Construction of Fairing Surface with Polynomial Interpolation

For constructing fairing polynomial interpolation surface,triangle meshes are obtained firstly from the given data points,and C1 piecewise quadric interpolation patch is constructed at the adjacent region of each point.The unknown quantities of the patch on each triangle are obtained based on the degrees of the center point by minimizing the function of energy based on stretch energy and blend energy respectively.Finally,we achieve the fairing surface with the shape suggested by the given data points.Comparison example is also presented to show the validity of the new method.