Symbolic Computation of Equi-affine Evolute for Plane B-Spline Curves

摘要

In Euclidean plane geometry, the evolute of both B-spline and NURBS curves are NURBS curves. Moreover, this evolute can be computed symbolically. This article extends those results to the equi-affine plane geometry. Analogously to Euclidean geometry, the equi-affine evolute of both B-spline and NURBS curves are NURBS curves and an algorithm for the symbolic computation is given for B-spline curves. This results in a new method to analyze the global affine differential properties of B-spline curves and assess B-spline curve quality in an affine invariant context.