Research On Quadrilateral Partition Method Based Manifold Mesh In Reverse Engineering

With the development of the digital measure technology, RE( Reverse Engineering ), RP(Rapid Prototyping) and NC(numerical control) together have become the key technologies of RPD(Rapid Product Development). Reconstructing manifold mesh model is one of valid methods for massive disheveled data. however, this method cannot still be used in precision machining directly. Therefore exact parsing method should be founded. At the present time, popular modeling technologies like NURBS are based on rectangle topology, quadrilateral region partition is a precondition of NURBS surface reconstruction based on manifold mesh, and it is also a difficulty.Firstly, for the point clouds without obvious topology and with redundancy, we defined some basal concepts including the mesh boundary, the star adjacent field, the semi-star adjacent field, the average plane, the curvature, the shape factor and so on. And we present the mesh simplification method considering the vertex curvature and the distance to the average plane and put forward the rule of optimized mesh which guarantees the reasonable data structure for the arithmetic and is based on short edge deleted and the long edge bisected. Thereout, the mapping method and matching method are presented, which are for the quadrilateral partition of the moderate manifold mesh. Due to the complicated geometrical operation and the mathematic groundwork are needed for the quadrilateral partition on the complicated spatial mesh, the mapping method makes the spatial mesh model mapped to the simple topology field on the plane by harmonic mapping, which makes us manage the complicated model like managing the plane. Therefore, the rapid quadrilateral partition of the complicated manifold mesh is implemented by the definition of the simple mapping field for rectangle and circle, the reasonable region intersected template, the reverse mapping, shortest path boundary, and the interior triangular rapid tracing arithmetic. At the same time, in view of good triangular quality and lesser amounts on some simplification models, and based on thesimple idea of two neighboring triangles combined one quadrangle, the matching model of the manifold mesh is founded, which is guided by the related theory of the undirected graph. Besides, the complexity of time and space is analyzed, and some examples areindicated feasibility and validity of the method.