Linear Precision for Toric Surface Patches
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- Graf von Bothmer, H., Ranestad, K. & Sottile, F. Found Comput Math (2010) 10: 37. doi:10.1007/s10208-009-9052-6
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.