Last update, March 30, 2004

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Publications by Prof., Dr. Wolfgang Boehm et al.

• Bézier and B-Spline Techniques, 2002.
• Mathematical aspects of Computer Aided Geometric Design, 1994.
• Geometric Concepts for Geometric Design, 1994
• On Cyclides in Geometric Modeling, 1990

BibTeX references.

A few chapters (2, 5, 13) :

Available on-line.

Computer Aided Geometric Design (CAGD) is concerned with the design, computation, and representation of curved objects on a computer. Therefore, not surprisingly, CAGD has traditionally had strong ties to some classical mathematical disciplines such as approximation theory (approximation by polynomial and piecewise polynomial functions), differential geometry (parametric surfaces), algebraic geometry (algebraic surfaces), functional analysis and differential equations (surface design by minimizing functionals), and numerical analysis. In addition, work in CAGD also requires a solid background in computer science.

URLs:

• Geometric center @ Karlsruhe University : http://i33www.ira.uka.de/

Comments

"Often, a solution to a problem lies simply in finding its correct description. It is this underlying concept that consolidates the text of this unique and lively survey of geometric ideas. The authors provide a way to visualize a variety of geometric problems and present the tools for their accurate representation. Disassociating fundamental ideas and methods from special applications, they clarify these concepts for the reader and allow him to apply the material to other problems of a geometric nature. Relying on the idea that a picture "is worth a thousand words," the text is beautifully illustrated with figures and diagrams. Anyone attracted to or wishing to gain a deeper understanding of the beauty of geometric mysteries will find this book engaging and invaluable."

1. Some Linear Algebra (p.1)
   1. Linear Systems
   2. Linear Spaces
   3. Least Squares
2. Images and Projections (p.29)
   1. Parallel Projections
   2. Moving the Object
   3. Perspective Drawings
   4. The Mapping Matrix
   5. Reconstruction
3. Affine Geometry (p.77)
   1. Affine Space
   2. The Barycentric Calculus
   3. Affine Maps
   4. Affine Figures
   5. Quadrics in Affine Spaces
   6. More on Affine Quadrics
   7. Homothetic Pencils
4. Euclidean Geometry (p.153)
   1. The Euclidean Space
   2. Some Euclidean Figures
   3. Quadrics in Euclidean Space
   4. Focal Properties
5. Some Projective Geometry (p.205)
   1. The Projective Space
   2. Projective Maps
   3. Some Projective Figures
   4. Projective Quadrics
6. Some Descriptive Geometry (p.265)
   1. Associated Projections
   2. Penetrations
7. Basic Algebraic Geometry (p.297)
   1. Implicit Curves and Surfaces
   2. Parametric Curves and Surfaces
   3. Some Elimination Methods
   4. Implicitization, Inversion and Intersection
8. Differential Geometry (p.351)
   1. Curves
   2. Curves on Surfaces
   3. Surfaces
9. Bibliography (p.389)
10. Index (p.395)

Page created & maintained by Frederic F. Leymarie, 1998-2004.
Comments, suggestions, etc., mail to: leymarie@lems.brown.edu