Mathematical Foundations in Visualization
This work addresses the need for structured educational foundations in visualization for students and researchers, but it is incremental as it samples literature rather than introducing new methods.
The paper tackles the problem of categorizing and identifying essential mathematical concepts in visualization by providing a taxonomy and recommending foundational mathematics for teaching in visualization research.
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.