Injectivity of 2D Toric Bezier Patches
Rational B′ezier functions are widely used as mapping functions in surface reparameterization, finite element analysis, image warping and morphing. The injectivity (one-toone property) of a mapping function is typically necessary for these applications. Toric B′ezier 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 B′ezier 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.
B′ezier patches Toric patches Injectivity Mapping
国际会议
2011国际计算机辅助设计与图形学学术会议(CAD/Graphics 2011)
济南
英文
1-4
2011-09-15（万方平台首次上网日期，不代表论文的发表时间）