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Journal for Geometry and Graphics 27 (2023), No. 1, 059--067
Copyright Heldermann Verlag 2023

Enforcing Surface Rigidity by Shadow-Line Constraints

Hans Hagen
Technische Universitšt, Kaiserslautern, Germany

A surface is under pressure and deforming. Is it bending without or with deforming the surface-metric? This is an important question in many applications. Mathematical concepts to deal with this kind of problems are differential geometry and infinitesimal bendings. Shadow-curves are an intuitive visualization tool. We prove in this paper that as long as the shadow-lines stay stationary during the deformation the surface is infinitesimally rigid.

Keywords: Differential geometry, computer aided design, computer graphics, computational geometry.

MSC: 65D17; 65D18.

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