Ellipsoid Packing Structures on Freeform Surfaces
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Pacific Graphics 2018 |
Qun-Ce Xu1 |
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| 1University of Bath |
| 2Cardiff University |
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. |
Results |
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| We present an optimization-based framework that can generate plausible ellipsoid packing structures on freeform surfaces. The
optimization is initialized by anisotropic remeshing of the underlying surface (left). The ellipsoids are densely packed on the surface and
coincide with local surface features (middle). Other appealing structures can be easily derived from the ellipsoid packing structure, including
hexagon-dominant mesh, hybrid mesh, and ellipse packing structure (right). |
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| we develop an optimization framework for generating ellipsoid packing structures on freeform surfaces. We define an anisotropic metric on the surface which is adaptive to local surface features, and carefully formulate a non-linear
optimization to optimize the compactness of the ellipsoids. To ensure
the success of the optimization, we also propose to use anisotropic remeshing to obtain feature-adaptive meshes to better initialize the
optimization. The left museum roof is original mesh. The middle one is the mesh after anisotropic remeshing. The right one is model with packed ellipsoids. |
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| A gallery of 3D ellipsoid packing and derived structures on different freeform surfaces. We test our framework on a variety
of freeform surfaces with different geometry and topology. The
results demonstrate the effectiveness of our framework for generating useful ellipsoid packing structures that are adaptive to surface
features. |
Acknowledgements |
| We are grateful to the anonymous reviewers for their comments and
suggestions. We thank Shi-Min Hu, Yu-Kun Lai, Peter Hall, and
Christian Richardt for helpful discussions. The models used in the
paper are courtesy of Caigui Jiang, Alexander Schiftner, and Johannes Wallner. The work was supported by CAMERA, the RCUK
Centre for the Analysis of Motion, Entertainment Research and
Applications, EP/M023281/1. |
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BibTex
@ARTICLE{EllipsoidPacking2018,
title = {Ellipsoid Packing Structures on Freeform Surfaces},
author = {Xu, Qun-Ce and Deng, Bailin and Yang, Yong-Liang},
journal = {Computer Graphics Forum (Pacific Graphics 2018)},
volume = {37},
issue = {7},
year = {2018}
}
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