B-spline free-form deformation of polygonal object as trimmed Bézier surfaces

Free-form deformation is a powerful shape modification tool. How to approximate or compute the real deformation of a polygonal object is still problematic. In this paper, a new solution is proposed for this problem. First, a special initial B-spline volume is defined whose Jacobian is an identity matrix. The accurate deformation is as trimmed tensor-product Bézier surfaces. The description of the trimmed surfaces is consistent with that in the industrial standard, STEP. The degrees of the Bézier surfaces are lower than the theoretical results. Compared with previous algorithms, the proposed algorithm has the advantages of both storage and run-time.