Digital geometry processing with discrete exterior calculus

Abstract

These notes provide an introduction to working with real-world geometric data, expressed in the language of discrete exterior calculus (DEC). DEC is a simple, flexible, and efficient framework which provides a unified platform for geometry processing. The notes provide essential mathematical background as well as a large array of real-world examples, with an emphasis on applications and implementation. The material should be accessible to anyone with some exposure to basic linear algebra and vector calculus, though most of the key concepts are reviewed as needed. Coding exercises depend on a basic knowledge of C++, though knowledge of any programming language is likely sufficient: we do not make heavy use of paradigms like inheritance, templates, etc. The notes also provide guided written exercises that can be used to deepen understanding of the material.