Section: New Results

A 3D+t Laplace Operator for Temporal Mesh Sequences

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 have defined 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 has been provided as example.

Figure 7. Spacetime editing of a temporal mesh sequence using the proposed 3D+t Laplace operator [1].

This work has been published in Computer & Graphics [1] and presented at the Shape Modeling International (SMI) 2016 conference.