In this paper, the Maximum Opposite Angulation Approach (MOAA) for 3-D including the topology optimization is discussed. The MOAA algorithm is developed to generate meshes in 2-D and 3-D. The basic principles of the algorithm both in 2-D applications and in 3-D applications, is to pre-set uniformity to the initial data set to form point pairs yielding possible shortest line segments. These line segments are connected with the points providing the maximum angle for the vertex of the triangular mesh to be constructed. Thus, the algorithm provides triangular meshes having well balanced interior angles and good aspect ratios. The MOAA algorithm can be proved similar to the Delaunay’s approach in 2-D from the principle and with the quickest speed. In 3-D, it was also shown that it is much more efficient than many Delaunay class algorithms with mesh architectures preserving the topology, for uniformly organized data points. In this study, the topology optimization together with the MOAA algorithm is presented to improve the precision of reconstruction of the original surface. In this context, topology judgment for intersection problem in 3-D, distortion phenomenon, the possibility of loosing some characteristics of the original surface is thoroughly investigated.
Graph Logics with Rational Relations and the Generalized Intersection Problem
