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Proceedings of CAD'14, 2014, 153-155
Interpolating Curved Grids using Quasi-developable Bi-cubic Gregory Patches
Abstract. A surface is developable if it can be flattened onto a plane without distortion, i.e., without any stretching or compression. Developable surfaces are widely used in the engineering fields such as ship-building, garment manufacture, etc. Much work has been done on how to represent a developable surface using polynomial patches. One approach to achieve this is to use developable or quasi-developable polynomial patches to interpolate a set of boundary curves with G0, G1 and/or G2 continuity. Another approach is to use piecewise linear approximations: the free-from surface is tessellated, typically using triangles, and an optimization model is constructed to minimize some form of distortion of the mesh in a 2-parameter space. Since a developable surface can be regarded as a one parameter family of straight lines, it can be mapped to one space curve in the dual space. Some researchers convert the modeling of developable surfaces by an equivalent modeling of a curve in dual space. This conversion can guarantee that the final surface is developable; unfortunately the modeling process is not geometrically intuitive and therefore not popular among designers. Our objective is to find a quasi-developable surface to interpolate four given boundary curves, while ensuring G1 continuity along the shared boundaries of adjacent patches.
Keywords. Developable surface, Gregory surface, surface interpolation, curve network