Quadric Polynomial Interpolation Based on Minimum Local Stretching Energy

Abstract

This paper presents a method to construct C1 polynomial surface with scattered data points. At first the given data points are divided into triangular networks, and then at the adjacent region of each point a C1 piecewise quadric interpolation patch is constructed. Objective function according to the stretching strain energy is constructed. Minimizing the objective function to determine the unknown quantities, and at last achieves fair interpolating surface. The constructed surface has the shape suggested by the given data points. At last comparison examples are included to prove the efficiency of the new method.