1. CAGD history and outlook
Gerald Farin
Arizona State University

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

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

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

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

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

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