Curves and Surfaces in Geometric Modeling by Jean Gallier
Curves and Surfaces in Geometric Modeling - Table of Contents
1. Introduction
PART-I BASICS OF AFFINE GEOMETRY
2. Basics of Affine Geometry
PART-II POLYNOMIAL CURVES AND SPLINE CURVES
3. Introduction to Polynomial Curves
4. Multiaffine Maps and Polar Forms
5. Polynomial Curves as Bézier Curves
6. B-Spline Curves
PART-III POLYNOMIAL SURFACES AND SPLINE SURFACES
7. Polynomial Surfaces
8. Subdivision Algorithms for Polynomial Surfaces
9. Polynomial Spline Surfaces and Subdivision Surfaces
10. Embedding an Affine Space in a Vector Space
11. Tensor Products and Symmetric Tensor Products
PART-IV APPENDICES
A. Linear Algebra
B. Complements of Affine Geometry
C. Topology
D. Differential Calculus
What You Will Learn in Curves and Surfaces in Geometric Modeling
"Curves and Surfaces in Geometric Modeling: Theory & Algorithms" by Jean Gallier is a detailed introduction to the mathematics behind "geometric modeling", providing both theoretical and practical insights. The book explains how "curves" and "surfaces" are represented, manipulated, and applied in computer graphics, CAD, and design. Gallier focuses on clear explanations, combining mathematical rigor with real-world applications.
The book covers key topics such as "parametric representations", Bézier and B-spline curves, and surface construction methods. It demonstrates how these mathematical tools are essential for creating smooth, accurate models in engineering and graphics. By linking theory with computation, Gallier shows how mathematical concepts directly impact the design and visualization of complex shapes.
Designed for students, researchers, and professionals, the text balances abstract mathematics with computational methods. It emphasizes practical problem-solving while deepening understanding of the structures behind modern modeling. Readers gain insight into how geometric principles guide the creation of sophisticated curves and surfaces, making this book a cornerstone reference for anyone working in "geometric modeling", computer graphics, or related fields.
Book Details & Specifications
Title:
Curves and Surfaces in Geometric Modeling by Jean Gallier
Publisher:
Morgan Kaufmann
Year:
1999
Pages:
502
Type:
PDF
Language:
English
ISBN-10 #:
1558605991
ISBN-13 #:
978-1558605992
License:
External Educational Resource
Amazon:
Amazon
About the Author: Jean Gallier
The author
Jean Gallier
is a French-American "computer scientist" and mathematician, renowned for his work in "computational geometry" and algorithms. He is a professor at the University of Pennsylvania, with research spanning automated theorem proving, geometric computation, and applications in computer graphics and robotics. His contributions bridge rigorous mathematics with practical computational tools. In "Curves and Surfaces in Geometric Modeling", Gallier explores the mathematical foundations of representing and designing shapes. The book focuses on "geometric modeling", providing theory, algorithms, and examples for "curves", "surfaces", and "computer graphics" applications, making it a key reference for students and researchers in the field.
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