几何质心的定义和计算

发布时间：2018-05-02 15:12

  本文选题：几何质心 + 三维流形　； 参考：《计算机辅助设计与图形学学报》2017年05期

【摘要】：针对传统的物理质心在形状弯曲的情况下有可能落在物体外部的问题,提出基于惯性矩的几何质心定义及计算方法.根据惯性矩把传统的质心定义拓展到三维流形上,首先基于热传导方程计算物体内部距离得到物体关于某点的惯性矩;然后采用梯度下降法寻找惯性矩的极小值得到几何质心.该几何质心一定落于物体的内部,并且当输入模型为凸时退化为物理质心.实验结果表明,该方法对噪声和姿势变化不敏感,可用于形状分析等目的..
[Abstract]:In order to solve the problem that the traditional physical centroid may fall outside the body in the case of shape bending, the definition and calculation method of geometric centroid based on moment of inertia are proposed. According to the moment of inertia, the traditional definition of the center of mass is extended to the three-dimensional manifold. First, the moment of inertia of the body is obtained by calculating the distance between the interior of the body based on the heat conduction equation, and then the gradient descent method is used to find the minimum value of the moment of inertia to the geometric center of mass. The geometric centroid must fall inside the object and degenerate into the physical centroid when the input model is convex. The experimental results show that the method is insensitive to noise and posture changes and can be used for shape analysis.
【作者单位】： 宁波大学信息科学与工程学院;浙江大学宁波理工学院信息科学与工程学院;宁波大红鹰学院信息工程学院;
【基金】：国家自然科学基金(61300168,11226328,61571247) 浙江省自然科学基金(LY17F020018,LZ16F030001) 浙江省重中之重开放课题(XKXL1429,XKXL1406) 浙江省教育厅科研项目(Y201534799) 宁波市自然科学基金(2016A610041) 宁波大学研究生教育教学研究项目(JGZDI201501) 宁波大学教研项目(JYXMxsj201405)
【分类号】：TP301.6
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本文编号：1834426