This monograph reviews both the theory and practice of the numerical computation of
geodesic distances on Riemannian manifolds. The notion of Riemannian manifold allows …

Triangle meshes are used in many important shape-related applications including geometric
modeling, animation production, system simulation, and visualization. However, these …

Geometric and topological inference deals with the retrieval of information about a geometric
object using only a finite set of possibly noisy sample points. It has connections to manifold …

We give a provably correct algorithm to reconstruct ak-dimensional manifold embedded in d-
dimensional Euclidean space. Input to our algorithm is a point sample coming from an …

CGALmesh is the mesh generation software package of the Computational Geometry
Algorithm Library (CGAL). It generates isotropic simplicial meshes—surface triangular …

This paper introduces a particle-based approach for anisotropic surface meshing. Given an
input polygonal mesh endowed with a Riemannian metric and a specified number of …

The convexity of a set can be generalized to the two weaker notions of positive reach and r-
convexity; both describe the regularity of a set's boundary. For any compact subset of R d …

We present a novel method to generate high-quality simplicial meshes with specified
anisotropy. Given a surface or volumetric domain equipped with a Riemannian metric that …

Surface meshing plays a fundamental important role in Visualization and Computer
Graphics, which produces discrete meshes to approximate a smooth surface. Many …

Anisotropic simplicial meshes are triangulations with elements elongated along prescribed
directions. Anisotropic meshes have been shown well suited for interpolation of functions or …