Efficient Hausdorff Distance computation for freeform geometric models in close proximity

Yong Joon Kim, Young Taek Oh, Seung Hyun Yoon, Myung Soo Kim, Gershon Elber

Research output: Contribution to journalArticlepeer-review


We present an interactive-speed algorithm for computing the Hausdorff Distance (HD) between two freeform geometric models represented with NURBS surfaces. The algorithm is based on an effective technique for matching a surface patch from one model to the corresponding nearby surface patch on the other model. To facilitate the matching procedure, we employ a bounding volume hierarchy (BVH) for freeform NURBS surfaces, which provides a hierarchy of Coons patches and bilinear surfaces approximating the NURBS surfaces (Kim et al., 2011 [1]). Comparing the local HD upper bound against a global HD lower bound, we can eliminate the majority of redundant surface patches from further consideration. The resulting algorithm and the associated data structures are considerably simpler than the previous BVH-based HD algorithms. As a result, we can compute the HD of two freeform geometric models efficiently and robustly even when the two models are in close proximity. We demonstrate the effectiveness of our approach using several experimental results.

Original languageEnglish
Pages (from-to)270-276
Number of pages7
JournalCAD Computer Aided Design
Issue number2
StatePublished - Feb 2013


  • Bounding volume hierarchy (BVH)
  • Coons patch
  • Geometric algorithm
  • Hausdorff Distance
  • Hierarchical data structure
  • NURBS surface

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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