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Your search keyword '"Monotone Surfaces"' showing total 2 results
Start Over Descriptor "Monotone Surfaces" Publisher hal ccsd
2 results on '"Monotone Surfaces"'

1. Piecewise Polynomial Reconstruction of Functions from Simplified Morse-Smale complex

Author

Léo Allemand-Giorgis, Georges-Pierre Bonneau, Stefanie Hahmann, Models and Algorithms for Visualization and Rendering (MAVERICK), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Hahmann, Stefanie

Subjects
Monotone Surfaces, Computer Science::Graphics, Geometric Modeling, [INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Morse-Smale Complex, Scalar field, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Visualization
Abstract

International audience; Piecewise Polynomial Reconstruction of Functions from Simplified Morse-Smale complex: The main contribution is the application of a shapepreserving 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.

Published
2014

2. Piecewise polynomial monotonic interpolation of 2D gridded data

Author

Léo Allemand-Giorgis, Georges-Pierre Bonneau, Stefanie Hahmann, Fabien Vivodtzev, Models and Algorithms for Visualization and Rendering (MAVERICK), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), Centre d'études scientifiques et techniques d'Aquitaine (CESTA), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Bennett, Janine, Vivodtzev, Fabien, Pascucci, Valerio, Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Mathematical analysis, Monotone cubic interpolation, Monotonic function, 010103 numerical & computational mathematics, 01 natural sciences, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Interpolation, 010101 applied mathematics, Maxima and minima, Monotone Surfaces, Monotone polygon, Saddle point, Piecewise, Partial derivative, 0101 mathematics, Mathematics, Visualization
Abstract

International audience; A method for interpolating monotone increasing 2D scalar data with a monotone piecewise cubic C$^1$-continuous surface is presented. Monotonicity is a sufficient condition for a function to be free of critical points inside its domain. The standard axial monotonicity for tensor-product surfaces is however too restrictive. We therefore introduce a more relaxed monotonicity constraint. We derive sufficient conditions on the partial derivatives of the interpolating function to ensure its monotonicity. We then develop two algorithms to effectively construct a monotone C$^1$ surface composed of cubic triangular Bézier surfaces interpolating a monotone gridded data set. Our method enables to interpolate given topological data such as minima, maxima and saddle points at the corners of a rectangular domain without adding spurious extrema inside the function domain. Numerical examples are given to illustrate the performance of the algorithm.

Published
2014

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