Differential topology, and specifically Morse theory, provide a suitable setting for formalizing
and solving several problems related to shape analysis. The fundamental idea behind …

The goal of this paper is to establish the fundamental tools to analyze signals defined over a
topological space, ie a set of points along with a set of neighborhood relations. This setup …

This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order
generalization of the graph Laplacian. We will discuss basic properties including …

This book describes the theoretical and computational aspects of the mimetic finite
difference method for a wide class of multidimensional elliptic problems, which includes …

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical
and physical systems including conservation laws, symmetry and positivity of solutions …

We present a novel framework for finite element particle-in-cell methods based on the
discretization of the underlying Hamiltonian structure of the Vlasov–Maxwell system. We …

The field of discrete calculus, also known as" discrete exterior calculus", focuses on finding a
proper set of definitions and differential operators that make it possible to operate the …

Direction fields and vector fields play an increasingly important role in computer graphics
and geometry processing. The synthesis of directional fields on surfaces, or other spatial …

In this paper we revisit local feature detectors/descriptors developed for 2D images and
extend them to the more general framework of scalar fields defined on 2D manifolds. We …

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