, Volume 10, Issue 1, pp 37-66,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 12 Aug 2009

Linear Precision for Toric Surface Patches

Abstract

We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification 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. Furthermore, Bézier triangles and tensor product patches are special cases of trapezoidal patches.