Research On Adaptive Triangulation Algorithm And Key Techniques

Triangulation for3D surfaces is widely used in such areas as the ScientificVisualization, reverse engineering, three-dimensional pretreatment of finite elementmethod, medical visualization,3D scanning system, etc., which is one of the keyparts in the field of computer-aided design, geometric modeling and computergraphics. As an input of surface mesh generation, many geometrical features areusually contained in complex geometry models. To generate a good triangular meshfor numerical analyses, the high resolution should be small near the features toachieve high geometry accuracy and element quality, and large elsewhere to avoidincreasing the number of mesh elements unnecessarily. However, manual resolutioncontrol on complex models is time consuming and prone to errors to achieve suchgoals. Instead, the adaptive triangulation algorithm for three dimensionalunorganized point clouds is capable of overcoming this bottleneck problem,effectively.An adaptive triangulation algorithm for three dimensional unorganized pointclouds is proposed in this paper, since the most existing algorithms are not veryadaptable and are difficult to express the detail characters of the real surface well. Inthe proposed method，we combine4D Shepard surface with multi-resolution analysisand implement the modified octree algorithm, which the curvature of each point inthe point cloud is calculated. Then a hierarchical grid with adaptive resolution isconstructed for generating a triangular mesh from point clouds. Experimental resultsshow that the original algorithm can preserve more characters, but inefficient and notflexible; the improved algorithm is greatly advanced and generally applicable, andforms high quality triangle grid surface and reproduces initial3D object’s detailcharacters, which is suited to popularize in CAGD and surface modeling.Limitations of current3D acquisition technology often lead to triangle meshesexhibiting a number of topological defects. In this paper we present a new methodfor model repair which takes as input an arbitrary mesh and outputs a valid2-manifold triangle mesh. By means of a defect detecting technology based onadaptive hierarchical grid, our method allows users to conveniently identify areaswith potential topological errors. Then using morphological operators, the topologyof the model can be modified. The experiment validate the feasibility and accuracy of the repair strategies.The conversion of the corrected model back into a2-manifold triangle mesh isable to be finished quickly through topological mesh operators based on Handlebodyand Stellar theory. This approach avoids the formation of handles and cavities andguarantees a topologically correct reconstruction of the object’s surface.Experimental results show that the proposed algorithm is greatly advanced andgenerally applicable, and forms high quality triangle grid surface, which is suited topopularize in CAGD and surface modeling.In this paper we present a topology completeness detection algorithm fortriangular meshes based on the Euler characterlstic and the scale factor. Bycalculating Euler characterlstic, some complex calculations, such as triangularmeshes reconstruction, differential geometry property re-estimate, etc., are avoided,which simplified the problem so that the extraction efficiency for topological featureof mesh model is greatly enhanced. Through introducing the scale factor, meshsurfaces are able to observed on larger scale. According to surface shape, differentscales are adopted in geometric features on different scales, which large scalesurfaces are detected on large scale, and small scale surfaces are detected on smallscale. The precision and efficiency of reconstructed model are improved remarkably.