Robust Geometric Modeling Free From Computational Errors

为了消除计算误差引起的不稳定性，建立了一个健壮的几何造型系统，针对一种基于面的数据结构，建立了多面体的处理算法，并将其推广到曲面对象，在多面体的处理算法中，由于顶点、边和面等几何元素的退化会导致几何与拓扑的不一致，我们引入了一个发病率标准。它是四面体的最小高度，使用四个平面方程的行列式值计算。结合关联检验，得到了它们的关联模式。我们从集合运算和特征运算的干涉环中得到了一个全局拓扑结构。在顶点的退化处，我们通过对那里的面段进行扇区测试来跟踪相交。为了防止顶点周围的模糊形状的错误积累，并保持拓扑结构的一致性，我们在 关于我们 本文介绍了一种确定局部拓扑结构的算法，该算法用树结构表示，不需要生成小面，由于曲面的行列式不能计算四面体的最小距离，因此必须计算三个面的交点到一个面的垂线的足长，并考虑面与面、面与曲线、曲线与曲线的相切。我们已经开发了三个面的交点，从一个点到一个面的垂线，两个面的最小距离位置，以及边界和交点之间的最小距离位置的算法。然后，结合它们，我们确定简并的模式。我们已经检查了用于检测和连接由于误差而不形成环路的交点的方法。我们已经展示了一个算法，以确定局部拓扑的模糊形状周围的顶点为一个弯曲的固体类似的多面体。我们未来的研究工作是在一个系统上通过实验来验证这些算法。少

In order to make a robust geometric modeling system by eliminating instability caused by computational errors, we have established algorithms of processing polyhedra for an introduced face-based data structure, and then extended them to curved objects.In the algorithms for polyhedra, since inconsistency between geometry and topology occurs at the degeneracy of geometric elements such as vertices, edges and faces, we have introduced a criterion of incidence among them. It is the minimum height of a tetrahedron which is calculated using a determinant value from four plane equations. Combining incidence tests, we obtained their incidence patterns. We get a global topological structure from the interference loop for the set operation and feature operation. At the degeneracy for a vertex, we trace the intersection by the sector test for the face segments there. To prevent the accumulation of errors for the ambiguous shape around the vertex and to keep consistency of the topology, we have in … More troduced an algorithm to determine the local topology which is represented as a tree structure not to make small faces.Since we cannot calculate the minimum distance of the tetrahedron from the determinant for curved faces, we have to calculate a foot leng of perpendicular from an intersection point of three faces to a face and consider tangency between faces, a face and a curve and a curve and a curve. We have developed algorithms for an intersection point of three faces, a perpendicular from a point to a face, a minimum distance position of two faces, and a minimum distance position between a boundary and an intersection. Then, combining them, we determine the patterns of the degeneracy. We have examined methods for detecting and connecting the intersection points which do not make a loop because of errors. We have shown an algorithm to determine the local topology of the ambiguous shape around the vertex for a curved solid as similarly as for a polyhedron. Our future research is to confirm the algorithms by experiments on a system. Less