Proceedings: GI 1996

Surface intersection using affine arithmetic

Luiz de Figueiredo

Proceedings of Graphics Interface '96: Toronto, Ontario, Canada, 22 - 24 May 1996, 168-175

DOI 10.20380/GI1996.20

  • BibTeXex

     title = {Surface intersection using affine arithmetic},
     author = {Luiz Henrique de Figueiredo},
     booktitle = {Proceedings of the Graphics Interface 1996 Conference, May 22-24, 1996, Toronto, Ontario, Canada},
     year = {1996},
     month = {May},
     isbn = {0-9695338-5-3},
     publisher = {Canadian Human-Computer Communications Society},
     url = {},
     pages = {168--175}


We describe a variant of a domain decomposition method proposed by Gleicher and Kass for intersecting and trimming parametric surfaces. Instead of using interval arithmetic to guide the decomposition, the variant described here uses affine arithmetic, a tool recently proposed for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and sub-formulas, generally providing much tighter bounds for the computed quantities. As a consequence, the quadtree domain decompositions are much smaller and the intersection algorithm runs faster.