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 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
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
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
Subdivision Surfaces
• Arbitrary topology• Automatic smoothness• Texture mapping
• Not IGES• Point evaluation• Processing
NURBS
• “All-encompassing”• Industry standard• Weights• Curves on quadrics• Developable surfaces• Data reduction
• Derivatives • Weights
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