Mesh Morphing Based On Conformal Geometry And Differential Coordinates

With the rapid development of hardware technology and computer graphics,the acquisition of three-dimensional object model becomes more and more simple,and the research on all aspects of 3D model is becoming more and more hot.The three-dimensional model has strong realism and various technology related to 3D model is widely used in film and television,commercial advertising,game simulation,industrial design and other fields.Three-dimensional model of the mesh morphing,as arn important research direction in the computer graphics field,refers to a smooth,natural gradient process from one object to another object.This technique can be applied to any industrial or commercial field where it is necessary to achieve deformation between objects or to construct new objects through existing objects.Generally speaking,the mesh morphing generally consists of two steps:mesh registration and shape interpolation.The mesh registration refers to the establishment of the corresponding relationship between the source mesh and the target mesh(including the corresponding relationship between the vertex and mesh connection).Mesh registration can be divided into three steps:parameterization,feature point registration and construction of super mesh.The shape interpolation is the process of constructing the intermediate time interpolation sequence to two surface mesh according to the interpolation method.In this paper,we focus on the morphing of surface triangular meshes on the surface of 3D model.Firstly,the related techniques and methods used in the process of morphing are presented and summarized in detail.Then combined with the requirements of mesh morphing to the shape maintain during the deformation process and the shortcomings of the current mesh morphing research interpolation method at present,this paper present a mesh morphing method based on a conformal geometry and differential coordinate interpolation.At the mesh registration stage,the source mesh and the target mesh are mapped to the common parameter domain by using the conformal mapping,and the feature points selected by the user are registered by the radial basis interpolation function.Finally,constructing the super mesh to obtain the source interpolation mesh and the target interpolation mesh with the same connection relation and vertex.At the shape interpolation stage,firstly calculating the differential coordinates which are based on the tangent weight respectively,and then interpolate to it,and in turn to find the absolute coordinates to get the interpolation results.The use of conformal mapping(also known as angle preserving mapping)not only has good shape retention characteristics,but also without angular deformation in the parameterization process.In addition,taking some shortcomings of the current mesh morphing shape interpolation and the good nature of tangent weights in the parametric application into account,this paper use the differential coordinates which are based on the tangent weight to interpolate.The experimental results show that the method proposed in this paper has good feasibility and effectiveness.Compared with other methods,the method proposed in this paper has the advantages of small deformation of parameterized process,smooth and natural effect of deformation sequence,and also has good expansibility.