Compatible Remeshing For 3D Models

Many applications in computer graphics usually use mesh to discretize the input model,and also involve the transfer of mesh information,such as texture coordinates,gradient fields and geometric features.Such applications often need to compute a set of meshes that have the same connectivity and are similar in geometry to the given shapes,that is,the compatible meshes.However,existing compatible remeshing methods gen-erally rely on surface mapping,and few methods can generate the final results efficiently and with high quality.Therefore,based on the optimization objectives of high quality,low complexity and bounded error,three efficient generation and optimization methods are proposed in this paper to work on a class of special shape models(PolyCube)and other general shape models.PolyCube is a common structure in computer graphics,and it is usually necessary to calculate the compatible meshes of a model with arbitrary shape and its PolyCube in manny applications.However,traditional method cannot be extended and applied to the construction of compatible meshes of this kind of special shape models.This is mainly because of the construction of PolyCube is non-trivial,and it is not easy to identify a set of sparse corresponding landmarks on the input model and its PolyCube.Therefore,a geometric-enhanced algorithm is introduced in chapter three.Given a sur-face and its pre-axis-aligned shape,this method first constructs the PolyCube by solving a constrained optimization problem,and then uses the mesh segmentation algorithm to compute the bijective mapping between the input surface and its PolyCube with low isometric distortion.In this paper,an erasing-and-filling strategy is proposed to solve the above constrained optimization problem,and a quad mesh optimization process is used to realize the mesh segmentation.Compared with other methods,this voxel-based construction method can obtain bijective PolyCube-maps with low isometric distortion more robustly.However,this geometric-enhanced compatible remeshing method cannot be ex-tended and applied to general shape models.The compatible remeshing method of general shape models is also very important in many applications of computer graphics(such as shape interpolation,model editing and principal component analysis).There-fore,a volume-enhanced compatible remeshing method is introduced in chapter four.Given two surfaces and a set of sparse corresponding landmarks,the method first gener-ates the initial compatible meshes by computing a bijective inter-surface mapping,and then improves the meshes quality by a volume-enhanced process.Since many nonlinear and non-convex energy optimization problems are involved in this method,a monotone preconditioned conjugate gradient method is proposed to solve these problems effi-ciently.Compared with other methods,this volume-enhanced compatible remeshing method can obtain higher mesh quality and computing efficiency.Nevertheless,the volume-enhanced compatible remeshing method still has some limitations:for example,the geometric similarity between the compatible mesh and the input mesh is not controllable,the mesh quality and the number of vertices of the re-sulting compatible mesh will be greatly affected by the input mesh.In order to solve these problems,an error-bounded compatible remeshing method is introduced in chap-ter five.This method can generate high-quality compatible meshes that satisfy five conditions simultaneously(compatibility condition,low distortion condition,regular-ity condition,error-bounded condition and low complexity condition).Since these five conditions are coupled with each other and cannot be satisfied easily,a decoupling algo-rithm with more strictly enhanced properties is developed.Given two surfaces and a set of sparse corresponding landmarks,the method first generates the initial error-bounded compatible meshes by a robust method based on the plane parameterization and the tar-get edge length fields,and then reduces the complexity of the initial compatible meshes by iteratively updating the target edge length field on the premise of not violating the other conditions.Compared with other methods,this method can obtain the compatible meshes with lower complexity under the condition of error-bounded,and can guarantee that the mapping between surfaces has lower distortion.