Deformations Preserving Gauß Curvature

Anne Berres 1 Hans Hagen 1 Stefanie Hahmann 2
2 IMAGINE - Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In industrial surface generation, it is important to consider surfaces with minimal areas for two main reasons: these surfaces require less material than non-minimal surfaces, and they are cheaper to manufacture. Based on a prototype, a so-called masterpiece, the final product is created using small deformations to adapt a surface to the desired shape. We present a linear deformation technique preserving the total curvature of the masterpiece. In particular, we derive sufficient conditions for these linear deformations to be total curvature preserving when applied to the masterpiece. It is useful to preserve total curvature of a surface in order to minimise the amount of material needed, and to minimise bending energy.
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Anne Berres, Hans Hagen, Stefanie Hahmann. Deformations Preserving Gauß Curvature. Bennett, Janine; Vivodtzev, Fabien; Pascucci, Valerio. Topological and statistical methods for complex data -- Tackling large-scale, high-dimensional, and multivariate data sets, Springer, pp.143-163, 2014, Mathematics and Visualization, 978-3-662-44899-1. ⟨10.1007/978-3-662-44900-4_9⟩. ⟨hal-01070861⟩

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