On discrete differential geometry in twistor space

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

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 of Twistor Spaces

To motivate the construction, let us begin by looking at the much simpler situation that arises in real dimension 2. First of all, we all know that a complex curve (or Riemann surface) is the same thing as an oriented 2manifoldM equipped with a conformal class [g] of Riemannian (i.e. positivedefinite) metrics. If g is any Riemannian metric on M , and if u : M → R is any smooth positive function...

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...