Discrete differential geometry

Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there are polygons, meshes, and simplicial complexes. It is used in the study of computer graphics, geometry processing and topological combinatorics.

Discrete differential geometry (DDG) aims not merely to discretize objects or equations, but to discretize the entire theory of classical differential geometry. In this context, classical differential geometry is expected to emerge as a limit of refinement of the discretization. Furthermore, in the process of refinement, DDG places an emphasis on the so-called “mimetic” viewpoint, that is, whether the essential properties of the system from the smooth setting are exactly preserved regardless of the size of the mesh elements.

Generally, for a given smooth geometry, one can suggest many different discretizations with the same continuous limit. In other words, there is no single “correct” way to discretize a given geometric quantity; rather, there are various different ways, each suited to specific purposes. Therefore, it is necessary to choose the appropriate discretization suited to your purpose (the so-called “game” of DDG).

This article is issued from Wikipedia. The text is available under Creative Commons Attribution-Share Alike 4.0 unless otherwise noted. Additional terms may apply for the media files.