| 摘要: |
| 研究有理B样条曲线的区间隐式化问题，即对给定的一条有理B样条曲线，寻求低次的区间隐式B样条包含给定的曲线，要求区间隐式B样条曲线的宽度尽量小，并且尽量避免多余分支的出现．将该问题分为求解近似隐式曲线和边界曲线两步，并将问题转化为求解局部的线性最优化问题．最后给出几个算例． |
| 关键词: B样条曲线 隐式B样条曲线 区间算法 区间隐式B样条曲线 区间隐式化 |
| DOI： |
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| 基金项目:Supported by the National Science Fund for Distinguished Young Scholars under Grant No．60225002(国家杰出青年基金)；the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE，China(国家教育部优秀青年教师奖励计划)；the National Research Foundation for the Doctoral Program of Higher Education of China No．20010358003(国家教育部博士点基金) |
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| Interval Implicitization of Rationll B-Spline Curves |
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FAN Xu-Chuan,CHEN Fa-Lai
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| Abstract: |
| Study the interval implicitization of rational B-spline curves，that is，finding a lower degree interval implicit B-spline curve which bounds a given B-spline curve such that the width of the interval implict B-spline curve is as small as possible．The problem is solved in two steps：finding an approximate implicit B-spline curve and finding the bounding implicit curves by solving some linear problems．Some examples are provided to demonstrate the algorithm． |
| Key words: B-spline curve implicit B-spline curve intorval arithmetic interval implicit B-spline curve interval implicitization |
