TY - GEN
T1 - Computing and visualizing constant-curvature metrics on hyperbolic 3-manifolds with boundaries
AU - Yin, Xiaotian
AU - Jin, Miao
AU - Luo, Feng
AU - Gu, Xianfeng David
PY - 2008
Y1 - 2008
N2 - Almost all three dimensional manifolds admit canonical metrics with constant sectional curvature. In this paper we proposed a new algorithm pipeline to compute such canonical metrics for hyperbolic 3- manifolds with high genus boundary surfaces. The computation is based on the discrete curvature flow for 3-manifolds, where the metric is deformed in an angle-preserving fashion until the curvature becomes uniform inside the volume and vanishes on the boundary. We also proposed algorithms to visualize the canonical metric by realizing the volume in the hyperbolic space H 3, both in single period and in multiple periods. The proposed methods could not only facilitate the theoretical study of 3-manifold topology and geometry using computers, but also have great potentials in volumetric parameterizations, 3D shape comparison, volumetric biomedical image analysis and etc.
AB - Almost all three dimensional manifolds admit canonical metrics with constant sectional curvature. In this paper we proposed a new algorithm pipeline to compute such canonical metrics for hyperbolic 3- manifolds with high genus boundary surfaces. The computation is based on the discrete curvature flow for 3-manifolds, where the metric is deformed in an angle-preserving fashion until the curvature becomes uniform inside the volume and vanishes on the boundary. We also proposed algorithms to visualize the canonical metric by realizing the volume in the hyperbolic space H 3, both in single period and in multiple periods. The proposed methods could not only facilitate the theoretical study of 3-manifold topology and geometry using computers, but also have great potentials in volumetric parameterizations, 3D shape comparison, volumetric biomedical image analysis and etc.
UR - https://www.scopus.com/pages/publications/68649089948
U2 - 10.1007/978-3-540-89639-5_69
DO - 10.1007/978-3-540-89639-5_69
M3 - Conference contribution
AN - SCOPUS:68649089948
SN - 3540896384
SN - 9783540896388
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 720
EP - 730
BT - Advances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings
T2 - 4th International Symposium on Visual Computing, ISVC 2008
Y2 - 1 December 2008 through 3 December 2008
ER -