CAGDCAGD history and outlook
Gerald FarinArizona State University
Ben Jakober
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
CAGD
Computing with geometric objects
Representation and Approximation of curves and surfaces
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
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
Dawn of CAGD
• R. Liming: Practical Analytical Geometry with Applications to Aircraft. 1944
• Numerical applications of conics
CAD = Calculator Aided Design
1950’s: NC
• Milling machines
• Lathes
• Plotters
Bezier Methods
• 1959 de Casteljau
• 60’s Bezier
• 1987 de Casteljau / Ramshaw
• 1987 Farouki/Rajan
Bezier Methods
• Standard in -CAD/CAM-Font Design-Animation
• Numerical Stability• no local control
• No local control• Smoothness• Not periodic
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
B-spline Methods
• Standard in -Approximation Theory-CAD/CAM
• Numerical stability• Local control
• Bookkeeping• Topology
Implicit Methods
• 1983 Sederberg
• 1992 Bajaj
Implicit Methods
• Easy ray tracing etc.• Rich shapes
• Evaluation• Unwanted branches• Shape(?)
Geometry Processing
• PH methods• Symbolic methods
-Groebner bases• ODE methods
• Trimmed surfaces• High degrees• Topology
Patrikalakis/Maekawa 2001
Bezier Triangles
• 1959 de Casteljau
• 1971 Zensiek
• 1976 Sabin
• 1980 Farin
• 1987 Ramshaw
• 1987 Alfeld/Schumaker
Schumaker / Lai 2004
Bezier Triangles
• pp spaces• 3D Studio, Nvidia, • Arbitrary topology
• Smoothness / Shape• Not IGES
Triangle Meshes
• FEM
• Digitizers / Rapid prototyping / STL
• 1987 Lorensen / Cline
• 1992 Hoppe et al
Triangle Meshes
• Piecewise linear• Multiresolution• arbitrary topology
• Piecewise linear• Data volume• Class A surfaces
Subdivision Surfaces
• 1953 de Rham
• 1972 Chaikin
• 1978 Doo/Sabin & Catmull/Clark
• 1987 Loop
• 1990 Dyn/Gregory/Levin
• 1994 Reif
Doo-Sabin
Catmull-Clark
Subdivision Surfaces
• Arbitrary topology• Automatic smoothness• Texture mapping
• Not IGES• Point evaluation• Processing
NURBS
• 1966 Coons / Forrest
• 1984 Versprille
NURBS
• “All-encompassing”• Industry standard• Weights• Curves on quadrics• Developable surfaces• Data reduction
• Derivatives • Weights
Coons Patches
• 1960’s Coons
• 1960’s Gordon
• 1970’s Barnhill, Gregory
Coons Patches
• Use in FEM • Twists• Not IGES• Procedural
Procedural: Result of operation is not element of finite-dimensional linear space
Shape
• 1962 Geise
• 1970’s+ Manning, Nielson, Barsky,...
• 1980’s Hoschek, Kellander
• 1990 Shirman/Sequin
Geometric Continuity
• Shape parameters• Reverse engineering• Surface Splines
• Shape parameters• Curve to Surface• Effort / Results
New Topics
• New Geometries
• Volume modeling
• Scattered data approximation
• Med / bio / geo /
• games / animation
Future
tonight
