An Algorithm for the Euclidean Cell Decomposition of a Cusped Strictly Convex Projective Surface∗
نویسندگان
چکیده
Cooper and Long generalised Epstein and Penner’s Euclidean cell decomposition of cusped hyperbolic n–manifolds of finite volume to non-compact strictly convex projective n–manifolds of finite volume. We show that Weeks’ algorithm to compute this decomposition for a hyperbolic surface generalises to strictly convex projective surfaces.
منابع مشابه
A full Nesterov-Todd step infeasible interior-point algorithm for symmetric cone linear complementarity problem
A full Nesterov-Todd (NT) step infeasible interior-point algorithm is proposed for solving monotone linear complementarity problems over symmetric cones by using Euclidean Jordan algebra. Two types of full NT-steps are used, feasibility steps and centering steps. The algorithm starts from strictly feasible iterates of a perturbed problem, and, using the central path and feasi...
متن کاملA Generalization of the Epstein-penner Construction to Projective Manifolds
We extend the canonical cell decomposition due to Epstein and Penner of a hyperbolic manifold with cusps to the strictly convex setting. It follows that a sufficiently small deformation of the holonomy of a finite volume strictly convex real projective manifold is the holonomy of some nearby projective structure with radial ends, provided the holonomy of each maximal cusp has a
متن کاملA Recurrent Neural Network for Solving Strictly Convex Quadratic Programming Problems
In this paper we present an improved neural network to solve strictly convex quadratic programming(QP) problem. The proposed model is derived based on a piecewise equation correspond to optimality condition of convex (QP) problem and has a lower structure complexity respect to the other existing neural network model for solving such problems. In theoretical aspect, stability and global converge...
متن کاملAssessment of the Log-Euclidean Metric Performance in Diffusion Tensor Image Segmentation
Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI) segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this ...
متن کاملThe Generalized Tilt Formula
A convex hull consmaction in Minkowski space defines a canonical cell decomposition for a cusped hyperbolic n-manifold. An algorithm to compute the canonical cell decomposition uses the concept of the 'tilt' of an n-simplex relative to each of its (n 1)-dimensional faces. An essential tool for computing tilts is the tilt theorem. The tilt theorem was previously known only in dimensions n < 3, a...
متن کامل