780 research outputs found
Linear precision for toric surface patches
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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