Computational Geometry from the Viewpoint of Affine Differential Geometry
published: Dec. 5, 2008, recorded: November 2008, views: 1824
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Incidence relations (configurations of vertexes, edges, etc.) are important in computational geometry. Incidence relations are invariant under the group of affine transformations. On the other hand, affine differential geometry is to study hypersurfaces in an affine space that are invariant under the group of affine transformation. Therefore affine differential geometry gives a new sight in computational geometry.
From the viewpoint of affine differential geometry, algorithms of geometric transformation and dual transformation are discussed. The Euclidean distance function is generalized by a divergence function in affine differential geometry. A divergence function is an asymmetric distance-like function on a manifold, and it is an important object in information geometry. For divergence functions, the upper envelope type theorems on statistical manifolds are given. Voronoi diagrams determined from divergence functions are also discussed.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !