A fast numerical solver for local barycentric coordinates

Tao, Jiong, Deng, Bailin ORCID: https://orcid.org/0000-0002-0158-7670 and Zhang, Juyong 2019. A fast numerical solver for local barycentric coordinates. Computer Aided Geometric Design 70 , pp. 46-58. 10.1016/j.cagd.2019.04.006

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Abstract

The local barycentric coordinates (LBC), proposed in Zhang et al (2014), demonstrate good locality and can be used for local control on function value interpolation and shape deformation. However, it has no closed- form expression and must be computed by solving an optimization problem, which can be time-consuming especially for high-resolution models. In this paper, we propose a new technique to compute LBC efficiently. The new solver is developed based on two key insights. First, we prove that the non-negativity constraints in the original LBC formulation is not necessary, and can be removed without affecting the solution of the optimization problem. Furthermore, the removal of this constraint allows us to reformulate the computation of LBC as a convex constrained optimization for its gradients, followed by a fast integration to recover the coordinate values. The reformulated gradient optimization problem can be solved using ADMM, where each step is trivially parallelizable and does not involve global linear system solving, making it much more scalable and efficient than the original LBC solver. Numerical experiments verify the effectiveness of our technique on a large variety of models.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA76 Computer software
Publisher:	Elsevier
ISSN:	0167-8396
Date of First Compliant Deposit:	26 March 2019
Date of Acceptance:	21 March 2019
Last Modified:	21 Nov 2024 14:45
URI:	https://orca.cardiff.ac.uk/id/eprint/121128

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