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arXiv · 0806.3230

Linear precision for toric surface patches

Hans-Christian Graf von Bothmer·Kristian Ranestad·Frank Sottile
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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 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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Hans-Christian Graf von Bothmer, Kristian Ranestad, Frank Sottile. 2008-06-19. Linear precision for toric surface patches. https://doi.org/10.1007/s10208-009-9052-6

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