One hundred years after the introduction of the Bernstein polynomial basis, we survey the
historical development and current state of theory, algorithms, and applications associated …

This paper surveys the construction, properties, and applications of generalized barycentric
coordinates on polygons and polyhedra. Applications include: surface mesh parametrization …

In this paper, we introduce a new approach based on distance fields to exactly impose
boundary conditions in physics-informed deep neural networks. The challenges in satisfying …

Neural Radiance Fields (NeRFs) have revolutionized novel view synthesis for captured
scenes, with recent methods allowing interactive free-viewpoint navigation and fast training …

Thoroughly revised, this third edition focuses on modern techniques used to generate
synthetic three-dimensional images in a fraction of a second. With the advent of …

In the present paper we introduce a Virtual Element Method (VEM) for the approximate
solution of general linear second order elliptic problems in mixed form, allowing for variable …

Mesh parameterization is a powerful geometry processing tool with numerous computer
graphics applications, from texture map** to animation transfer. This course outlines its …

It is well known that rational interpolation sometimes gives better approximations than
polynomial interpolation, especially for large sequences of points, but it is difficult to control …

We introduce Green Coordinates for closed polyhedral cages. The coordinates are
motivated by Green's third integral identity and respect both the vertices position and faces …

This article gives a general description of the CEDRE® system. CEDRE® is a multi-physics
platform working on general unstructured meshes intended to both advance research and …