K-set tilable surfaces

Chi Wing FU; Chi Fu LAI; Ying HE; Daniel COHEN-OR

doi:10.1145/1833349.1778781

K-set tilable surfaces

Chi Wing FU
, Chi Fu LAI
, Ying HE
, Daniel COHEN-OR

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

32 Citations (Scopus)

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.

Original language	English
Title of host publication	SIGGRAPH '10: ACM SIGGRAPH 2010 papers
Editors	Hugues HOPPE
Publisher	Association for Computing Machinery, Inc
Number of pages	6
ISBN (Electronic)	9781450302104
DOIs	https://doi.org/10.1145/1833349.1778781
Publication status	Published - 2010
Externally published	Yes
Event	SIGGRAPH '10: Special Interest Group on Computer Graphics and Interactive Techniques Conference - Los Angeles, United States Duration: 26 Jul 2010 → 30 Jul 2010

Conference

Conference	SIGGRAPH '10: Special Interest Group on Computer Graphics and Interactive Techniques Conference
Country/Territory	United States
City	Los Angeles
Period	26/07/10 → 30/07/10

Bibliographical note

We thank anonymous reviewers for the constructive comments and Lim Tze Yuen of Game Lab. for helping to create the architectural scenes.

Funding

This work was supported in part by the Singapore A*Star PSF SERC grant (SERC grant no. 092 101 0063), NTU Startup Grant (M58020007.500000), Israel Science Foundation founded by the Israel Academy of Sciences and Humanities, and NRF IDM grant NRF2008IDM-IDM-004-006.

Keywords

Architectural geometry
Computational differential geometry
Computer-aided-geometric design
Freeform surface
Tiling

Access to Document

10.1145/1833349.1778781

Cite this

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title = "K-set tilable surfaces",

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.",

keywords = "Architectural geometry, Computational differential geometry, Computer-aided-geometric design, Freeform surface, Tiling",

author = "FU, \{Chi Wing\} and LAI, \{Chi Fu\} and Ying HE and Daniel COHEN-OR",

note = "We thank anonymous reviewers for the constructive comments and Lim Tze Yuen of Game Lab. for helping to create the architectural scenes.; SIGGRAPH '10: Special Interest Group on Computer Graphics and Interactive Techniques Conference ; Conference date: 26-07-2010 Through 30-07-2010",

year = "2010",

doi = "10.1145/1833349.1778781",

language = "English",

editor = "Hugues HOPPE",

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AU - FU, Chi Wing

AU - LAI, Chi Fu

AU - HE, Ying

AU - COHEN-OR, Daniel

N1 - We thank anonymous reviewers for the constructive comments and Lim Tze Yuen of Game Lab. for helping to create the architectural scenes.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Architectural geometry

KW - Computational differential geometry

KW - Computer-aided-geometric design

KW - Freeform surface

KW - Tiling

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U2 - 10.1145/1833349.1778781

DO - 10.1145/1833349.1778781

M3 - Conference paper (refereed)

AN - SCOPUS:84878340406

BT - SIGGRAPH '10: ACM SIGGRAPH 2010 papers

A2 - HOPPE, Hugues

PB - Association for Computing Machinery, Inc

T2 - SIGGRAPH '10: Special Interest Group on Computer Graphics and Interactive Techniques Conference

Y2 - 26 July 2010 through 30 July 2010

ER -

K-set tilable surfaces

Abstract

Conference

Bibliographical note

Funding

Keywords

Access to Document

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