MOAA and Topology Optimization for Mesh Construction

摘要

In this paper, the Maximum Opposite Angulation Approach-MOAA is presented for the construction of triangular meshes in 3-D space having 'high quality' from a set of unorganized data points. In the proposed method, the topology optimization is also included to improve the quality and the precision of the reconstructed surface. The MOAA method is capable of producing triangular meshes both in 2-D and 3-D space by presetting uniformity to the unorganized point data set. This pre-set uniformity is achieved by the algorithm, i.e. by forming point pairs yielding possible shortest line segments. Then those line segments are connected with proper data points which will provide the vertices of the triangular meshes in such a way that each candidate vertex point provides the maximum opposite angle for the line segment of interest. The MOAA is same as Delaunay approach in 2-D with good efficiency, but much more efficient in forming triangular meshes in 3-D surface reconstruction when it is compared with many other algorithms with respect to preservation capability of the original surface topology. Besides, the topology optimization and thus topology judgment are included in the MOAA to prevent distortion which is related with data points in the neighbourhood of corners, boundaries and sharp edges, to provide high precision on the reconstructed surface. The algorithm developed for this purpose is also presented in this study.