Unfolding Of Surfaces

Jean-Marie Morvan 1 Boris Thibert
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This paper deals with the approximation of the unfolding of a smooth developpa- ble surface with a triangle mesh. First of all, we give an explicit approximat- ion of the unfolding of a smooth developable surface with the unfolding of a developable triangle mesh close to the smooth surface. The quality of the approximation depends on the maximal angle between the normals of the two surfaces and the relative curvature distance of the smooth surface (which is linked to the curvature of the smooth surface and the Hausdorff distance between the two surfaces). We give examples of sequences of developable triangle meshes inscribed on a sphere of radius 1, with a number of vertices and edges tending to infinity.
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Jean-Marie Morvan, Boris Thibert. Unfolding Of Surfaces. RR-4615, INRIA. 2002. ⟨inria-00071970⟩

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