Ellipsoid packing structures on freeform surfaces

Xu, Qun-Ce, Deng, Bailin ORCID: https://orcid.org/0000-0002-0158-7670 and Yang, Yong-Liang 2018. Ellipsoid packing structures on freeform surfaces. Computer Graphics Forum 37 (7) , pp. 87-95. 10.1111/cgf.13550

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Abstract

Designers always get good inspirations from fascinating geometric structures gifted by the nature. In the recent years, various computational design tools have been proposed to help generate cell packing structures on freeform surfaces, which consist of a packing of simple primitives, such as polygons, spheres, etc. In this work, we aim at computationally generating novel ellipsoid packing structures on freeform surfaces. We formulate the problem as a generalization of sphere packing structures in the sense that anisotropic ellipsoids are used instead of isotropic spheres to pack a given surface. This is done by defining an anisotropic metric based on local surface anisotropy encoded by principal curvatures and the corresponding directions. We propose an optimization framework that can optimize the shapes of individual ellipsoids and the spatial relation between neighboring ellipsoids to form a quality packing structure. A tailored anisotropic remeshing method is also employed to better initialize the optimization and ensure the quality of the result. Our framework is extensively evaluated by optimizing ellipsoid packing and generating appealing geometric structures on a variety of freeform surfaces.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Publisher:	Wiley
ISSN:	0167-7055
Funders:	RCUK
Date of First Compliant Deposit:	3 September 2018
Date of Acceptance:	29 August 2018
Last Modified:	30 Nov 2024 04:45
URI:	https://orca.cardiff.ac.uk/id/eprint/114539

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