On organizing principles of discrete differential geometry. Geometry of spheres

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...

Geometry II - 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...

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...

Recurrent metrics in the geometry of second order differential equations

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...