Recursive Curves and Surfaces in Grassmann Space for Computer Modeling and Animation

Abstract

This study gives the new definition of the rational L curve and surface in Grassmann space, where convert these rational recursive curves and surfaces’ equations to normal polynomial. So we can use blossom algorithms and duality principle to deduce the derivative equations of these curves and surfaces. Thus, the rational L spline curve and surface are defined and constructed based on blossom algorithms and ensuring the continuity of L curve segment and surface patch. Next, we prove that rational L spline curve and surface are the generalization of many interpolation or approach parameter curves and surfaces (Lagrange, rational Lagrange, Bezier, rational Bezier, B spline, NURBS curves and surfaces, etc.). These recurrence curves and surfaces are used to establish the universal storage data file format for different CAD systems.