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 …

Voronoi diagrams partition space according to the influence certain sites exert on their
environment. Since the 17th century, such structures play an important role in many areas …

Centroidal Voronoi tessellation (CVT) is a particular type of Voronoi tessellation that has
many applications in computational sciences and engineering, including computer graphics …

Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a bounded geometric
domain such that the generating points of the tessellations are also the centroids (mass …

This paper introduces L p-Centroidal Voronoi Tessellation (L p-CVT), a generalization of
CVT that minimizes a higher-order moment of the coordinates on the Voronoi cells. This …

In this paper, we propose a generic framework for 3D surface remeshing. Based on a metric-
driven Discrete Voronoi Diagram construction, our output is an optimized 3D triangular mesh …

Additive manufacturing enables the fabrication of objects embedding meta-materials. By
creating fine-scale structures, the object's physical properties can be graded (eg elasticity …

Agglomeration-based strategies are important both within adaptive refinement algorithms
and to construct scalable multilevel algebraic solvers. In order to automatically perform …

During the next decade and beyond, climate system models will be challenged to resolve
scales and processes that are far beyond their current scope. Each climate system …