Computing general geometric structures on surfaces using Ricci flow

Systematically generalizing planar geometric algorithms to manifold domains is of fundamental importance in computer aided design field. This paper proposes a novel theoretic framework, geometric structure, to conquer this problem. In order to discover the intrinsic geometric structures of general surfaces, we developed a theoretic rigorous and practical efficient method, Discrete Variational Ricci flow. Different geometries study the invariants under the corresponding transformation groups. Same geometry can be defined on various manifolds, same manifold allows different geometries. Geometric structures allow different geometries to be defined on various manifolds, therefore algorithms based on the corresponding geometric invariants can be applied on the manifold domains directly. Surfaces have natural geometric structures, such as spherical structure, affine structure, projective structure, hyperbolic structure and conformal structure. Therefore planar algorithms based on thes...

• Type: Journal
• Year: 2007
• Where: CAD
• Authors: Miao Jin, Feng Luo 0002, Xianfeng David Gu
• Keywords: CAD 2007, Discrete Variational Ricci, Geometric Structure, Manifolds, Theoretical Computer Science