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Descripción
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| In this paper we classify and derive closed formulas for geometric elements of quadrics in rational Bézier triangular form (such as the center, the conic at infinity, the vertex and the axis of paraboloids and the principal planes), using just the control vertices and the weights for the quadric patch. The results are extended also to quadric tensor product patches. Our results rely on using techniques from projective algebraic geometry to find suitable bilinear forms for the quadric in a coordinate-free fashion, considering a pencil of quadrics that are tangent to the given quadric along a conic. Most of the information about the quadric is encoded in one coefficient, involving the weights of the patch, which allows us to tell apart oval from ruled quadrics. This coefficient is also relevant to determine the affine type of the quadric. Spheres and quadrics of revolution are characterised within this framework. | |
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Internacional
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Si |
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Nombre congreso
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Building Mathematics and Mutual Understanding |
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Tipo de participación
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960 |
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Lugar del congreso
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Madrid |
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Revisores
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Si |
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ISBN o ISSN
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1072-6691 |
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DOI
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Fecha inicio congreso
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14/07/2014 |
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Fecha fin congreso
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15/07/2014 |
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Desde la página
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0 |
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Hasta la página
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0 |
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Título de las actas
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2014 Madrid Conference on Applied Mathematics in honor of Alfonso Casal, Electron. J. Diff. Eqns., Conference 22 (2015) |