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