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Title: Achieving developability of a polygonal surface by minimum deformation : a study of global and local optimization approaches
Authors: Tang, Kai
Wang, Charlie C. L.
Keywords: Developable surface
Polygonal mesh
Assembled patches
Issue Date: 2004
Citation: The visual computer, v. 20, no. 8-9, November 2004, p. 521-539
Abstract: Surface developability is required in a variety of applications in product design, such as clothing, ship hulls, automobile parts, etc. However, most current geometric modeling systems using polygonal surfaces ignore this important intrinsic geometric property. This paper investigates the problem of how to minimally deform a polygonal surface to attain developability, or the so called developability-by-deformation problem. In our study, this problem is first formulated as a global constrained optimization problem, and a penalty function based numerical solution is proposed for solving this global optimization problem. Next, as an alternative to the global optimization approach which usually requires lengthy computing time, we present an iterative solution based on a local optimization criterion which achieves near real-time computing speed. Both approaches preserve the topology and continuity of the original polygonal surface in the case when more than one individual polygonal patches comprise the surface. Experimental examples are provided to demonstrate the functionality of the proposed two approaches as well as their comparison in terms of computing cost, effectiveness of attaining developability, dimensional difference between the surfaces before and after the optimization, and other important aspects.
Rights: The original publication is available at
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