Injectivity of 2D Toric Bzier Patches Conference Paper uri icon

abstract

  • Rational Bzier functions are widely used as mapping functions in surface reparameterization, finite element analysis, image warping and morphing. The injectivity (one-to-one property) of a mapping function is typically necessary for these applications. Toric Bezier patches are generalizations of classical patches (triangular, tensor product) which are defined on the convex hull of a set of integer lattice points. We give a geometric condition on the control points that we show is equivalent to the injectivity of every 2D toric Bezier patch with those control points for all possible choices of weights. This condition refines that of Craciun, et al., which only implied injectivity on the interior of a patch. 2011 IEEE.

name of conference

  • 2011 12th International Conference on Computer-Aided Design and Computer Graphics

published proceedings

  • 2011 12th International Conference on Computer-Aided Design and Computer Graphics

author list (cited authors)

  • Sottile, F., & Zhu, C.

citation count

  • 13

complete list of authors

  • Sottile, Frank||Zhu, Chun-Gang

publication date

  • September 2011