Proceedings: GI 2005

Distance extrema for spline models using tangent cones

David Johnson , Elaine Cohen

Proceedings of Graphics Interface 2005: Victoria, British Columbia, Canada, 9 - 11 May 2005, 169-175

DOI 10.20380/GI2005.21

  • Bibtex

    author = {Johnson, David and Cohen, Elaine},
    title = {Distance extrema for spline models using tangent cones},
    booktitle = {Proceedings of Graphics Interface 2005},
    series = {GI 2005},
    year = {2005},
    issn = {0713-5424},
    isbn = {1-56881-265-5},
    location = {Victoria, British Columbia, Canada},
    pages = {169--175},
    numpages = {7},
    doi = {10.20380/GI2005.21},
    publisher = {Canadian Human-Computer Communications Society},
    address = {School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada},


We present a robust search for distance extrema from a point to a curve or a surface. The robustness comes from using geometric operations rather than numerical methods to find all local extrema. Tangent cones are used to search for regions where distance extrema conditions are satisfied and patch refinement hierarchically improves the search. Instead of preprocessing and storing a large hierarchy, elements are computed as needed and retained only if useful. However, for spatially coherent queries, this provides a significant speedup.