, Volume 81, Issue 2–3, pp 199–213 | Cite as

An algorithm for the construction of intrinsic delaunay triangulations with applications to digital geometry processing

  • M. Fisher
  • B. Springborn
  • P. Schröder
  • A. I. Bobenko


The discrete Laplace–Beltrami operator plays a prominent role in many digital geometry processing applications ranging from denoising to parameterization, editing, and physical simulation. The standard discretization uses the cotangents of the angles in the immersed mesh which leads to a variety of numerical problems. We advocate the use of the intrinsic Laplace–Beltrami operator. It satisfies a local maximum principle, guaranteeing, e.g., that no flipped triangles can occur in parameterizations. It also leads to better conditioned linear systems. The intrinsic Laplace–Beltrami operator is based on an intrinsic Delaunay triangulation of the surface. We detail an incremental algorithm to construct such triangulations together with an overlay structure which captures the relationship between the extrinsic and intrinsic triangulations. Using a variety of example meshes we demonstrate the numerical benefits of the intrinsic Laplace–Beltrami operator.


Delaunay Triangulation Beltrami Operator Intrinsic Geometry Input Mesh Overlay Graph 
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Copyright information

© Springer 2007

Authors and Affiliations

  • M. Fisher
    • 1
  • B. Springborn
    • 2
  • P. Schröder
    • 1
  • A. I. Bobenko
    • 2
  1. 1.California Institute of Technology (CALTECH), Computer SciencePasadenaUSA
  2. 2.TU BerlinBerlinGermany

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