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 includes, as a proper subset, the classification of toric surface patches from geometric modeling which have linear precision. Besides the well-known tenso...

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Bibliographic Details
Published inFoundations of computational mathematics Vol. 10; no. 1; pp. 37 - 66
Main Authors Graf von Bothmer, Hans-Christian, Ranestad, Kristian, Sottile, Frank
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 01.02.2010
Springer
Springer Nature B.V
Subjects
Applications of Mathematics
Computer Science
Economics
Geometry
Linear algebra
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Polynomials
Cremona transformation
Geometric modeling
14M25
Bézier patches
65D17
Linear precision
Toric patch
Online AccessGet full text
ISSN1615-3375
1615-3383
1615-3383
DOI10.1007/s10208-009-9052-6

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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1615-3375
1615-3383
1615-3383
DOI:10.1007/s10208-009-9052-6