B-spline free-form deformation of polygonal objects through fast functional composition

Free-form deformation, abbreviated to FFD, plays an important role in both computer animation and geometric modeling. When polygonal objects are deformed by the traditional FFD scheme, however aliasing will appear since the deformation only acts on the sample points of the objects. To eliminate this problem, a new method of accurate B-spline FFD was proposed by authors previously, which is based on functional composition. Unfortunately it is a time consuming process because generalized de Casteljau algorithm is adopted to solve the functional composition. In this paper we propose a fast accurate B-spline FFD method. The proposed method makes use of the polynomial interpolation and symbolic computation to solve the functional composition. Both theoretical analysis and implementation results show that the proposed method runs faster than the original one.