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CAGD

CAGD. Evolution of a Discipline.

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CAGD

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  1. CAGD Evolution of a Discipline

  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

  3. Ben Jakober

  4. CAGD • A view of history • Ockham’s razor • Trends

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

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

  7. A mechanical spline

  8. 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 Liming’s benefits

  9. Who was first?

  10. CAGD • A view of history • Ockham’s razor • Trends

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

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

  13. Blossoms • B-spline-to-Bezier • Compositions • Derivatives

  14. B-splines • Spline curve interpolation • Tensor products

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

  16. CAGD • A view of history • Ockham’s razor • Trends

  17. SIAM - Fields Institute WorkshopJune 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

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

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

  20. 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

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

  22. Survival of the Fittest? • NURBS • Subdivision • Triangle Meshes • Implicit

  23. Open Areas • Med/bio modeling • Animation • Architecture

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