" In this chapter, we introduce some of the very basics that are used throughout the book.
First, we give the definition of a topological space and related notions of open and closed …

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

Massive simulations and arrays of sensing devices, in combination with increasing
computing resources, have generated large, complex, high-dimensional datasets used to …

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 …

High-pressure chemistry is known to inspire the creation of unexpected new classes of
compounds with exceptional properties. Here, we employ the laser-heated diamond anvil …

This system paper presents the Topology ToolKit (TTK), a software platform designed for the
topological analysis of scalar data in scientific visualization. While topological data analysis …

The emerging field of computational topology utilizes theory from topology and the power of
computing to solve problems in diverse fields. Recent applications include computer …

The medical domain provides excellent opportunities for the application of computer
graphics, visualization and virtual environments, with the potential to help improve …

With the onset of extreme-scale computing, I/O constraints make it increasingly difficult for
scientists to save a sufficient amount of raw simulation data to persistent storage. One …

This handbook provides an up-to-date compendium of fundamental computer science
topics, techniques, and applications. Along with updating and revising many of the existing …