有理B样条曲面的区间隐式化

Interval Implicitization of Rational B-Spline Surfaces

提出有理B样条曲面的区间隐式化方法,即对一个有理B样条曲面,寻求包含给定的曲面的区间隐式B样条曲面,使得区间隐式B样条曲面的“厚度”尽量小,同时尽量避免出现多余分支.该问题等价于求区间隐式B样条曲面的2个边界曲面.针对该问题建立一个最优化模型并求解.

We study the interval implicitization of rational B-spline surfaces; that is, finding an interval implicit B-spline surface which bounds a given rational B-spline surface such that the width of the interval implicit B-spline surface is as small as possible. This problem is equivalent to finding the two bounding surfaces of interval implicit B-spline surface. To achieve this goal, we establish an optimization model and give the solution.