mirror of https://github.com/CGAL/cgal
62 lines
2.4 KiB
TeX
62 lines
2.4 KiB
TeX
\section{Curve\label{bi_cha:Curve}}
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Curves exit in various kind. Currently, we concentrate on
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non-linear algebraic curves of different degree. We
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distinguish conics, cubics, and curves of arbitrary degree.
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\subsection{Conics\label{bi_sec:Arrangement2Conics}}
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A conic is defined by the zero set of a two-variate polynomial
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of degree 2. A circle is a special conic.
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The following files contain contain randomly generated conics.
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Each instance of one file inlcudes the same number of conics. Not that
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a generic conic may also be unbounded.
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\begin{itemize}
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\item \ccBenchmarkInstance{Curve/Conics/random/number10/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number20/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number30/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number40/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number50/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number75/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number100/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number125/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number150/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number175/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number200/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number300/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number400/}
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\item \ccBenchmarkInstance{Curve/Conics/random/number500/}
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\end{itemize}
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\subsection{Cubics}
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A conic is defined by the zero set of a two-variate polynomial
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of degree 3.
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The following files contain contain randomly generated cubics. The
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files differ in the number of contained cubics.
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SeveraEach instance of one file inlcudes the same number of conics. Note
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that a generic cubic is usally unbounded.
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\ccBenchmarkInstance{Curve/Cubics/random/rand*.bff}
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This set contains instances whose cubics have increasing bitlenght of the
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coefficients.
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\ccBenchmarkInstance{Curve/Cubics/bitgrowth/rand*.bff}
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\subsection{Curves of Arbitrary Degree\label{bi_ssec:AlgebraicCurve2}}
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There are also initial instances for algebraic curves of arbitrary degree.
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The attached archive
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lists selected curves that have interesting features like covertical
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$x$-extremal points, several cusps, high-degree singularities, et cetera.
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\ccBenchmarkInstance{Curve/ArbitraryDegreeCurves/examples/}
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Full families of instances will be provided in the future. Until then,
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one could combine single curves to pairs or sets to analyse the intersection
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or to compute an arrangement of curves of arbitrary degree.
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