图学学报
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摘要: 三维空间中离散点集的最小包围球,在碰撞检测、计算几何和模式识别等领域都 有广泛应用。为了更好地理解和构造最小包围球算法,首先对最小包围球的性质进行分析。然 后,基于对随机增量算法的分析,提出了构造较大初始包围球和减少迭代过程中最小包围球更 新次数两种策略。依据后一种策略提出的方法称为随机点组-重算最远点算法。计算机随机生成 数据和现实三维模型采样数据的多组实验结果表明,随机点组-重算最远点算法相比于之前的经 典算法能够有效地提高时间效率。
关键词: 最小包围球, 随机增量算法, 随机点组-重算最远点算法
Abstract: The minimum enclosing ball (MEB) of discrete point set in the 3D space has been widely used in many fields, such as collision detection, computational geometry, pattern recognition and so on. In order to better understand and construct MEB, its character is analyzed firstly. After analyzing the classical randomized incremental algorithm, we propose two strategies to improve time efficiency. One strategy is to construct a bigger initial enclosing ball and another strategy is to decrease the number of updating MEB. Based on the second strategy, a new algorithm called random point group-recalculation farthest point is proposed. Multi-group experimental results, whose data are both randomly generated by computer and realistic 3D model sampling, show that the random point group-recalculation farthest point algorithm can effectively improve the time efficiency compared with the classical algorithms.
Key words: minimum enclosing ball, randomized incremental algorithm, random point grouprecalculation farthest point
李世林, 李红军. 改进的最小包围球随机增量算法[J]. 图学学报, DOI: 10.11996/JG.j.2095-302X.2016020166.
Li Shilin, Li Hongjun. An Improved Randomized Incremental Algorithm for Generating Minimum#br# Enclosing Ball of Discrete Point Set[J]. Journal of Graphics, DOI: 10.11996/JG.j.2095-302X.2016020166.
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链接本文: http://www.txxb.com.cn/CN/10.11996/JG.j.2095-302X.2016020166
http://www.txxb.com.cn/CN/Y2016/V37/I2/166