Spectral Processing of Tangential Vector Fields. (22nd June 2016)

• Record Type: Journal Article
• Authors: Brandt, Christopher; Scandolo, Leonardo; Eisemann, Elmar; Hildebrandt, Klaus
• Is Part Of: Computer graphics forum. Volume 36:Number 6(2017)
• Page Start: 338
• Page End: 353
• Publication Date: 2016-06-22
• Subjects: tangential vector fields -- discrete Hodge–aplace -- spectral geometry processing -- Hodge decomposition -- fur editing -- vector field design -- Computer Graphics I.3.5 Computational Geometry and Object Modelling; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.12942
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract : We propose a framework for the spectral processing of tangential vector fields on surfaces. The basis is a Fourier‐type representation of tangential vector fields that associates frequencies with tangential vector fields. To implement the representation for piecewise constant tangential vector fields on triangle meshes, we introduce a discrete Hodge–Laplace operator that fits conceptually to the prominent cotan discretization of the Laplace–Beltrami operator. Based on the Fourier representation, we introduce schemes for spectral analysis, filtering and compression of tangential vector fields. Abstract: We propose a framework for the spectral processing of tangential vector fields on surfaces. The basis is a Fourier‐type representation of tangential vector fields that associates frequencies with tangential vector fields. To implement the representation for piecewise constant tangential vector fields on triangle meshes, we introduce a discrete Hodge–Laplace operator that fits conceptually to the prominent cotan discretization of the Laplace–Beltrami operator. Based on the Fourier representation, we introduce schemes for spectral analysis, filtering and compression of tangential vector fields. Moreover, we introduce a spline‐type editor for modelling of tangential vector fields with interpolation constraints for the field itself and its divergence and curl. Using the spectral representation, we propose a numerical scheme that allows for real‐time modelling of tangential vector fields.