DFG Research

SFB Transregio 109 - Project C05

Konrad Polthier

Jul 01, 2016 — Jun 30, 2020

In project C05 “Computational and structural aspects of point set surfaces”, we develop discrete differential geometric representations for point set surfaces and effective computational algorithms. Instead of first reconstructing a triangle based mesh, our operators act directly on the point set data. The concepts have contact to meshless methods and ansatz spaces of radial basis functions. As proof of concept of our theoretical investigations we transfer and implement key algorithms from ...

DFG Research — finished

Project Polyhedral Surfaces - Discrete Implicit Surfaces

Konrad Polthier

Feb 01, 2008 — Apr 30, 2012

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 ...

SFB Transregio 109 - Project A04

Folkmar Bornemann, Konrad Polthier

Jul 01, 2012 — Jun 30, 2016

This project is based on combined efforts in discrete differential geometry and finite element methods for geometric partial differential equations. Especially, discretizations using polyhedral surfaces and piecewise linear functions on them proved to be very successful in both theory and applications. This development led to the creation of counterparts of geometric and metric properties of smooth surfaces on polyhedral surfaces and to insights on convergence properties of them. A geometric ...