Research Of Triangle Mesh Simplification Algorithm Based On Quadric Error Metrics

Triangle Mesh is a kind of polygonal meshes,and it is also a data structure for modeling various irregular objects in computer graphics.Since arbitrary polygons can be subdivided into triangles,it is general to use triangular meshes represent the surfaces of objects.Under the development of three-dimensional scanner and three-dimensional modeling software,with describing the surface of the object more accurately and obtaining more elaborate mesh model,the data size of model becomes larger and larger.Among them,some models has millions or even billions triangular faces,which reduces the computation efficiency greatly.Therefore,it's very necessary to study model simplified algorithm.QEM(Quadric Error Metrics)is one of commonly used methods in the model simplification study.It has the advantages of simplicity and high-efficiency,but it does not retain sufficient details of models,especially when simplify by a wide margin,model contour features will be seriously lost.Aiming at this problem,on the basis of QEM,the thesis researches the edge collapse algorithm and triangle collapse algorithm.The main research and achievements of this thesis is as follows:(1)Introducing the triangular shape factor to correct the calculation of vertex normal vector.(2)Using vertex approximate curvature to describe the change rate of triangular mesh model's local geometric features.(3)Studying the influence of the triangle area of the first-order neighborhood,the approximate curvature of the vertex,the length and triangle regularity have on model geometric characteristics.In addition,these influence factors are used into the edge collapse algorithm and the triangle collapse algorithm,which increases the collapse error of model detailed features and changes the order of collapse.Therefore,the flat area of the model is preferentially simplified and the geometric characteristics of the model is effectively maintained.The thesis make some comparative experiments with various triangle mesh models.According to simplification effect and simplification time,the effectiveness of the algorithm this thesis presents has been proved.Then,analyzes the otherness between the edge collapse algorithm and the triangle collapse algorithm.Finally,some application suggestions for the two algorithms is given.