Continuous Deformation of a Developable Surface

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Continuous Deformation of a Developable Surface

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Title: Continuous Deformation of a Developable Surface
Author: Hsu, Chili Ping
Abstract: A developable surface can be developed from a piece of planar region, or vice versa. Several methods are known to construct an isometric mapping between the developable and the planar region. A simple and efficient algorithm based on the differential geometry and differential equations is presented to construct such an isometric mapping. This algorithm contains a deformation parameter ^, where ^ varies between 0 and 1, that can trace the development of the surface in a fashion that ^ = 0 corresponds to the planar region and ^ = 1 recovers the developable. An error estimation shows the error, in the sense of the developability of a developable, which depends on the method of solving the DE. Several numerical experiments have shown satisfactory results.
Date: 1996-02

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