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

Combining concepts from topology and algorithms, this book delivers what its title promises:
an introduction to the field of computational topology. Starting with motivating problems in …

Differential invariants of curves and surfaces such as curvatures and their derivatives play a
central role in Geometry Processing. They are, however, sensitive to noise and minor …

We present a novel approach for optimizing real‐valued functions based on a wide range of
topological criteria. In particular, we show how to modify a given function in order to remove …

Given a smoothly embedded 2-manifold in ℝ3, we define the elevation of a point as the
height difference to a canonically defined second point on the same manifold. Our definition …

Interactions between atoms have a major influence on the chemical properties of molecular
systems. While covalent interactions impose the structural integrity of molecules …

Morse theory offers a natural and mathematically‐sound tool for shape analysis and
understanding. It allows studying the behavior of a scalar function defined on a manifold …

Analysis of the results obtained from material simulations is important in the physical
sciences. Our research was motivated by the need to investigate the properties of a …

The Morse-Smale complex is a useful topological data structure for the analysis and
visualization of scalar data. This paper describes an algorithm that processes all mesh …

Many applications of geometry processing and computer vision rely on geometric properties
of curves, particularly, their curvature. Several methods have already been proposed to …