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.