Surface Parametrization For Quad Remeshing

As one of the most common representations of digital 3D models,the polygon mesh model is widely used in digital film,animation,computer games,finite element analysis,architectural design,virtual simulation and other fields due to its simple data structure and easy rendering.With the development of 3D scanning technology,vision reconstruction technology and computer processing capabilities,the acquisition of 3D mesh models has become faster and easier.However,the obtained model is usually a triangle mesh model,which has the disadvantages of large data volume and poor mesh quality,and is far from the actual application requirements.Quad mesh is more widely used in the above fields due to its unique structural characteristics.Quad mesh is categorized as static mesh and dynamic mesh.The static mesh represents a single shape.Its quality is greatly affected by the number and positions of singularities.There is no robust solution on how to effectively control the number and positions of singularities based on the given topology and geometry of the 3D model till now.The dynamic quad mesh represents a continuous change between a series of 3D shapes.How to represent the continuous shape change with quad mesh of the same topology while maintaining the quality of each frame of the dynamic mesh is a hot topic in current research.In view of the above mesh quality problems of the static mesh and the dynamic mesh,this dissertation studies the parametrization based quad remeshing for static and dynamic meshes to meet the practical requirements of mesh quality and robustness of mesh generation.The main contributions are as follows:(1)A closed mesh cutting strategy for explicit construction of parameter domain is proposed.Aiming at explicit construction of the seamless parameter domain for prescribed singularities,a closed mesh cutting strategy suitable for arbitrary genus is given.It includes hole-chain cutting algorithms which is suitable for high genus models,as well as adjustments for low genus models with different singularity configurations.The obtained disk topology can not only be used to guide the explicit construction of the parameter domain,but also ensure the feasibility of constructing a seamless parameter domain.(2)A combination construction method of seamless parameter domain is proposed.Aiming at the problem that no strictly explicit control of singularity distribution in the existing parametrization methods,a combination construction method of seamless parameter domain for given singularities is proposed.Different from using parameter domain as a by-product of mapping optimization,an explicit construction method is proposed.Because numerical optimization is only applied to non-critical decisions,that is,it only affects the quality of parameterization and does not affect its correctness.This method can ensure that as long as a valid singularity configuration is given,a locally injective parameterization result can always be obtained.This avoids possible numerical problems in the mapping optimization process and makes the seamless parametrization method more robust,which provides a valid initial parametrization result for subsequent optimization.(3)A local parametrization method based on an extremal deformation metric is proposed.A local parametrization method based on an extremal deformation metric is proposed for dynamic quad remeshing.Considering the deformation process of a dynamic mesh,an extremal deformation metric is defined.And an anisotropic quad mesh is generated using the metric-aware local parameterization method.The dynamic mesh obtained by this method effectively avoids the problem of undersampling of the mesh which is easy to occur in the deformation process of the non-rigid model,and improves the mesh quality of the dynamic mesh in the worst case.