Application Of Geodesic Distance In Mesh Editing Algorithm

Geodesic,as an important characteristic line of differential geometry,determines some important features of the surface to a great extent.So far,most of the mesh processing algorithm in keeping the geometric characteristics are often not desirable,algorithms lack of geometry internality.The reason for this is that the mesh not subjected to the discrete geodesic distance field monitoring before and after processing,especially without considering make full use of the intrinsic geometric properties of the surface,e.g.the discrete curvature line and the discrete geodesic line;the distribution of these two feature lines on the mesh may be quite different before and after processing.This not only easily leads to the deformation of mesh geometry,but also seriously affects the rationality of mesh partitioning.In order to maintain the local details of the 3D model,correct the problem of distortion and folding of the as-rigid-as-possible(ARAP)mesh deformation used in large and non rigid deformation,An ARAP deformation method is proposed based on geometric field in heat.First,the Laplacian deformation of the model is carried out.On this basis,the rotation matrix of local cell is solved by singular value decomposition,and the rigid deformation energy of the model is calculated;Then by solving the sparse linear system,the deformation points are updated.By solving the two time sparse linear system,calculation of the deformation process of the geometric field deviation,and the deviation correct mesh deformation geometric field close to the results with the original mesh.Iterate the above steps until the geometric field deviation to meet certain requirements,finally the final deformation results are obtained.The example shows that the method can quickly complete the mesh point correction function in mesh deformation process,and it can also effectively avoid grid collapse when applied to large-scale deformation.Mesh simplification is a common problem in practical triangular mesh application.In view of the poor quality of existing parallel mesh simplification algorithm and the vertex clustering mesh simplification algorithm may change the topology of mesh,we proposed a fast mesh simplification algorithm based on the geodesic Delaunay triangulation.Firstly based on the random sampling method of probability distribution function,sampling mesh vertices to obtain high quality sampling vertices,we define sampling vertices as source vertices to do geodesic Voronoi diagram and geodesic Delaunay triangulation,and record each sampling vertex with its corresponding vertices in Voronoi region.Then,the quadric error matrix of each vertex is calculated in parallel,and the sampling vertex position is updated based on the quadric error matrix of the vertices in the Voronoi region.Finally by replacing Delaunay edge to mesh edge,we get the simplified mesh.In this paper,the experimental results show that compared with the existing parallel QEM mesh simplification algorithm,this algorithm can preserve the geometric characteristics of the original mesh avoid face flipping,compared with the existing vertex clustering simplification algorithm,has a better quality of the mesh.