Deformable Mesh Reconstruction Based On Force Constraint Model And Mesh Process

Digital product modeling based on measured data is one of the key technologies in digital manufacture, and also is the basic and precondition of the following process steps, such as finite element analysis, simulation about product feature and evaluation of digital muck-up. In product design and development, surface modeling of product based on measured data often is finished by some commercial software. In order to obtain the surface model that satifies the requirements in design or manufacture, a great deal of manually operating is needed. So studing the automatically reconstruction of large-scale point cloud and improving the efficiency of surface reoncstruction algorithm are very improtant in academic research and industrial application. Aiming to the topological mesh reconstrction of computing model of measure data of complex product, this thesis studies how to reconstruct automatically the triangular mesh from scattered point cloud to extract and express exactly the topological information. On the basic of the systemic analysis and study about the exiting reconstrucrtion algorithm of sacttered point cloud, this thesis presents one deformable mesh reconstruction algorithm based on force constraint model to process scattered point cloud. This algorithm is based on α-shape method. The validity of this reconstructing algorithm is demonstrated by several real computing examples. The result shows that this reconstruction algorithm can improve the consistency of triangular mesh model, which is very important to extracting automatically the shape feature and modeling of measure data of complex product. In this thesis, first, the geometrical feature structure and properties of the convex hull and delaunay triangles of scattered point cloud are analysed, the convex hull as the initial mesh are constructed quickly through extracting related point computed during constructing convex hull using space division and edge verdict. The initial mesh is chosen as the deforming start state of deformable mesh model, and the deforming direction is extracted based on the feature of convex hull; Second, based on the constraint model between coupled dynamic particle pair, the force constraint equation of deformation is constructed. Some physical feature weightes are are decided and evaluated in each equation items to express the mesh deformation from unstable toward the inherent stable station. The constraint, consisting the force between the unorgainzed point cloud and vertexes of mesh and the forces between the vertexes of mesh, are constructed to the mesh shrinking to the scatted data. Here, these scatted points that drive mesh shrinking are signed as operating points. In the phase, one hiberarchy confirmating algorithm combing distance rule, space segmentation and visible direction is presented for picking up operating points from the scatted points lying inside the convex hull and deleting the points that are noneffective on mesh shrink. Thus the number of points consided in constructing constratin of mesh shrinking is decreased and the computing quantity also is reduced. At last, the criterion of deformation finish is defined. So the initial mesh moves toward the inside of the convex hull and approaches the sampled surface of scattered pints based on the deforming constraaints. During reconnstruction of scattered point cloud, the maintenance of validity of mesh topology is one key problem. Here, suppose that the meausre data is sampled from closed surface of a product with local continuity, thus there should not be wrong topological connection, such as self-intersection, hole, collision and inner connection. During reconstrcting mesh, some ways about topology maintenance are designed and used to obtain the resulted mesh with right topology. Referencing the α-shape method, one virtual ball is used to express mesh deformation process. Define the criterion of deformation finish to controll motion of the virtual ball and ensure that the virtual ball just moves in the space between the surface of scatted points and convex hull, thus there is no inner connection; Using the visiability of points as one rule to extract the operating points, thus self-intersections do not occur; In each iterative step, analyzing the collision between facets and defining the criterion of collision and amending the connection to restrict the happen of collision; Though injointing the split triangles family to tackle the hole and half-edge inside the mesh. Though these ways, the obtained triangular mesh has the same toplogy as the sampled surface of scattered point cloud. In order to be utilized effectively in the following digital design and manufacture, the reconstrcted mesh not noly expresses exactly the topology feature of product, and avoides the long and narrow triangles. But, there are often conflicts between the triangular shape optimization and mesh space shape optimization, between the optimizating operation and topology consistency maintenance. Aiming to this question, one optimizating algorithm of triangular shape based on local knaggy geometrical feature and mesh topology is presented. First, analyzing the effection of different triangular connections on the triangular shpae andmesh sapce shape are analyzed, the extracted criterion of tackled coupled adjacent triangles pair based on maximize minimum angle rules and local smooth degree are defined; Then the local knaggy geometrical feature of mesh is analyzed; Last, the mesh is optimized using different subdivision method according to the local knaggy geometrical feature and mesh topology. Thus, based on constraint of topology consistency maintenance, the result mesh with good triangular shape and mesh space shape is obtained. One non-uniform simplifing algorithm based on forcible constraints is presented. Considing the requirement in manufacturing technics, using this algorithm, one non-uniform mesh is obtained through extending triangles based on several criterions, simplifying edge according to local and whole feature, ect, and express the feature of product using lesser triangles. In VC++, one software system, named MESHTACKLED, is developmented based on some basic data struct in CGAL. Here, CGAL is used as complementary library. This system can complete the deformable mesh reconstruction algorithm based on force constraint model of scattered point cloud, the optimizating algorithm, and the non-uniform simplifying algorithm. Through reconstruction of seveal examples with different shape and complexity proves the validity of algorithms.