mirror of https://github.com/CGAL/cgal
338 lines
8.6 KiB
TeX
338 lines
8.6 KiB
TeX
\begin{ccRefFunction}{intersection}
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\ccInclude{CGAL/intersections.h}
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\ccUnchecked{
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\ccFunction{Object intersection(Type1<Kernel> obj1, Type2<Kernel> obj2);}
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{Two objects \ccStyle{obj1} and \ccStyle{obj2} intersect if there is a point
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\ccStyle{p} that is part of both \ccStyle{obj1} and \ccStyle{obj2}.
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The \ccHtmlNoLinksFrom{intersection} region of those two objects is defined as the set of all
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points \ccStyle{p} that are part of both \ccStyle{obj1} and \ccStyle{obj2}.
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Note that for objects like triangles and polygons that enclose a
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bounded region, this region is considered part of the object.
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If a segment lies completely inside a triangle, then those two objects
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intersect and the \ccHtmlNoLinksFrom{intersection} region is the complete segment.
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}}
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The possible value for types \ccStyle{Type1} and \ccStyle{Type2} and the
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possible return values wrapped in \ccc{Object} are the
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following:
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\begin{ccTexOnly}
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\begin{longtable}[c]{|l|l|l|}
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%\caption{All available intersection computations}\\
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\multicolumn{3}{l}{\sl \ \ }
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\endfirsthead
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\multicolumn{3}{l}{\sl continued}
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\endhead
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\hline
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type A & type B & \parbox{4 cm}{\vspace{1 mm}{return type}} \\
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\hline
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\ccStyle{Line_2} & \ccStyle{Line_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Line_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Segment_2} & \ccStyle{Line_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Segment_2} & \ccStyle{Segment_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Ray_2} & \ccStyle{Line_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Ray_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Ray_2} & \ccStyle{Segment_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Ray_2} & \ccStyle{Ray_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\\ \ccStyle{Ray_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Triangle_2} & \ccStyle{Line_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Triangle_2} & \ccStyle{Segment_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Triangle_2} & \ccStyle{Ray_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Triangle_2} & \ccStyle{Triangle_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\\ \ccStyle{Triangle_2}
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\\ \ccStyle{std::vector<Point_2>}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Iso_rectangle_2} & \ccStyle{Line_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Iso_rectangle_2} & \ccStyle{Segment_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Iso_rectangle_2} & \ccStyle{Ray_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_2}
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\\ \ccStyle{Segment_2}
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\vspace{1 mm}} \\
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\hline
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\ccStyle{Iso_rectangle_2} & \ccStyle{Iso_rectangle_2} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Iso_rectangle_2}
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\vspace{1 mm}} \\
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\hline
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{\ccStyle{Plane_3}} & {\ccStyle{Line_3}} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_3} \\
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\ccStyle{Line_3}
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\vspace{1 mm}} \\
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\hline
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{\ccStyle{Plane_3}} & {\ccStyle{Ray_3}} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_3} \\
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\ccStyle{Ray_3}
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\vspace{1 mm}} \\
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\hline
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{\ccStyle{Plane_3}} & {\ccStyle{Segment_3}} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Point_3} \\
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\ccStyle{Segment_3}
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\vspace{1 mm}} \\
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\hline
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{\ccStyle{Plane_3}} & {\ccStyle{Plane_3}} & \parbox{4 cm}{\vspace{1 mm}
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\ccStyle{Line_3} \\
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\ccStyle{Plane_3}
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\vspace{1 mm}} \\
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\hline
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\end{longtable}
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\end{ccTexOnly}
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\begin{ccHtmlOnly}
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<DIV ALIGN="CENTER">
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<TABLE CELLPADDING=3 BORDER="1">
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<TR> <TH> type A </TH>
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<TH> type B </TH>
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<TH> return type </TH>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Line_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Ray_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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<TR><TD>Ray_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD VALIGN="CENTER" > Triangle_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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<TR><TD>Triangle_2</TD></TR>
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<TR><TD>std::vector<Point_2></TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD VALIGN="CENTER" > Line_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD VALIGN="CENTER" > Segment_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD VALIGN="CENTER" > Ray_2 </TD>
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<TD><TABLE>
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<TR><TD>Point_2</TD></TR>
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<TR><TD>Segment_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD VALIGN="CENTER" > Iso_rectangle_2 </TD>
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<TD><TABLE>
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<TR><TD>Iso_rectangle_2</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD VALIGN="CENTER" > Line_3 </TD>
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<TD><TABLE>
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<TR><TD>Point_3</TD></TR>
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<TR><TD>Line_3</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD VALIGN="CENTER" > Ray_3 </TD>
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<TD><TABLE>
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<TR><TD>Point_3</TD></TR>
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<TR><TD>Ray_3</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD VALIGN="CENTER" > Segment_3 </TD>
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<TD><TABLE>
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<TR><TD>Point_3</TD></TR>
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<TR><TD>Segment_3</TD></TR>
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</TABLE></TD>
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</TR>
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<TR>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD VALIGN="CENTER" > Plane_3 </TD>
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<TD><TABLE>
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<TR><TD>Line_3</TD></TR>
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<TR><TD>Plane_3</TD></TR>
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</TABLE></TD>
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</TR>
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</TABLE>
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</DIV>
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\end{ccHtmlOnly}
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There is also an intersection function between 3 planes.
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\ccFunction{Object intersection(const Plane_3<Kernel>& pl1,
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const Plane_3<Kernel>& pl2,
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const Plane_3<Kernel>& pl3);}
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{returns the intersection of 3 planes, which can be either a point, a line,
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a plane, or empty.}
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\ccExample
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The following example demonstrates the most common use of
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\ccc{intersection} routines.
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\begin{verbatim}
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#include <CGAL/intersections.h>
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void foo(CGAL::Segment_2<Kernel> seg, CGAL::Line_2<Kernel> line)
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{
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CGAL::Object result;
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CGAL::Point_2<Kernel> ipoint;
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CGAL::Segment_2<Kernel> iseg;
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result = CGAL::intersection(seg, line);
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if (CGAL::assign(ipoint, result)) {
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\end{verbatim}%
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\ccHtmlLinksOff%
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\begin{verbatim}
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// handle the point intersection case.
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\end{verbatim}%
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\ccHtmlLinksOn%
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\begin{verbatim}
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} else
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if (CGAL::assign(iseg, result)) {
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\end{verbatim}%
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\ccHtmlLinksOff%
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\begin{verbatim}
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// handle the segment intersection case.
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\end{verbatim}%
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\ccHtmlLinksOn%
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\begin{verbatim}
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} else {
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\end{verbatim}%
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\ccHtmlLinksOff%
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\begin{verbatim}
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// handle the no intersection case.
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}
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}
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\end{verbatim}%
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\ccHtmlLinksOn%
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\ccSeeAlso
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% \ccRefIdfierPage{CGAL::assign} \\
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\ccRefIdfierPage{CGAL::do_intersect} \\
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\ccRefIdfierPage{CGAL::Object} \\
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\end{ccRefFunction}
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