A 3D+t Laplace operator for temporal mesh sequences

Victoria Fernández Abrevaya (1) , Sandeep Manandhar (2, 3) , Franck Hétroy-Wheeler (3) , Stefanie Wuhrer (3)

1 UBA - Universidad de Buenos Aires [Buenos Aires]
2 UB - Université de Bourgogne
3 MORPHEO - Capture and Analysis of Shapes in Motion

The Laplace operator plays a fundamental role in geometry processing. Several discrete versions have been proposed for 3D meshes and point clouds, among others. We define here a discrete Laplace operator for temporally coherent mesh sequences, which allows to process mesh animations in a simple yet efficient way. This operator is a discretization of the Laplace-Beltrami operator using Discrete Exterior Calculus on CW complexes embedded in a four-dimensional space. A parameter is introduced to tune the influence of the motion with respect to the geometry. This enables straightforward generalization of existing Laplacian static mesh processing works to mesh sequences. An application to spacetime editing is provided as example.

Mots clés: Laplace operator; mesh animation; discrete exterior calculus

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]

Victoria Fernández Abrevaya, Sandeep Manandhar, Franck Hétroy-Wheeler, Stefanie Wuhrer. A 3D+t Laplace operator for temporal mesh sequences. Computers and Graphics, 2016, Shape Modeling International 2016, 58, pp.12-22. ⟨10.1016/j.cag.2016.05.018⟩. ⟨hal-01318763⟩