Riemannian Geometry for Scientific Visualization

Overview

KVL, in a collaboration led by Prof. Markus Hadwiger, presents a tutorials introducing the most important basics of Riemannian geometry and related concepts with a specific focus on applications in scientific visualization

Work Summary

The two main goals of this tutorial are:

• Introduce Riemannian geometry to scientific visualization researchers and practitioners
• Introduce researchers working in/with differential geometry or mathematical physics to important applications in scientific visualization.

We try to particularly highlight the additional insight that can be gained from employing concepts from Riemannian geometry in scientific visualization, however, we also discuss computational advantages. In addition to Riemannian metrics, we also introduce the most important related concepts from modern, coordinate-free differential geometry, in particular general (non-Cartesian) tensor fields and differential forms, smooth mappings between manifolds, Lie derivatives, and Lie groups and Lie algebras. Throughout the tutorial, we use several examples from the scientific visualization literature, dealing with scalar, vector, or tensor fields, respectively, and highlight their implicit or explicit connections to Riemannian geometry.

• Riemannian Geometry in Scientific Visualization Project Page
• SIGGRAPH Asia 2022 Course Notes

Impact

This long-term project with KAUST faculty is an example of KVL's wide-ranging collaborative efforts to provide training on state-of-the-art visualization techniques for scientific discovery.