Implicit Objects in Computer Graphics

Implicit definition and description of geometric objects and surfaces plays a critical role in the appearance and manipulation of computer graphics. In addition, the mathematical definition of shapes, using an implicit form, has pivotal applications for geometric modeling, visualization and animation.
Until recently, the parametric form has been by far the most popular geometric representation used in computer graphics and computer-aided design. Whereas parametric objects and the techniques associated with them have been exhaustively developed, the implicit form has been used as a complementary geometric representation, mainly in the restricted context of specific applications. However, recent developments in graphics are changing this situation, and the community is beginning to draw its attention to implicit objects. This is reflected in the current research of aspects related to this subject. Employing a coherent conceptual framework, Implicit Objects in Computer Graphics addresses the role of implicitly defined objects in the following parts: mathematical foundations of geometric models, implicit formulations for the specification of shapes, implicit primitives, techniques for constructing and manipulating implicit objects, modeling, rendering and animating implicit objects.

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

Manifolds.- Parametric and Implicit Manifolds.- Space Decompositions.- Shape and Space.- Implicit Objects.- Manipulating Implicit Objects.- Combining Implicit Objects.- Computational Methods.- Approximating Implicit Objects.- Primitive Implicit Objects.- Skeleton-Based Implicit Primitives.- 13. Multiscale Implicit Objects.- Modeling.- Visualization.- Animation.- n-dimensional Implicit Problems.- Conclusions.