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Piecewise Polynomial Reconstruction of Scalar Fields from Simplified Morse-Smale Complexes

  • Léo Allemand-Giorgis
  • Georges-Pierre Bonneau
  • Stefanie Hahmann
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Morse-Smale complexes have been proposed to visualize topological features of scalar fields defined on manifold domains. Herein, three main problems have been addressed in the past: (a) efficient computation of the initial combinatorial structure connecting the critical points; (b) simplification of these combinatorial structures; (c) reconstruction of a scalar field in accordance to the simplified Morse-Smale complex. The present paper faces the third problem by proposing a novel approach for computing a scalar field coherent with a given simplified MS complex that privileges the use of piecewise polynomial functions. Based on techniques borrowed from shape preserving design in Computer Aided Geometric Design, our method constructs the surface cell by cell using piecewise polynomial curves and surfaces. The benefit and limitations of using polynomials for reconstruction surfaces from topological data are presented in this paper.

Keywords

Scalar Field Morse Theory Junction Point Integral Line Shape Preserve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This research was partially funded by the ERC advanced grant EXPRESSIVE (no. 291184).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Léo Allemand-Giorgis
    • 1
  • Georges-Pierre Bonneau
    • 1
  • Stefanie Hahmann
    • 1
  1. 1.Université Grenoble Alpes, CNRS, LJK, INRIAGrenobleFrance

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