Discrete Differential Geometry

Discrete Differential Geometry 655 Workshop : Discrete Differential Geometry

Discrete Differential Geometry is a broad new area where differential geometry (studying smooth curves, surfaces and other manifolds) interacts with discrete geometry (studying polyhedral manifolds), using tools and ideas from all parts of mathematics. This report documents the 29 lectures at the first Oberwolfach workshop in this subject, with topics ranging from discrete integrable systems, p...

Geometry II - Discrete Differential Geometry

Discrete Differential Geometry and Discrete Mechanics

IN:SHOP-using telepresence and immersive VR for a new shopping experience p. 3 Hardware accelerated texture extraction for a photo-realistic predictive display p. 11 Image-based rendering from handheld cameras using quad primitives p. 19 An efficient point location method for visualization in large unstructured grids p. 27 ADB-trees : controlling the error of time-critical collision detection p...

Discrete Differential Geometry: an Applied Introduction

domain M parameterization immersed surface Remember that, like the cartographers of yore, our goal is to parameterize a given surface over the plane. In particular, we want to find a map that preserves angles. How can we express this condition more explicitly? Well, we know how to express 90-degree rotations on the surface, using the complex structure J . And we know how to express 90-degree ro...

On organizing principles of discrete differential geometry. Geometry of spheres

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consis...