Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

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

[thumbnail of FLBC-GMP.pdf]
Preview
PDF - Accepted Post-Print Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (969kB) | Preview

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: 08 Nov 2023 08:13
URI: https://orca.cardiff.ac.uk/id/eprint/121128

Citation Data

Cited 6 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item Edit Item

Downloads

Downloads per month over past year

View more statistics