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CAGD history and outlook

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1 CAGD history and outlook
Gerald Farin Arizona State University

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3 Ben Jakober

4 I have never been very enthusiastic about calling our field 'Computer Aided Geometric Design‘. Ivor Faux and I once wrote a book called 'Computational Geometry', which I think was a better name, but that got hijacked by another bunch of people who are mostly much more remote from the real world than we are! M. Pratt

5 CAGD Representation and Approximation of curves and surfaces
Computing with geometric objects

6 CAGD topics Bezier metods B-spline methods Coons/Gordon methods
Algebraic methods Triangular patches Triangle meshes Subdivision surfaces NURBS Geometric continuity Geometry processing New topics

7 CAGD Books Faux/Pratt 78 Farin 88, 90, 93, 96 Bartels/Beatty/Barsky 86
Yamaguchi 88 Farin/Hansford 00 Boehm/Prautzsch/ Paluzny 01 Su/Liu 89 Mortenson 85, 98 Hoschek/Lasser 93 Rockwood/Chambers 96 Gallier 98 Marsh 99 Cohen/Riesenfeld/ Elber 02

8 CAD = Calculator Aided Design
Dawn of CAGD R. Liming: Practical Analytical Geometry with Applications to Aircraft Numerical applications of conics CAD = Calculator Aided Design

9 1950’s: NC Milling machines Lathes Plotters

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13 Bezier Methods 1959 de Casteljau 60’s Bezier
1987 de Casteljau / Ramshaw 1987 Farouki/Rajan

14 Bezier Methods Standard in -CAD/CAM -Font Design -Animation
Numerical Stability no local control No local control Smoothness Not periodic

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16 B-spline Methods 1933 Popoviciu 1949 Schoenberg
60’s + 70’s de Boor (+Cox / Mansfield) 1974 Gordon, Riesenfeld 1980 Boehm 1980 Cohen, Lyche, Riesenfeld 1987 Ramshaw / de Casteljau

17 B-spline Methods Standard in -Approximation Theory -CAD/CAM
Numerical stability Local control Bookkeeping Topology

18 Implicit Methods 1983 Sederberg 1992 Bajaj

19 Implicit Methods Easy ray tracing etc. Rich shapes Evaluation
Unwanted branches Shape(?)

20 Geometry Processing Patrikalakis/Maekawa 2001 PH methods
Symbolic methods -Groebner bases ODE methods Trimmed surfaces High degrees Topology Patrikalakis/Maekawa 2001

21 Bezier Triangles 1959 de Casteljau 1971 Zensiek 1976 Sabin 1980 Farin
1987 Ramshaw 1987 Alfeld/Schumaker Schumaker / Lai 2004

22 Bezier Triangles pp spaces 3D Studio, Nvidia, Arbitrary topology
Smoothness / Shape Not IGES

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24 Triangle Meshes FEM Digitizers / Rapid prototyping / STL
1987 Lorensen / Cline 1992 Hoppe et al

25 Triangle Meshes Piecewise linear Multiresolution arbitrary topology
Data volume Class A surfaces

26 Subdivision Surfaces 1953 de Rham 1972 Chaikin
1978 Doo/Sabin & Catmull/Clark 1987 Loop 1990 Dyn/Gregory/Levin 1994 Reif

27 Doo-Sabin

28 Catmull-Clark

29 Subdivision Surfaces Arbitrary topology Automatic smoothness
Texture mapping Not IGES Point evaluation Processing

30 NURBS 1966 Coons / Forrest 1984 Versprille

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32 NURBS “All-encompassing” Industry standard Weights Curves on quadrics
Developable surfaces Data reduction Derivatives Weights

33 Coons Patches 1960’s Coons 1960’s Gordon 1970’s Barnhill, Gregory

34 Coons Patches Use in FEM Twists Not IGES Procedural Procedural: Result of operation is not element of finite-dimensional linear space

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36 Shape 1962 Geise 1970’s+ Manning, Nielson, Barsky,...
1980’s Hoschek, Kellander 1990 Shirman/Sequin

37 Geometric Continuity Shape parameters Reverse engineering
Surface Splines Shape parameters Curve to Surface Effort / Results

38 New Topics New Geometries Volume modeling Scattered data approximation
Med / bio / geo / games / animation

39 Future tonight


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