Implicit objects in computer graphics

The implicit description of geometric objects plays a critical role in computer graphics. The mathematical definition of shapes using an implicit form also has great importance for modeling, visualization, and animation problems.Implicit Objects in Computer Graphics employs a coherent conceptual framework to address the expanding role of implicitly defined objects, which increasingly draw attention for uses beyond a complementary representation. The book rigorously delves into the mathematical foundations of geometric models, implicit formulations for the specification of shapes, techniques for constructing implicit objects, and the modeling, rendering, and animation of implicit surfaces. In addition, it demonstrates how implicit models offer a powerful alternative to traditional parametric models in computer graphics and computer-aided design.Features:

• Covers implicitly defined shapes, from modeling aspects to applications
• Provides a broad analysis of the fundamental algorithms and ideas
• Offers an integrated, up-to-date overview of the main developments in the area
• Integrates theory and practice in a clearly organized and cohesive presentation
• Explores key problems and challenges for the field

This unique monograph examines the implicit description of geometric shapes in computer graphics and related areas, such as modeling, visualization, and animation. Researchers, practitioners, and professionals in computer graphics, scientific visualization, CAD/CAM, and special effects will find the book an indispensable tool and resource. Contents

1. Manifolds
2. Parametric and implicit manifolds
3. Space decompositions
4. Shape and space
5. Implicit objects
6. Manipulating implicit objects
7. Combining implicit objects
8. Computational methods
9. Approximating implicit objects
10. Primitive implicit objects
11. Skeleton-based implicit primitives
12. Multiscale implicit objects
13. Modeling
14. Visualization
15. Animation.
16. n-dimensional implicit problems