an anisoptropic surface remeshing strategy combining higher dimensional embedding with radial basis functions

Abstract Many applications heavily rely on piecewise triangular meshes to describe complex surface geometries. High-quality meshes significantly improve numerical simulations. In practice, however, one often has to deal with several challenges. Some regions in the initial mesh may be overrefined, others too coarse. Additionally, the triangles may be too thin or not properly oriented. We present a novel mesh adaptation procedure which greatly improves the problematic input mesh and overcomes all of these drawbacks. By coupling surface reconstruction via radial basis functions with the higher dimensional embedding surface remeshing technique, we can automatically generate anisotropic meshes. Moreover, we are not only able to fill or coarsen certain mesh regions but also align the triangles according to the curvature of the reconstructed surface. This yields an acceptable trade-off between computational complexity and accuracy

A Parallel Feature-preserving Mesh Variable Offsetting Method with Dynamic Programming

Mesh offsetting plays an important role in discrete geometric processing. In this paper, we propose a parallel feature-preserving mesh offsetting framework with variable distance. Different from the traditional method based on distance and normal vector, a new calculation of offset position is proposed by using dynamic programming and quadratic programming, and the sharp feature can be preserved after offsetting. Instead of distance implicit field, a spatial coverage region represented by polyhedral for computing offsets is proposed. Our method can generate an offsetting model with smaller mesh size, and also can achieve high quality without gaps, holes, and self-intersections. Moreover, several acceleration techniques are proposed for the efficient mesh offsetting, such as the parallel computing with grid, AABB tree and rays computing. In order to show the efficiency and robustness of the proposed framework, we have tested our method on the quadmesh dataset, which is available at [https://www.quadmesh.cloud]. The source code of the proposed algorithm is available on GitHub at [https://github.com/iGame-Lab/PFPOffset]

A curvature-adapted anisotropic surface remeshing method

We present a new method for remeshing surfaces that respect the intrinsic anisotropy of the surfaces. In particular, we use the normal informations of the surfaces, and embed the surfaces into a higher dimensional space (here we use 6d). This allow us to form an isotropic mesh optimization problem in this embedded space. Starting from an initial mesh of a surface, we optimize the mesh by improving the mesh quality measured in the embedded space. The mesh is optimized by combining common local modifications operations, i.e., edge flip, edge contraction, vertex smoothing, and vertex insertion. All operations are applied directly on the 3d surface mesh. This method results a curvature-adapted mesh of the surface. This method can be easily adapted to mesh multi-patches surfaces, i.e., containing corner singularities and sharp features. We present examples of remeshed surfaces from implicit functions and CAD models

A novel surface remeshing scheme via higher dimensional embedding and radial basis functions

Many applications heavily rely on piecewise triangular meshes to describe complex surface geometries. High-quality meshes significantly improve numerical simulations. In practice, however, one often has to deal with several challenges. Some regions in the initial mesh may be overrefined, others too coarse. Additionally, the triangles may be too thin or not properly oriented. We present a novel mesh adaptation procedure which greatly improves the problematic input mesh and overcomes all of these drawbacks. By coupling surface reconstruction via radial basis functions with the higher dimensional embedding surface remeshing technique, we can automatically generate anisotropic meshes. Moreover, we are not only able to fill or coarsen certain mesh regions but also align the triangles according to the curvature of the reconstructed surface. This yields an acceptable trade-off between computational complexity and accuracy

An efficient rotation-free triangle for drape/cloth simulations - Part I: model improvement, dynamic simulation and adaptive remeshing

This series of two papers aim to improve the rotation-free (RF) triangle model previously developed by the authors and apply it for drape/cloth simulations. To avoid a previously un-observed drawback, the membrane strain obtained from the three-node displacement interpolation is replaced by the one obtained from the six-node interpolation. Dynamic simulations are made possible by explicit time integration. Instead of using dense structural meshes, the quality of draped patterns is improved by global adaptive remeshing. The works in this paper provide important and necessary techniques for practical applications of the RF triangle in the drape simulation. In part II, other techniques including collision handling and garment construction are further discussed and some practical applications of garments on still and moving human body model would be presented.postprin

Dr. KID: Direct Remeshing and K-set Isometric Decomposition for Scalable Physicalization of Organic Shapes

Dr. KID is an algorithm that uses isometric decomposition for the physicalization of potato-shaped organic models in a puzzle fashion. The algorithm begins with creating a simple, regular triangular surface mesh of organic shapes, followed by iterative k-means clustering and remeshing. For clustering, we need similarity between triangles (segments) which is defined as a distance function. The distance function maps each triangle's shape to a single point in the virtual 3D space. Thus, the distance between the triangles indicates their degree of dissimilarity. K-means clustering uses this distance and sorts of segments into k classes. After this, remeshing is applied to minimize the distance between triangles within the same cluster by making their shapes identical. Clustering and remeshing are repeated until the distance between triangles in the same cluster reaches an acceptable threshold. We adopt a curvature-aware strategy to determine the surface thickness and finalize puzzle pieces for 3D printing. Identical hinges and holes are created for assembling the puzzle components. For smoother outcomes, we use triangle subdivision along with curvature-aware clustering, generating curved triangular patches for 3D printing. Our algorithm was evaluated using various models, and the 3D-printed results were analyzed. Findings indicate that our algorithm performs reliably on target organic shapes with minimal loss of input geometry