Smooth rational motion of a rigid triangle in R/sup 3/

Abstract

Using rational motions it is possible to apply many fundamental Bezier spline (or B-spline) techniques to the designs of motion. The paper develops and tests a simple automatic algorithm for representing C/sup 1/ smooth motion of a rigid triangle /spl Delta/ in R/sup 3/, by means of piecewise parametric rational curves of degree 2m/2m for some m, when measurements of the positions of the vertices of the triangle /spl Delta/ at a sequence of times t/sub i/, i=0, 1, ..., n, in R/sup 3/ are given. The method presented in the paper can be applied to various problems in computer animation as well as in robotics.