Subdivision Algorithm For The Triangular Spline Surface (original) (raw)

Subdivision algorithms for rendering of box spline surfaces have been independently developed by Boehm, Cohen, Lyche, Riesenfeld, Dahmen, Michelli and Prautzsch. The algorithm refine the control net of any box spline surface so that the refined control nets converge to the spline. The aim of this paper is to study multivariate B-splines and triangular spline surface. The study will consider the divided difference of a function f which can be expressed in terms of a multiple integral. From here, we give a geometric interpretation of B-splines and the definition of triangular spline on uniform mesh. Subdivision algorithms for rendering of triangular spline surfaces are developed and the triangular spline surfaces are then generated.