Computer Graphics and Geometric Modelling

1. Front Matter

   Pages i-xiv

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2. Linear Algebra Topics

   Pages 1-62

3. Affine Geometry

   Pages 63-125

4. Projective Geometry

   Pages 126-207

5. Advanced Calculus Topics

   Pages 208-280

6. Point Set Topology

   Pages 281-320

7. Combinatorial Topology

   Pages 321-357

8. Algebraic Topology

   Pages 358-458

9. Differential Topology

   Pages 459-556

10. Differential Geometry

    Pages 557-673

11. Algebraic Geometry

    Pages 674-812

12. Back Matter

    Pages 813-959

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Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Mathematics, contains the mathematical background needed for the geometric modeling topics in computer graphics covered in the first volume. This volume begins with material from linear algebra and a discussion of the transformations in affine & projective geometry, followed by topics from advanced calculus & chapters on general topology, combinatorial topology, algebraic topology, differential topology, differential geometry, and finally algebraic geometry. Two important goals throughout were to explain the material thoroughly, and to make it self-contained. This volume by itself would make a good mathematics reference book, in particular for practitioners in the field of geometric modelling. Due to its broad coverage and emphasis on explanation it could be used as a text for introductory mathematics courses on some of the covered topics, such as topology (general, combinatorial, algebraic, and differential) and geometry (differential & algebraic).

• Analysis
• computer
• computer graphics
• geometric modeling
• geometric modelling
• modeling
• numerical analysis
• topology

• Cupertino, USA

  Max K. Agoston

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