Biharmonic distance

Yaron Lipman, Raif M. Rustamov, Thomas A. Funkhouser

Research output: Contribution to journalArticlepeer-review

161 Scopus citations


Measuring distances between pairs of points on a 3D surface is a fundamental problem in computer graphics and geometric processing. For most applications, the important properties of a distance are that it is a metric, smooth, locally isotropic, globally "shape-aware," isometry-invariant, insensitive to noise and small topology changes, parameter-free, and practical to compute on a discrete mesh. However, the basic methods currently popular in computer graphics (e.g., geodesic and diffusion distances) do not have these basic properties. In this article, we propose a new distance measure based on the biharmonic differential operator that has all the desired properties. This new surface distance is related to the diffusion and commute-time distances, but applies different (inverse squared) weighting to the eigenvalues of the Laplace-Beltrami operator, which provides a nice trade-off between nearly geodesic distances for small distances and global shape-awareness for large distances. The article provides theoretical and empirical analysis for a large number of meshes.

Original languageEnglish (US)
Article number27
JournalACM Transactions on Graphics
Issue number3
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design


  • Mesh distance
  • Mesh processing
  • Shape analysis


Dive into the research topics of 'Biharmonic distance'. Together they form a unique fingerprint.

Cite this