polynomial X(u,v,w)
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R1 = (C2-C1)R = (C2-C1) CY1
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B-repBoundary Representation
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Cell DecompositionVoxels
OCTREE 3DQUATREE 2D
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Most used Solid Modeling systems are based on CSG & B-RepTranslators are needed to Translate from one representationto another
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Lesson XIV: CAD SYSTEM ARCHITECTURE
OpenGL.org
IGES: Initial Graphics Exchange Specification ISO
STEP
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Evolution of Standards in CAD/CAM
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Lesson XV: IGES STEP
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151Sample IGES file
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STEP
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INTEGRATED RESOURSES
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EXPRESS Language Description Methods
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APPLICATION PROTOCOLS
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IMPLEMENTATION METHODS
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SUPPORTED INDUSTRY SECTORS
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SUPPORTED INDUSTRY SECTORS
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PRODUCT BOM DOCUMENT BOM
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WRONG
TODAY
FUTURE
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STEP Series
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STEP Series
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IGES File:
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The last DE number in '..\igs\126-000.IGS' is 1
************** Global Section **************
Parameter Delimiter Character = ","Record Delimiter Character = ";"Product ID from Sender = "126-000"File Name = "126-000.IGS"System ID = "{unspecified}"Pre-processor Version = "IGESXTRACT(tm) Version 5.3 (Jul 29 1997)"Number of Bits for Integers = 32Single Precision Magnitude = 38Single Precision Signif icance = 15Double Precision Magnitude = 308Double Precision Significance = 15Product ID for Receiver = "126-000"Model Space Scale = 1.00000Unit Flag = 1 - InchesUnits = "INCH"Maximum Number of Line Weights = 8Size of Maximum Line Width = 0.0160000Date & Time Stamp = "970731.034906"Minimum User-intended Resolution = 0.000100000Approximate Maximum Coordinate = 0.000000Name of Author = "dennette@wiz-worx.com"Author's Organization = "Legacy PDD AP Committee"IGES Version Number = 11 - USPRO/IPO-100-1996 (IGES 5.3)Drafting Standard Code = 0 - None SpecifiedModel Creation/Change Date = "920717.080000"Application Protocol/Subset ID =
177
************ Terminate Section *************
1 records in Start Section4 records in Global Section2 records in Directory Entry Section (1 entities)5 records in Parameter Data Section
******************* DE = 1 *******************
Entity Type Number = 126 - Rational B-Spline CurveParameter Data (Count) = 1 (5)Structure = 0Line Font Pattern = 1 - SolidLevel = 0View = 0Transformation Matrix = 0Label Display = 0Blank Status = 0 - VisibleSubord. Entity Switch = 0 - IndependentEntity Use Flag = 0 - GeometryHierarchy = 1 - Global deferLine Weight Number = 0Color Number = 2 - RedForm Number = 0 - Entity Label (Subscript) = ()
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******************* Parameter Data Record *******************K = 8M = 3PROP1 = 1 - PlanarPROP2 = 0 - Open CurvePROP3 = 1 - PolynomialPROP4 = 0 - Non-periodicT(-3) = 0.000000T(-2) = 0.000000T(-1) = 0.000000T(0) = 0.000000T(1) = 1.00000T(2) = 2.00000T(3) = 3.00000T(4) = 4.00000T(5) = 5.00000T(6) = 6.00000T(7) = 6.00000T(8) = 6.00000T(9) = 6.00000W(0) = 1.00000W(1) = 1.00000W(2) = 1.00000W(3) = 1.00000W(4) = 1.00000W(5) = 1.00000W(6) = 1.00000W(7) = 1.00000W(8) = 1.00000
179
XYZ(0) = 7.00000, 7.00000, 0.000000XYZ(1) = 7.01111, 7.15385, 0.000000XYZ(2) = 7.03333, 7.46154, 0.000000XYZ(3) = 6.86667, 8.15385, 0.000000XYZ(4) = 7.50000, 7.92308, 0.000000XYZ(5) = 8.13333, 8.15385, 0.000000XYZ(6) = 7.96667, 7.46154, 0.000000XYZ(7) = 7.98889, 7.15385, 0.000000XYZ(8) = 8.00000, 7.00000, 0.000000V(0) = 0.000000V(1) = 6.00000NORM = 0.000000, 0.000000, 1.00000*************** Associativities & Properties ****************NA = NP =
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The last DE number in '..\igs\128-000.IGS' is 1
************** Global Section **************
Parameter Delimiter Character = ","Record Delimiter Character = ";"Product ID from Sender = "NENTITY"File Name = "128-000.igs"System ID = "{unknown}"Pre-processor Version = "{unknown}"Number of Bits for Integers = 16Single Precision Magnitude = 6Single Precision Signif icance = 15Double Precision Magnitude = 13Double Precision Significance = 15Product ID for Receiver = "NENTITY"Model Space Scale = 1.00000Unit Flag = 1 - InchesUnits = "INCH"Maximum Number of Line Weights = 8Size of Maximum Line Width = 0.0160000Date & Time Stamp = "19970830.165254"Minimum User-intended Resolution = 0.000100000Approximate Maximum Coordinate = 0.000000Name of Author = "dennette@wiz-worx.com"Author's Organization = "Legacy PDD AP Committee"IGES Version Number = 10 - USPRO/IPO-100 (IGES 5.2) [USPRO93]Drafting Standard Code = 3 - ANSIModel Creation/Change Date = "920717.080000"
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************ Terminate Section *************
1 records in Start Section4 records in Global Section2 records in Directory Entry Section (1 entities)17 records in Parameter Data Section
******************* DE = 1 *******************
Entity Type Number = 128 - Rational B-Spline SurfaceParameter Data (Count) = 1 (17)Structure = 0Line Font Pattern = 1 - SolidLevel = 0View = 0Transformation Matrix = 0Label Display = 0Blank Status = 0 - VisibleSubord. Entity Switch = 0 - IndependentEntity Use Flag = 0 - GeometryHierarchy = 1 - Global deferLine Weight Number = 0Color Number = 2 - RedForm Number = 0 - Entity Label (Subscript) = ()
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******************* Parameter Data Record *******************K1 = 3K2 = 7M1 = 3M2 = 5PROP1 = 0 - Not ClosedPROP2 = 0 - Not ClosedPROP3 = 1 - PolynomialPROP4 = 0 - Non-periodic in 1st directionPROP5 = 0 - Non-periodic in 2nd directionS(-3) = 0.000000S(-2) = 0.000000S(-1) = 0.000000S(0) = 0.000000S(1) = 1.00000S(2) = 1.00000S(3) = 1.00000S(4) = 1.00000T(-5) = 0.000000T(-4) = 0.000000T(-3) = 0.000000T(-2) = 0.000000T(-1) = 0.000000T(0) = 0.000000T(1) = 1.00000T(2) = 2.00000T(3) = 3.00000T(4) = 3.00000T(5) = 3.00000T(6) = 3.00000T(7) = 3.00000T(8) = 3.00000
W(0,0) = 1.00000W(1,0) = 1.00000W(2,0) = 1.00000W(3,0) = 1.00000W(0,1) = 1.00000W(1,1) = 1.00000W(2,1) = 1.00000W(3,1) = 1.00000W(0,2) = 1.00000W(1,2) = 1.00000W(2,2) = 1.00000W(3,2) = 1.00000W(0,3) = 1.00000W(1,3) = 1.00000W(2,3) = 1.00000W(3,3) = 1.00000W(0,4) = 1.00000W(1,4) = 1.00000W(2,4) = 1.00000W(3,4) = 1.00000W(0,5) = 1.00000W(1,5) = 1.00000W(2,5) = 1.00000W(3,5) = 1.00000W(0,6) = 1.00000W(1,6) = 1.00000W(2,6) = 1.00000W(3,6) = 1.00000W(0,7) = 1.00000W(1,7) = 1.00000W(2,7) = 1.00000W(3,7) = 1.00000
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XYZ(0,0) = 8.50000, 9.50000, 1.00000XYZ(1,0) = 8.50000, 9.25000, 0.666667XYZ(2,0) = 8.50000, 9.00000, 0.333333XYZ(3,0) = 8.50000, 8.75000, 0.000000XYZ(0,1) = 8.49394, 9.44659, 1.00000XYZ(1,1) = 8.49394, 9.19659, 0.666667XYZ(2,1) = 8.49394, 8.94659, 0.333333XYZ(3,1) = 8.49394, 8.69659, 0.000000XYZ(0,2) = 8.43636, 9.39545, 1.00000XYZ(1,2) = 8.43636, 9.14546, 0.666667XYZ(2,2) = 8.43636, 8.89545, 0.333333XYZ(3,2) = 8.43636, 8.64545, 0.000000XYZ(0,3) = 8.21364, 9.48580, 1.00000XYZ(1,3) = 8.21364, 9.23580, 0.666667XYZ(2,3) = 8.21364, 8.98580, 0.333333XYZ(3,3) = 8.21364, 8.73580, 0.000000XYZ(0,4) = 7.78636, 9.82671, 1.00000XYZ(1,4) = 7.78637, 9.57671, 0.666667XYZ(2,4) = 7.78637, 9.32671, 0.333333XYZ(3,4) = 7.78636, 9.07671, 0.000000XYZ(0,5) = 7.56363, 9.80454, 1.00000XYZ(1,5) = 7.56363, 9.55454, 0.666667XYZ(2,5) = 7.56363, 9.30454, 0.333333XYZ(3,5) = 7.56363, 9.05454, 0.000000XYZ(0,6) = 7.50606, 9.62841, 1.00000XYZ(1,6) = 7.50606, 9.37841, 0.666667XYZ(2,6) = 7.50606, 9.12841, 0.333333XYZ(3,6) = 7.50606, 8.87841, 0.000000XYZ(0,7) = 7.50000, 9.50000, 1.00000XYZ(1,7) = 7.50000, 9.25000, 0.666667XYZ(2,7) = 7.50000, 9.00000, 0.333333XYZ(3,7) = 7.50000, 8.75000, 0.000000
U(0) = 0.000000U(1) = 1.00000V(0) = 0.000000V(1) = 3.00000*************** Associativities & Properties ****NA = NP =
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CAD HARDWARE COMPUTER GRAPHICS
WORKSTATIONS-Vector Display-Raster Scan Display-Flat Panel Display-Mouse Locator Selector-Light penPLOTTERS-Pen Plotter Vector Ploter-LASER Printer Raster printer/Plotter-Inkjet Printer Raster printer/Plotter-Electro-Static Printer Raster printer/PlotterSCANNERSDIGITIZERS - 2D/3D
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VECTOR DISPLAY
DISPLAYFILE
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RASTER DISPLAY
FRAME BUFFER
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COLOR RASTER DISPLAY
SCAN LINES
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Subtractive ColorsCyanMagentaYellow
Used For Printers(White Background)
Additive ColorsRedGreenBlue
Used for displaysBlack Background
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LIQUID CRYSTAL DISPLAY
Twisted Nematic Effect
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Time Multiplexing in LCD
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3D Display
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INTERACTION DEVICES-KEY BOARD -MOUSE = PURE LOCATOR DEVICE-LICHT PEN = PURE SELECTOR DEVICE
KEY = EVENT DRIVEN DEVICEMOUSE = SAMPLED DEVICELIGHT PEN = EVENT DRIVEN DEVICETOUCH SCREEN
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Mouse
Keyboard
Event Queue
ApplicationProgram
Sample DeviceDeviceHandler
Get
Commands:SetInputModeSetWaitEvent
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LIGHT PEN = PURE SELECTOR DEVICE
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Infrared Laser Diode
Infrared Sensitive DiodesInfrared Beams
Infrared LaserDiodes
TOUCH SCREEN
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PEN PLOTTER VECTOR PLOTTER
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LASER PRINTER RASTER PRINTER
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INKJET PRINTER RASTER PRINTER
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INKJET PRINTER RASTER PRINTER
219INKJET PRINTER RASTER PRINTER
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2243D ULTRASONIC DIGITIZER
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Microphone
2D ULTRASONIC DIGITIZER
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