Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Implicit equations of non-degenerate rational Bezier quadric triangles   In this paper we review the derivation of implicit equations for
non-degenerate quadric patches in rational Bezier triangular form. These are
the case of Steiner surfaces of degree two. We derive the bilinear forms for
such quadrics in a coordinate-free fashion in terms of their control net and
their list of weights in a suitable form. Our construction relies on projective
geometry and is grounded on the pencil of quadrics circumscribed to a
tetrahedron formed by vertices of the control net and an additional point which
is required for the Steiner surface to be a non-degenerate quadric.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas