Curved Quadrilateral Mesh Generation And Its Application In Fabric Mapping

As a discrete representation of continuous geometric models,meshes are widely used in many fields such as industrial simulation,animation,film and video,and game entertainment.However,mesh generation for complex geometric models is not an easy task,and it is a major performance bottleneck for numerical simulation techniques such as finite element method,finite volume method and finite difference method.The common forms of surface mesh cells are triangular cells and quadrilateral cells.Compared with triangular cells,quadrilateral cells are more popular because of their better numerical computational properties,especially structured quadrilateral meshes and block structured quadrilateral meshes with less singular structures.For surface shapes with complex boundary features for which structured quadrilateral meshes may not be available,chunked structured quadrilateral meshes are the best choice.For two-dimensional planar problems,the region decomposition method based on the scalar field has been proven to be able to be used for high-quality chunked structured quadrilateral mesh generation.However,for 3D surface problems,there is still no better method for generating chunked structured quadrilateral meshes.In this paper,we combine the theory of surface parametric mapping and the theory of2 D planar chunked structured quadrilateral mesh generation to study the chunked structured quadrilateral mesh generation method for 3D surfaces by first downscaling the surface to 2D planes using surface parametric mapping,then generating the mesh on 2D,and subsequently back-projecting the planar mesh back to 3D surfaces with the help of mapping.In this paper,we investigate the 3D solid surface boundary mesh misalignment problem and mesh distortion problem that arise during this process.Specifically,the work in this paper is as follows:(1)A mesh generation method based on piecewise parametric surface structure is proposed.First,the 3D surface model is decomposed by the model feature information,and the surface is projected to the 2D plane according to the surface parameterization.Subsequently,a regional decomposition of the planar region is performed in the 2D plane using the scale-frame field method.In order to keep the mesh consistent on the shared boundary for different segmented surfaces,integer programming is used to determine the number of discrete segments of the boundary at the feature line,and mesh smoothing is used to ensure that the boundary vertices at the feature line overlap.(2)To address the mesh mapping distortion problem at high curvature of the surface,a surface structure mesh generation method based on area distortion constraint is proposed to further improve the mesh quality.In the area decomposition,the distorted contour lines are extracted by quantizing the surface parametric area distortion fraction and introduced into the scale-frame field-based model partition to make the partition with distortion distribution characteristics.For the final quadrilateral mesh,the distorted vector field is extracted and introduced into the Laplacian mesh smoothing,so that the smoothed mesh cell distribution has distorted distribution characteristics.(3)Applying the above chunked structure mesh generation to the garment fabric mapping problem,a semi-automatic low-distortion fabric mapping application is proposed for the problem of parametric mapping distortion and low efficiency of fabric mapping extraction.Firstly,the initial fabric mapping is extracted by analyzing the repetition characteristics,then the fabric mapping is tilted and corrected by detecting the stitching quality;finally,the mapping is established by the mesh generation method in this paper to realize the low-distortion mapping.Through extensive numerical experiments,it is shown that for surface models,the method in this paper can effectively generate high quality quadrilateral meshes while satisfying the constraints of the geometric model boundary features.Based on this method,this paper designs a set of semi-automatic fabric mapping process and realizes fabric mapping with high quality.