This article defines a new way to perform intuitive and geometrically faithful regressions on
histogram-valued data. It leverages the theory of optimal transport, and in particular the …

Centroidal Voronoi tessellation (CVT) is a special type of Voronoi diagram such that the
generating point of each Voronoi cell is also its center of mass. The CVT has broad …

We introduce ReMatching, a novel shape correspondence solution based on the functional
maps framework. Our method, by exploiting a new and appropriate re-meshing paradigm …

We consider the problem of generalizing affine combinations in Euclidean spaces to triangle
meshes: computing weighted averages of points on surfaces. We address both the forward …

With the rapid progress in engineering simulation, there is an increasing industrial need for
accurate mesh generation methods. Furthermore, the development of data-driven methods …

Since the arrival of Automated Fiber Placement (AFP) in the 1980s and 1990s, the
manufacturing technique has been progressively improving in quality and reliability of the …

We introduce geodesic finite elements as a conforming way to discretize partial differential
equations for functions v: Ω→ M, where Ω is an open subset of and M is a Riemannian …

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates
in Gillette et al.(Adv Comput Math 37 (3), 417–439, 2012), we prove interpolation error …

We define Voronoi cells and centroids based on heat diffusion. These heat cells and heat
centroids coincide with the common definitions in Euclidean spaces. On curved surfaces …

We study a natural intrinsic definition of geometric simplices in Riemannian manifolds of
arbitrary finite dimension, and exploit these simplices to obtain criteria for triangulating …