A 3D+t Laplace operator for temporal mesh sequences. (August 2016)

• Record Type: Journal Article
• Authors: Fernández Abrevaya, Victoria; Manandhar, Sandeep; Hétroy-Wheeler, Franck; Wuhrer, Stefanie
• Is Part Of: Computers & graphics. Volume 58(2016)
• Page Start: 12
• Page End: 22
• Publication Date: 2016-08
• Subjects: Laplace operator -- Mesh animation -- Discrete Exterior Calculus; Computer graphics -- Periodicals; 006.6
• DOI: 10.1016/j.cag.2016.05.018
• Languages: English
• ISSNs: 0097-8493

Abstract

Abstract: 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 discretisation 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 generalisation of existing Laplacian static mesh processing works to mesh sequences. An application to spacetime editing is provided as example. Abstract : Graphical abstract: Abstract : Highlights: We define a discrete Laplace operator for temporally coherent mesh sequences. A parameter controls the influence of the motion and w.r.t. the geometry Application to spacetime editing is provided as example.