Linear precision for toric surface patches

Details Linear precision for toric surface patches Linear precision for toric surface patches

2008-06-19

arxiv.org/abs/0806.3230v2

Foundations of Computational Mathematics, Volume 10, Number 1 (2010), 37-66

Mathematics

Algebraic Geometry

Scientific paper

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 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 B\'ezier triangles, we identify a family of toric patches with trapezoidal shape, each of which has linear precision. B\'ezier triangles and tensor product patches are special cases of trapezoidal patches.

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