Discrete implicit surfaces

• Applicant: Professor Dr. Konrad Polthier
• Subject Area: Mathematics
• Term: from 2008 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5471407

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 the 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 curvature flows. A major application is the computation of (parametric) discrete minimal surfaces whose topology is a priori unknown.

• DFG Programme: Research Units
• Subproject of: FOR 565: Polyhedral Surfaces