| 判定线性不等式构成的凸集是否空集的位置算法 |
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| 引用本文： | 任世军 梁庆姿. 判定线性不等式构成的凸集是否空集的位置算法[J]. 哈尔滨工业大学学报, 2000, 32(2): 121-124 |
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| 作者姓名： | 任世军 梁庆姿 |
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| 作者单位： | 哈尔滨工业大学计算机科学与工程系!黑龙江哈尔滨150001(任世军，洪炳熔)，大庆石油管理局通信公司!黑龙江大庆163453(梁庆姿) |
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| 摘 要： | 给出了判定由一组线性不等式围成的凸空间是否为空集合的算法。证明了对于空间中的一个固定的点，如果不等式组中存在一不等式使得这一点满足这个不等式，同时不等式组中也存在一个不等式使得这一点不满足这个不等式，那么在该点不满足的不等式中一等有一个等式使得此不等式对应的等式与这且不等式构的凸集合的交集不空。
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| 关 键 词： | 凸空间 碰撞检测 空集 线性不等式 凸集 机器人 |
A point positioning algorithm to determine whether convex regions bounded by multiple linear constraints are empty |
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| REN Shi jun ,HONG Bing rong ,LIANG Qing zi. A point positioning algorithm to determine whether convex regions bounded by multiple linear constraints are empty[J]. Journal of Harbin Institute of Technology, 2000, 32(2): 121-124 |
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| Authors: | REN Shi jun HONG Bing rong LIANG Qing zi |
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| Affiliation: | REN Shi jun 1,HONG Bing rong 1,LIANG Qing zi 2 |
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| Abstract: | In this paper we present a point positioning algorithm to determine weather convex regions bounded by multiple linear constraints are empty or not. First we pick up a point in the n dimensional Euclidean space. If there is a inequality that is satisfied by the point and there is also another inequality that is not satisfied by the point, then there must be an inequality that is satisfied by the point such that the intersection of the region and the inequality is not empty. Also there is an inequality that is not satisfied by the point such that the intersection of the region and the inequality is not empty. That is to say we need only to consider the part that contains a less number of inequalities. |
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| Keywords: | linear constraints convex region linear programming |
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