Linear precision for toric surface patches
arXiv:0806.3230 · doi:10.1007/s10208-009-9052-6
Abstract
We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification also includes, as a proper subset, the classification of toric surface patches from geometric modeling which have linear precision. Besides the well-known tensor product patches and Bézier triangles, we identify a family of toric patches with trapezoidal shape, each of which has linear precision. Bézier triangles and tensor product patches are special cases of trapezoidal patches.