A (very) basic introduction to DEC

In order to grasp the scope of the Dxtr library, we need first to introduce its underlying mathematical principles:

• The theory of Exterior (Differential) Calculus (EC).
• its discretized version, Discrete Exterior Calculus (DEC).

Useful readings and references

For the non-specialist, the EC and DEC theories might look daring at first sight. They rely on concepts such a k-vectors fields, k-forms, wedge product and their discrete counterparts, k-chains and k-cochains respectively. If you are not already familiar with these concepts, we strongly advise a visite to Keenan Crane's course on Discrete Differential Geometry; It is, to our opinion and knowledge, the smoothest introduction to these concepts:

• Webpage of Keenan Crane's course, a must to get the basics.
• You can also directly download the .pdf of his course notes.
• To further ease the reading of this chapter we propose a small glossary of the main concepts addressed in the sections about EC and DEC but in a less formal and more "intuitive" manner: Glossary

To go further

This quick introduction is not meant to be exhaustive. It is rather an attempt to summarize the most striking features of EC and DEC that sparkled our motivation to develop the Dxtr library. For the interested reader who want to go deeper, we highly recommand the following lectures:

• The founding paper of DEC by Mathieu Desbrun and co-authors
• Anil Hirani's PhD thesis on DEC
• Melvin Leok's PhD thesis (3rd chapter) on DEC
• A very inspiring paper, also from the Caltec group, that ignited our will to build our own DEC library