Transcript Document
CAGD Evolution of a Discipline 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 Ben Jakober CAGD • A view of history • Ockham’s razor • Trends CAGD • A view of history • Ockham’s razor • Trends Levels of Abstraction • • • • • • B.C: manual Medevial: Geometric constructions 1600’s: splines 1944: Liming 1960: De Casteljau/Bezier 2000+: manual! A mechanical spline 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 Who was first? CAGD • A view of history • Ockham’s razor • Trends Ockham’s razor • If two theories explain the same thing, then the simpler one is to be preferred. • William of Ockham ~1300 Bernstein-Bezier • Clough-Tocher • Barycentric coordinates • Font design GN: just basis Blossoms • B-spline-to-Bezier • Compositions • Derivatives B-splines • Spline curve interpolation • Tensor products Evolution dead ends • Local coordinates / Wilson-Fowler • Transfinite interpolation / Coons-Gordon • Geometric continuity for curves / tension CAGD • A view of history • Ockham’s razor • Trends 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 Open Problems • surfaces with good curvature distribution • Nonlinear vs linear optimization • Geometry augmented by function Open Problems • Fitting smooth surfaces to voxel data • Conversion algorithms: – – – – Parametric Subdivision Implicit Mesh 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 1025% 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 MS-Subdivision • Provides approximation of models at various levels of resolution – Concepts from wavelets(?) – So far: ad-hoc, waiting for theoretical basis – Nonstationary schemes? Survival of the Fittest? • NURBS • Subdivision • Triangle Meshes • Implicit Open Areas • Med/bio modeling • Animation • Architecture