CAGD history and outlook

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

7. 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/Chambers96 Gallier 98 Marsh 99 Cohen/Riesenfeld/ Elber 02 CAGD Books

8. Dawn of CAGD • R. Liming: Practical Analytical Geometry with Applications to Aircraft. 1944 • Numerical applications of conics CAD = CalculatorAidedDesign

9. 1950’s: NC • Milling machines • Lathes • Plotters

13. BezierMethods • 1959 de Casteljau • 60’s Bezier • 1987 de Casteljau / Ramshaw • 1987 Farouki/Rajan

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

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

18. Implicit Methods • 1983 Sederberg • 1992 Bajaj

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

20. PH methods Symbolic methods-Groebner bases ODE methods Trimmed surfaces High degrees Topology Geometry Processing Patrikalakis/Maekawa2001

21. BezierTriangles • 1959 de Casteljau • 1971 Zensiek • 1976 Sabin • 1980 Farin • 1987 Ramshaw • 1987 Alfeld/Schumaker Schumaker / Lai2004

22. pp spaces 3D Studio, Nvidia, Arbitrary topology Smoothness / Shape Not IGES BezierTriangles

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

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

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

30. NURBS • 1966 Coons / Forrest • 1984 Versprille

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

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

34. Use in FEM Twists Not IGES Procedural Coons Patches 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. Shape parameters Reverse engineering Surface Splines Shape parameters Curve to Surface Effort / Results Geometric Continuity

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

39. Future tonight