Developable Surfaces from Arbitrary Sketched Boundaries

Rose Kenneth, Sheffer Alla, Wither Jamie, Cani Marie-Paule, Thibert Boris
In Belyaev A. et Garland M. editors, 5th Eurographics Symposium on Geometry Processing, SGP 2007. Eurographics, Barcelone, Espagne, juillet 2007. ACM International Conference Proceeding Series volume 257, pages 163–172. Eurographics Association, 2007. (HTML) .
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Developable surfaces are surfaces that can be unfolded into the plane with no distortion. Although ubiquitous in our everyday surroundings, modeling them using existing tools requires significant geometric expertise and time. Our paper simplifies the modeling process by introducing an intuitive sketch-based approach for modeling developables. We develop an algorithm that given an arbitrary, user specified 3D polyline boundary, constructed using a sketching interface, generates a smooth discrete developable surface that interpolates this boundary. Our method utilizes the connection between developable surfaces and the convex hulls of their boundaries. The method explores the space of possible interpolating surfaces searching for a developable surface with desirable shape characteristics such as fairness and predictability. The algorithm is not restricted to any particular subset of developable surfaces. We demonstrate the effectiveness of our method through a series of examples, from architectural design to garments.

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author = {Kenneth Rose and Alla Sheffer and Jamie Wither and Marie-Paule Cani and Boris Thibert},
title = {Developable Surfaces from Arbitrary Sketched Boundaries},
booktitle = {5th Eurographics Symposium on Geometry Processing, SGP 2007, July, 2007},
series = {ACM International Conference Proceeding Series},
editor = {Alexander Belyaev and Michael Garland},
organization = {Eurographics},
address = {Barcelone, Espagne},
publisher = {Eurographics Association},
volume = 257,
pages = {163--172},
month = aou,
year = 2007

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