五次B-B曲面片构造G^1连续曲面重构方法

Reconstruction of complete G^1-Continuous Surface using Quintic Triangular B-B Patches Method

提出了用五次B-B曲面片构造整体G1连续曲面的计算方法。从G1连续曲面的充分条件推导了控制点的计算方法,并从方向导数的定义出发,通过最小二乘方法拟合已知点处的双变量函数,直接计算已知点的一阶,二阶方向导数来得到控制点的计算公式;分别对曲面片的内部和边界两种情况作了推导;这种方法在保证精度的情况下计算量较之六次B-B曲面片有较大的减少。

A method to reconstruct a complete G^1-continuous surface by interpolating scattered data with quintic triangular Bernstain-Bezier（B-B） patches was proposed and the formula for calculating control points of patches from sufficient conditions was introduced, A bivariate function was fit with the Least Square Method to calculate the first and the second derivatives at given point to obtain the unknown control points. Different tactics were adopted according to interior and exterior control points of patches. Vertex consistent problem, which usually occured in other methods, was solved by using this method. And the cost of computing is much less than senary triangular B-B patches.