GVU Technical Report Number:
GIT-GVU-92-27
Title:
Ray-Affine Functions: A General Dual Form to Describe Curves, Surfaces,
and Volumes
Authors:
Ergun Akleman
Larry F. Hodges
Russell M. Mersereau
Abstract:
In computer graphics modeling, two different forms are used to represent
curves and surfaces: implicit and parametric. Functions that can be
expressed both in implicit and parametric forms are called dual forms.
To date, the only known dual forms are monoids and superquadrics. In
this paper, we introduce a new dual form: ray-affine functions. Ray-affines
include both monoids and superquadrics and provide a wide range
of other modeling functions including exponentials and sinusoidals.
Ray-affines are closed under operations that implement morphing, union,
and interpolation. This feature of ray-affine functions lets the user
construct a ray-affine function to model a shape as a smooth aproximation
of a control shape given by set union or set intersection of shapes
defined by simpler ray-affine functions.
Keywords:
Dual forms, ray-affine functions, modeling functions
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