Computing and Visualizing Constant-Curvature Metrics on Hyperbolic 3-Manifolds with Boundaries

摘要: Almost all three dimensional manifolds admit canonical metricswith constant sectional curvature. In this paper we proposed a newalgorithm pipeline to compute such metrics for hyperbolic3-manifolds with high genus boundary surfaces. The computation isbased on the discrete curvature flow 3-manifolds, where themetric is deformed in an angle-preserving fashion until thecurvature becomes uniform inside volume and vanishes theboundary. We also algorithms visualize canonicalmetric by realizing hyperbolic spaceℍ3, both single period multiple periods.The methods could not only facilitate theoreticalstudy of 3-manifold topology geometry using computers, but alsohave great potentials volumetric parameterizations, 3D shapecomparison, biomedical image analysis etc.