Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces

Konstantinos Gavriil; Alexander Schiftner; Helmut Pottmann

doi:10.1016/j.cad.2019.01.006

Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces

Konstantinos Gavriil, Alexander Schiftner, Helmut Pottmann

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

Motivated by applications in architecture and design, we present a novel method for increasing the developability of a B-spline surface. We use the property that the Gauss image of a developable surface is 1-dimensional and can be locally well approximated by circles. This is cast into an algorithm for thinning the Gauss image by increasing the planarity of the Gauss images of appropriate neighborhoods. A variation of the main method allows us to tackle the problem of paneling a freeform architectural surface with developable panels, in particular enforcing rotational cylindrical, rotational conical and planar panels, which are the main preferred types of developable panels in architecture due to the reduced cost of manufacturing.

Original language	English (US)
Pages (from-to)	29-43
Number of pages	15
Journal	Computer-Aided Design
Volume	111
DOIs	https://doi.org/10.1016/j.cad.2019.01.006
State	Published - Feb 10 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We would like to thank Heinz Schmiedhofer for providing the scan and picture of the leather surface example in Fig. 8. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 675789.

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10.1016/j.cad.2019.01.006

https://repository.kaust.edu.sa/bitstream/10754/653031/1/main.pdf

Cite this

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title = "Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces",

abstract = "Motivated by applications in architecture and design, we present a novel method for increasing the developability of a B-spline surface. We use the property that the Gauss image of a developable surface is 1-dimensional and can be locally well approximated by circles. This is cast into an algorithm for thinning the Gauss image by increasing the planarity of the Gauss images of appropriate neighborhoods. A variation of the main method allows us to tackle the problem of paneling a freeform architectural surface with developable panels, in particular enforcing rotational cylindrical, rotational conical and planar panels, which are the main preferred types of developable panels in architecture due to the reduced cost of manufacturing.",

author = "Konstantinos Gavriil and Alexander Schiftner and Helmut Pottmann",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: We would like to thank Heinz Schmiedhofer for providing the scan and picture of the leather surface example in Fig. 8. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Grant Agreement No. 675789.",

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doi = "10.1016/j.cad.2019.01.006",

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AU - Gavriil, Konstantinos

AU - Schiftner, Alexander

AU - Pottmann, Helmut

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: We would like to thank Heinz Schmiedhofer for providing the scan and picture of the leather surface example in Fig. 8. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 675789.

PY - 2019/2/10

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N2 - Motivated by applications in architecture and design, we present a novel method for increasing the developability of a B-spline surface. We use the property that the Gauss image of a developable surface is 1-dimensional and can be locally well approximated by circles. This is cast into an algorithm for thinning the Gauss image by increasing the planarity of the Gauss images of appropriate neighborhoods. A variation of the main method allows us to tackle the problem of paneling a freeform architectural surface with developable panels, in particular enforcing rotational cylindrical, rotational conical and planar panels, which are the main preferred types of developable panels in architecture due to the reduced cost of manufacturing.

AB - Motivated by applications in architecture and design, we present a novel method for increasing the developability of a B-spline surface. We use the property that the Gauss image of a developable surface is 1-dimensional and can be locally well approximated by circles. This is cast into an algorithm for thinning the Gauss image by increasing the planarity of the Gauss images of appropriate neighborhoods. A variation of the main method allows us to tackle the problem of paneling a freeform architectural surface with developable panels, in particular enforcing rotational cylindrical, rotational conical and planar panels, which are the main preferred types of developable panels in architecture due to the reduced cost of manufacturing.

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JO - Computer-Aided Design

JF - Computer-Aided Design

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Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces

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