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Developable Surfaces and their Continuity Conditions

M. Jabeen, M. Hussain

Abstract



Gaussian curvature of ruled surfaces is zero. Developable surfaces are well-suited for the construction of surfaces that can be formed through metal sheet, leather, fiber e.g. clothes, ship lofts, four-wheelers bodies. In the underlying study, Lupas 𝓆-Bézier curves are used for the construction of developable surfaces. These computed developable surfaces inherit the special features of the Lupas curves. The features are the shape parameter 𝓆 and the weights. The shape parameters and weights are used for shape modification as well as for shape modelling of developable surfaces. These surfaces preserve duality of plane and points in projective space(3D). The geometric continuity conditions between the adjoining 𝓆-Bézier surfaces are also discussed. The usefulness and effectiveness of the proposed methodology are also illustrated by several practical and interesting numerical examples.

Keywords


cubic weighted Lupaş 𝓆-Bernstein basis, shape parameter, weights, continuity condition

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