AN AFFINE INVARIANT THEORY AND ITS APPLICATION IN COMPUTATIONAL GEOMETRY

In this paper, an affine invariant theory of parametric curves is first introduced into computational geometry by the authors. We prove a basie theorem that for a parametric curve of degreen, there are m(n-m) - 2 intrinsic affine invariants in an m-dimensional affine hyperspace. We further perfect the theory which is of importance to application in industries, and obtain, among other things, sufficient conditions for being convex everywhere on the plane Bézier curve of degreen; elassification of the plane cubic Bézier curves; distribation of inflexion-points of the plane quartic Bézier curve; cusps and double points for a class of the plane quintic parametric curves. Part of these results has been put into use in the shipbuilding, aeronautic, and automobile industry.