Implicit objects have gained increasing importance in geometric
modeling, visualisation, animation, and computer graphics, because
their geometric properties provide a good alternative to
traditional parametric objects. This book presents the mathematics,
computational methods and data structures, as well as the
algorithms needed to render implicit curves and surfaces, and shows
how implicit objects can easily describe smooth, intricate, and
articulatable shapes, and hence why they are being increasingly
used in graphical applications.
Divided into two parts, the first introduces the mathematics of
implicit curves and surfaces, as well as the data structures suited
to store their sampled or discrete approximations, and the second
deals with different computational methods for sampling implicit
curves and surfaces, with particular reference to how these are
applied to functions in 2D and 3D spaces.
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