Linear Precision for Toric Surface Patches |
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Authors: | Hans-Christian Graf von Bothmer Kristian Ranestad Frank Sottile |
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Institution: | 1. Mathematisches Institut, Georg-August-Universiti?t G?ttingen, Bunsenstr. 3-5, 37073, G?ttingen, Germany 2. Matematisk Institutt, Universitetet i Oslo, PO Box 1053, Blindern, 0316, Oslo, Norway 3. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA
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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. |
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Keywords: | |
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