Mathematical Foundations in Visualization

TL;DR

This chapter surveys the role of mathematical concepts in visualization, proposing a taxonomy and emphasizing essential mathematics for students to understand contemporary visualization techniques.

Contribution

It provides a taxonomy of mathematical usage in visualization and identifies key mathematical concepts to include in education for visualization research.

Findings

Taxonomy of mathematics in visualization

Identification of fundamental mathematical concepts

Guidance on teaching mathematics in visualization

Abstract

Mathematical concepts and tools have shaped the field of visualization in fundamental ways and played a key role in the development of a large variety of visualization techniques. In this chapter, we sample the visualization literature to provide a taxonomy of the usage of mathematics in visualization, and to identify a fundamental set of mathematics that should be taught to students as part of an introduction to contemporary visualization research. Within the scope of this chapter, we are unable to provide a full review of all mathematical foundations of visualization; rather, we identify a number of concepts that are useful in visualization, explain their significance, and provide references for further reading.