Computational Assessment of Curvatures and Principal Directions of Implicit Surfaces from 3D Scalar Data

  • Eric AlbinEmail author
  • Ronnie Knikker
  • Shihe Xin
  • Christian Oliver Paschereit
  • Yves D’Angelo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10521)


An implicit method based on high-order differentiation to determine the mean, Gaussian and principal curvatures of implicit surfaces from a three-dimensional scalar field is presented and assessed. The method also determines normal vectors and principal directions. Compared to explicit methods, the implicit approach shows robustness and improved accuracy to measure curvatures of implicit surfaces. This is evaluated on simple cases where curvature is known in closed-form. The method is applied to compute the curvatures of wrinkled flames on large triangular unstructured meshes (namely a 3D isosurface of temperature).


Implicit surface Curvature Principal directions Isosurface 3D scalar field Combustion analysis 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Eric Albin
    • 1
    Email author
  • Ronnie Knikker
    • 1
  • Shihe Xin
    • 1
  • Christian Oliver Paschereit
    • 2
  • Yves D’Angelo
    • 3
  1. 1.Univ. Lyon, CNRS, INSA-Lyon, Université Claude Bernard Lyon 1, CETHIL UMR5008VilleurbanneFrance
  2. 2.Institute of Fluid Dynamics and Technical Acoustics, Hermann-Föttinger-Institut.Technische Universität BerlinBerlinGermany
  3. 3.Laboratoire de Mathématiques J.A. Dieudonné, CNRS UMR 7351Université de Nice Sophia-AntipolisNiceFrance

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