Piecewise Polynomial Reconstruction of Functions from Simplified Morse-Smale complex

Léo Allemand-Giorgis 1 Georges-Pierre Bonneau 1 Stefanie Hahmann 2
1 MAVERICK - Models and Algorithms for Visualization and Rendering
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
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 : Piecewise Polynomial Reconstruction of Functions from Simplified Morse-Smale complex: The main contribution is the application of a shape preserving spline surfaces for reconstruction of a scalar field from a given Morse-Smale complex. In particular we approximate the jagged 1-cells on the complex with smooth B-splines. We introduce a C1 monotone Sibson spline interpolant and combine it with a reparameterization to reconstruct the 2-cells individually. The resulting surface piecewise smooth and obeys completely the given MS complex.
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Léo Allemand-Giorgis, Georges-Pierre Bonneau, Stefanie Hahmann. Piecewise Polynomial Reconstruction of Functions from Simplified Morse-Smale complex. IEEE Visualization conference 2014, SciVis Posters, Nov 2014, Paris, France. ⟨hal-01100280⟩

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