Research & Application Of Triangular Mesh Model's Hole Filling, Decimation And Stitching Algorithm

The Combination of Reverse Engineering and Dental Medicine produces a new cross-disciplinary subject called the digital dental restoration system. It's also the amalgamation of mechanics, computer, bio-material& medicine. According to RE'concept and its extended application in dental medicine, the main contributions of this paper are as follows:Firstly, this paper explains the relation of Image filtering and Triangular mesh filtering detailedly. This paper also implements the triangular mesh smoothing methods including Laplacian smoothing, Taubin smoothing, Mean curvature flow and Bilateral mesh denoising. We contrast and analyze the smoothing results of each smoothing method with the same Gaussian noisy model and given iteration times, and get the characteristic of each smoothing method.Secondly, this paper proposes a synthesis optimization triangular mesh decimation method which considers the triangle shape, dihedral angle between two triangles which share a common edge and edge lengths in the process of calculating edge collapse costs based on QEM, and also propose a virtual edge collapse method attempting to find a local optimization. The proposed optimization method can achieve much better regular decimation results under the condition of preserving visually important parts of the mesh details. The proposed optimization method also has smaller memory consumption and execution time than most of the published notable algorithms and can be widely used in multi-resolution model rendering, network transmission, computer animation and many other fields.Thirdly, this paper proposes a uniform processing method for triangular mesh's whole filling and stitching. It is mainly composed of the following steps:(1) Triangulate the boundary when hole filling and boundaries when mesh stitching, and get a coarse mesh patch in which the triangle is simply the connections between vertices of boundary (boundaries). (2) Refine the coarse mesh patch according to the mesh's (meshes') boundary density, and also relax interior edges when refining to maintain a Delaunay-like triangulation. After refining and relaxing, we get an optimized mesh patch. (3) Interpolating the boundary(boundaries)constraints and its(them) corresponding normal constraints by a smooth implicit surface based on radial basis function. Using Newton's iteration method, we map the optimized patch's vertices onto the corresponding points in the implicit surface, and get the final mesh patch which smoothly and continuously fitting across the boundary(boundaries). the uniform processing method is proved efficiently and robust in many experiments of different kinds of boundary conditions including filling and stitching.