Functional composition algorithms via blossoming

Tony D. DeRose, Ronald N. Goldman, Hans Hagen, Stephen Mann

Abstract:

In view of the fundamental role that functional composition plays in mathematics, it is not surprising that a variety of problems in geometric modeling can be viewed as instances of the following composition problem: given representations for two functions F and G, compute a representation of the function H = F o G. We examine this problem in detail for the case when F and G are given in either Bezier or B-spline form. Blossoming techniques are used to gain theoretical insight into the structure of the solution which is then used to develop efficient, tightly codable algorithms. From a practical point of view, if the composition algorithms are implemented as library routines, a number of geometric-modeling problems can be solved with a small amount of additional software.

Available in Transactions on Graphics, Vol 12, No 2, April 1993.