1. Evolution of a Discipline CAGD

2. 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

4. Ben Jakober

5. CAGD A view of history Ockham’s razor Trends

6. CAGD A view of history Ockham’s razor Trends

7. Levels of Abstraction B.C: manual Medevial: Geometric constructions 1600’s: splines 1944: Liming 1960: De Casteljau/Bezier 2000+: manual!

8. A mechanical spline

9. Liming’s benefits Increase in precision and accuracy Elimination of deviations resulting from the human element Uniformity of application of results Close coordination of design, lofting, and production engineering Close coordination with tooling procedures Cross-checking of graphical results Coordination of detailing and checking procedures Convenience in duplication of layouts Basis for continued investigation for new and improved techniques

12. Who was first?

13. CAGD A view of history Ockham’s razor Trends

14. Ockham’s razor If two theories explain the same thing, then the simpler one is to be preferred. William of Ockham ~1300

15. Bernstein-Bezier Clough-Tocher Barycentric coordinates Font design GN: just basis

17. Blossoms B-spline-to-Bezier Compositions Derivatives

18. B-splines Spline curve interpolation Tensor products

20. Evolution dead ends Local coordinates / Wilson-Fowler Transfinite interpolation / Coons-Gordon Geometric continuity for curves / tension

21. CAGD A view of history Ockham’s razor Trends

22. SIAM - Fields Institute Workshop June 25-26, 2001 Fast algorithms for calculating real time geometry; on-line inspection / digitizing Extracting information from large data sets that are not already being addressed in data mining conferences Data compression, translation, and transmission

23. Open Problems surfaces with good curvature distribution Nonlinear vs linear optimization Geometry augmented by function

24. Open Problems Fitting smooth surfaces to voxel data Conversion algorithms: –Parametric –Subdivision –Implicit –Mesh

25. Problems in current systems (b-rep) based on trimmed non-uniform b-spline surfaces (nurbs). Not watertight, since nurbs cannot represent curves of intersection and other derived curves. About 10- 25% of geometry/topology kernel code is devoted to resolving tolerance inconsistencies Models are becoming increasingly complex –Need wide range of representations (Coarse - fine grain) –Need local control of accuracy of model

26. MS-Subdivision Provides approximation of models at various levels of resolution –Concepts from wavelets(?) –So far: ad-hoc, waiting for theoretical basis –Nonstationary schemes?

27. Survival of the Fittest? NURBS Subdivision Triangle Meshes Implicit

28. Open Areas Med/bio modeling Animation Architecture