Discrete implicit surfaces
A discrete implicit surface is considered as the zero set of a
scalar-valued function on an ambient 3-dimensional simplicial complex.
In contrast to the discrete geometry of simplicial surfaces, the
differential operators of implicit surfaces live on the ambient grid.
The purpose of this project is to derive a discrete differential geometric
toolbox for implicit surfaces similar to (explicit) discrete surfaces.
This includes the development of discrete differential operators for
implicit surfaces including curvature operators, and the study of curvature
flows. A major application is the computation of (parametric) discrete
minimal surfaces whose topology is a priori unknown.