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K-set tilable surfaces

Published: 26 July 2010 Publication History

Abstract

This paper introduces a method for optimizing the tiles of a quad-mesh. Given a quad-based surface, the goal is to generate a set of K quads whose instances can produce a tiled surface that approximates the input surface. A solution to the problem is a K-set tilable surface, which can lead to an effective cost reduction in the physical construction of the given surface. Rather than molding lots of different building blocks, a K-set tilable surface requires the construction of K prefabricated components only. To realize the K-set tilable surface, we use a cluster-optimize approach. First, we iteratively cluster and analyze: clusters of similar shapes are merged, while edge connections between the K quads on the target surface are analyzed to learn the induced flexibility of the K-set tilable surface. Then, we apply a non-linear optimization model with constraints that maintain the K quads connections and shapes, and show how quad-based surfaces are optimized into K-set tilable surfaces. Our algorithm is demonstrated on various surfaces, including some that mimic the exteriors of certain renowned building landmarks.

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  • (2018)Design, Representations, and Processing for Additive ManufacturingSynthesis Lectures on Visual Computing10.2200/S00847ED1V01Y201804VCP03110:2(1-146)Online publication date: 22-Jun-2018
  • (2016)Construction with physical version of quad-edge data structuresComputers and Graphics10.1016/j.cag.2016.05.00858:C(172-183)Online publication date: 1-Aug-2016
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cover image ACM Conferences
SIGGRAPH '10: ACM SIGGRAPH 2010 papers
July 2010
984 pages
ISBN:9781450302104
DOI:10.1145/1833349
Permission to make digital or hard copies of all or part 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 components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 26 July 2010

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Author Tags

  1. architectural geometry
  2. computational differential geometry
  3. computer-aided-geometric design
  4. freeform surface
  5. tiling

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SIGGRAPH '10 Paper Acceptance Rate 103 of 390 submissions, 26%;
Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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Cited By

View all
  • (2021)Modeling and fabrication with specified discrete equivalence classesACM Transactions on Graphics10.1145/3450626.345984340:4(1-12)Online publication date: Aug-2021
  • (2018)Design, Representations, and Processing for Additive ManufacturingSynthesis Lectures on Visual Computing10.2200/S00847ED1V01Y201804VCP03110:2(1-146)Online publication date: 22-Jun-2018
  • (2016)Construction with physical version of quad-edge data structuresComputers and Graphics10.1016/j.cag.2016.05.00858:C(172-183)Online publication date: 1-Aug-2016
  • (2015)Die Netzschale der Jinji Lake MallStahlbau10.1002/stab.20159006884:S1(101-110)Online publication date: 15-Jun-2015
  • (2014)Freeform Honeycomb StructuresComputer Graphics Forum10.1111/cgf.1244433:5(185-194)Online publication date: 23-Aug-2014
  • (2014)The grid‐shell of Jinji Lake MallSteel Construction10.1002/stco.2014200397:4(258-261)Online publication date: 17-Nov-2014
  • (2010)Triangle surfaces with discrete equivalence classesACM SIGGRAPH 2010 papers10.1145/1833349.1778783(1-7)Online publication date: 26-Jul-2010
  • (2010)Triangle surfaces with discrete equivalence classesACM Transactions on Graphics10.1145/1778765.177878329:4(1-7)Online publication date: 26-Jul-2010

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