Digital Calculus Frameworks and Comparative Evaluation of their Laplace-Beltrami operators ⋆ - École Centrale de Lyon Access content directly
Conference Papers Year : 2024

Digital Calculus Frameworks and Comparative Evaluation of their Laplace-Beltrami operators ⋆

Abstract

Defining consistent calculus frameworks on discrete meshes is useful for processing the geometry of meshes or model numerical simulations and variational problems onto them. However digital surfaces (boundary of voxels) cannot benefit directly from the classical mesh calculus frameworks, since their vertex and face geometry is too poor to capture the geometry of the underlying smooth Euclidean surface well enough. This paper proposes two new calculus frameworks dedicated to digital surfaces, which exploit a corrected normal field, in a manner similar to the recent digital calculus of [3]. First we build a corrected interpolated calculus by defining inner products with position and normal interpolation in the Grassmannian. Second we present a corrected finite element method which adapts the standard Finite Element Method with a corrected metric per element. Experiments show that these digital calculus frameworks seem to converge toward the continuous calculus, offer a valid alternative to classical mesh calculus, and induce effective tools for digital surface processing tasks.
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Dates and versions

hal-04486655 , version 1 (02-03-2024)

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  • HAL Id : hal-04486655 , version 1

Cite

Colin Weill-Duflos, David Coeurjolly, Jacques-Olivier Lachaud. Digital Calculus Frameworks and Comparative Evaluation of their Laplace-Beltrami operators ⋆. IAPR Third International Conference on Discrete Geometry and Mathematical Morphology, Apr 2024, Florence, Italy. ⟨hal-04486655⟩
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