In digital geometry processing, remeshing plays a crucial role in converting raw scan data or complex CAD models into high-quality meshes suitable for simulation, rendering, or manufacturing. The goal is to produce a new triangulation that closely approximates the original shape while improving mesh regularity—ideally yielding triangles that are as close to equilateral as possible. In this project, we implemented a parameterization-based remeshing pipeline that systematically adjusts vertex positions to achieve an even, isotropic tessellation across the surface.
Our approach begins by mapping the input mesh to a 2D parameter domain, where we perform a Weighted Centroidal Voronoi Tessellation (WCVT). By relocating each vertex to the weighted centroid of its Voronoi cell in parameter space, we enforce uniform sampling density. The new 2D connectivity is then lifted back onto the 3D surface by projecting through the original mesh’s triangulation, preserving geometric fidelity. A sequence of local mesh operations—edge flips, splits, and collapses—ensures the final mesh both approximates the input within a user-defined error threshold and exhibits well-shaped, size-controlled triangles.
By iterating between parameter-space relaxation and 3D reprojection, the algorithm converges to a remeshed surface that balances approximation error and triangle quality. The result is a visually smooth, simulation-ready mesh that outperforms naive subdivision or decimation methods, particularly on highly curved or scanned surfaces.
Key Challenges
- Mastering CGAL’s Remeshing APIs: Learning the intricacies of the Computational Geometry Algorithms Library, from mesh data structures to its built-in parameterization and Voronoi routines.
- Performance Optimization: Refactoring the WCVT and local operator loops, introducing spatial acceleration structures, and parallelizing vertex updates so that large meshes remesh in minutes rather than hours.