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Your search keyword '"Monotone Surfaces"' showing total 6 results
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6 results on '"Monotone Surfaces"'

1. Visualization of Monotone Data by Rational Bi-cubic Interpolation

Author

Hussain, Malik Zawwar, Hussain, Maria, Sarfraz, Muhammad, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Gavrilova, Marina L., editor, and Tan, C. J. Kenneth, editor

Published
2010
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2. Visualization of Monotone Data by Rational Bi-cubic Interpolation.

Author

Hussain, Malik Zawwar, Hussain, Maria, and Sarfraz, Muhammad

Abstract

The most general piecewise rational cubic function (GPRC) for monotone curve design has been extended to the rational bi-cubic partially blended function to preserve the shape of 3D monotone data. The rational bi-cubic partially blended function involves eight parameters in its description (four along each coordinate axes). Out of these eight shape parameters, four are constrained to preserve the shape of monotone data. The rest of the four parameters are free parameters and have been left free for the users to refine the shape of surface as desired. The developed method not only preserves the monotonicity of the data, but also assures that the visual display is smooth and pleasant. [ABSTRACT FROM AUTHOR]

Published
2011
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3. Visualization of data preserving monotonicity

Author

Hussain, Malik Zawwar and Hussain, Maria

Subjects
*NUMERICAL analysis, *INTERPOLATION, *CURVES, *ENUMERATIVE geometry
Abstract

Abstract: A rational cubic function [M. Tian, Y. Zhang, J. Zhu, Q. Duan, Convexity-preserving piecewise rational cubic interpolation, ISCIAS, Hefei, China, 2005] has been used to visualize monotone data in the view of monotone curves by making constraints on free parameters in the description of rational cubic function. The rational cubic function is extended to rational bicubic partially blended function (Coons Patches). Simple constraints are derived on free parameters in the description of rational bicubic partially blended patches to visualize the monotone data in the view of monotone surfaces. The scheme of the paper is economical to compute and visually pleasant. [Copyright &y& Elsevier]

Published
2007
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4. 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

5. 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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