1987
DOI: 10.1177/026635118700200405
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Post-Formfinding Determination of Geodesic Lines in Cutting Pattern Design for Membrane Structures

Abstract: This paper describes a numerical procedure for determining geodesies on a surface. The surface is defined by a mesh of planar triangular finite elements. Examples are presented to illustrate the relevance of this procedure in the development of cutting patterns for membrane structures.

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Cited by 6 publications
(6 citation statements)
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“…From differential geometry, it is known that a surface can only be developed onto a plane if it is generated by a family of straight lines such that along each of these generators it has the same tangent plane. Hence it is unavoidable that the attempt to fabricate the doubly curved surface from flat strips only gives an approximation to the true shape [1].…”
Section: General Reviewmentioning
confidence: 99%
See 3 more Smart Citations
“…From differential geometry, it is known that a surface can only be developed onto a plane if it is generated by a family of straight lines such that along each of these generators it has the same tangent plane. Hence it is unavoidable that the attempt to fabricate the doubly curved surface from flat strips only gives an approximation to the true shape [1].…”
Section: General Reviewmentioning
confidence: 99%
“…Ishii [7] obtained the differential equation of geodesic lines for a surface given in the form z = f (x, y) , as (1) Equation 1is a non-linear differential equation and requires numerical solution by techniques such as the finite difference method. A geodesic line on the surface is uniquely defined either by specifying its direction through a point on the surface, or by giving two points on the surface through which it passes.…”
Section: Review Of Geodesic Patterningmentioning
confidence: 99%
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“…Since the membrane structure can be realized by connecting several planar sheets, it is desirable to design the cutting pattern so that uniform in-plane tension stress is generated in the membrane. The most conventional approach utilizes the geodesic line [5] to obtain approximate cutting patterns from the target curved surface [6,7]. Punurai et al [8] proposed an optimization approach using genetic algorithm.…”
Section: Introductionmentioning
confidence: 99%