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Delaunay lofts: a new class of space-filling shapes

Published: 28 July 2019 Publication History

Abstract

We have developed an approach to construct and design a new class of space-filling shapes, which we call Delaunay Lofts. Our approach is based on interpolation of a stack of planar tiles whose dual tilings are Delaunay diagrams. We construct control curves that interpolate Delaunay vertices. Voronoi decomposition of the volume using these control curves as Voronoi sites gives us lofted interpolation of original polygons in planar tiles. This, combined with the use of wallpaper symmetries allows for the design of space-filling shapes in 3-space. In the poster exhibition, we will also demonstrate 3D printed examples of the new class of shapes (See Figures 1 and 3).

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References

[1]
Pedro Gómez-Gálvez, Pablo Vicente-Munuera, Antonio Tagua, Cristina Forja, Ana M Castro, Marta Letrán, Andrea Valencia-Expósito, Clara Grima, Marina Bermúdez-Gallardo, Óscar Serrano-Pérez-Higueras, and others. 2018. Scutoids are a geometrical solution to three-dimensional packing of epithelia. Nature communications 9, 1 (2018), 2960.
[2]
Vinod Srinivasan, Ergun Akleman, and Jianer Chen. 2002. Interactive construction of multi-segment curved handles. In Proceedings of 10th Pacific Conference on Computer Graphics and Applications, 2002. IEEE, New Jersey, 429--430.

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cover image ACM Conferences
SIGGRAPH '19: ACM SIGGRAPH 2019 Posters
July 2019
148 pages
ISBN:9781450363143
DOI:10.1145/3306214
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

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Publication History

Published: 28 July 2019

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  1. delaunay diagrams
  2. lofting
  3. space filling shapes
  4. voronoi decomposition

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