利用三角剖分算法进行小天体物理属性计算

提出了一种利用三维散乱点对小天体表面进行三角剖分,并对小天体的多个物理属性进行估计的简单快速算法.先将小天体表面的散乱点映射到单位球面上,再进一步映射到平面上进行三角网格剖分,避免了非凸边界对原有拓扑结构的破坏.在形成三角网格的基础上,将对体积的积分转化为对多面体顶点坐标的计算,并采用分割小四面体的算法简化了利用格林公式进行多次积分转化的计算过程,从而求出小天体的体积、表面积、质心、转动惯量、惯量主轴及其引力势、引力场分布等多个重要的物理量.通过仿真分析了散乱点数目对计算精度的影响,验证了该算法的正确性.

Physical properties calculation of small body using points triangulations

This paper presents a simple and rapid algorithm for small body surface triangulations and physical properities calculation based on 3-D arbitrary points. In order to avoid destroying the original topology due to the non-convex boundary, the arbitrary points are first mapped on the unit sphere and then mapped on a 2-D plane to complete the triangular mesh generation. Based on this, the volume integral can be transformed into polyhedron vertex computation, and the processes of integral reduction using Green formula can be simplified by decomposing the polyhedron into a series of tetrahedrons. Thus the physical properties such as volume, surface aera, center of mass, moment of inertia, principal axis of intertia, gravitational potential, gravitational field intensity of the small body can be computed. Simulation shows the relationship between points number and the calculation accuracy as well as the correctness of the algorithm.