Based on analysis of cubic spline interpolation, the differentiation formulas of the cubic spline interpolation on the three boundary conditions are put up forward in this paper. At last, this calculation method is illustrated through an example. The numerical results show that the spline numerical differentiations are quite effective for estimating first and higher derivatives of equally and u...

We provide su cient conditions for the Bernstein-B ezier (BB) form of an implicitly de ned bivariate polynomial over a triangle, such that the zero contour of the polynomial de nes a smooth and single sheeted real algebraic curve segment. We call a piecewise G-continuous chain of such real algebraic curve segments in BB-form as an A-spline (short for algebraic spline). We prove that the degree ...

In this article, we address the problem of interpolating data points lying on a regular grid by C 1-continuous L1-bicubic spline surfaces. Our algorithm is based on a local univariate L1 minimization method which enable us to calculate first derivative values for C 1-cubic spline curves. In order to construct the interpolation surface, we calculate four derivative values at each data point usin...

The metamorphosis between two user-specified objects offers an intuitive metaphor for designing animations of deforming shapes. We present a new technique for interactively editing such deformations and for animating them in realtime. Besides the starting and ending shapes, our approach offers easy to use additional control over the deformations. The new Bezier Interpolating Polyhedron (BIP) pr...