mirror of https://github.com/CGAL/cgal
76 lines
2.3 KiB
TeX
76 lines
2.3 KiB
TeX
\begin{ccRefClass}{Direction_3<R>}
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\ccInclude{CGAL/Direction_3.h}
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\ccDefinition
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An object of the class \ccRefName\ is a vector in the three-dimensional
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vector space $\R^3$ where we forget about their length. They can be
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viewed as unit vectors, although there is no normalization internally,
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since this is error prone. Directions are used whenever the length of
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a vector does not matter.
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They also characterize a set of parallel lines that have the same orientation
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or the direction normal to parallel planes that have the same orientation.
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For example, you can ask for the direction
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orthogonal to an oriented plane, or the direction of an oriented line.
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\ccCreation
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\ccCreationVariable{d}
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\ccHidden \ccConstructor{Direction_3();}
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{introduces an uninitialized direction \ccVar.}
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\ccHidden \ccConstructor{Direction_3(const Direction_3<R> &d);}
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{copy constructor.}
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\ccConstructor{Direction_3(const Vector_3<R> &v);}
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{introduces a direction \ccVar\ initialised with the
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direction of vector $v$.}
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\ccConstructor{Direction_3(const R::RT &x, const R::RT &y, const R::RT &z);}
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{introduces a direction \ccVar\ initialised with the direction
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from the origin to the point with Cartesian coordinates $(x, y, z)$.}
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\ccOperations
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%\ccSetTwoOfThreeColumns{5cm}{4cm}
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\ccSetThreeColumns{Direction_3<R> & }{}{\hspace*{7.8cm}}
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\ccHidden \ccMethod{Direction_3<R> & operator=(const Direction_3<R> &e);}
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{Assignment.}
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\ccMethod{R::RT delta(int i) const;}
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{returns values, such that \ccVar \ccc{== Direction_2<R>(delta(0),delta(1),delta(2))}.
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\ccPrecond: $0 \leq i \leq 2$.}
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\ccMethod{R::RT dx() const;}
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{returns \ccc{delta(0)}.}
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\ccGlue
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\ccMethod{R::RT dy() const;}
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{returns \ccc{delta(1)}.}
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\ccGlue
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\ccMethod{R::RT dz() const;}
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{returns \ccc{delta(2)}.}
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\ccMethod{bool operator==(const Direction_3<R> &e) const;}
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{Test for equality.}
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\ccGlue
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\ccMethod{bool operator!=(const Direction_3<R> &e) const;}
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{Test for inequality.}
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\ccMethod{Direction_3<R> operator-() const;}
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{The direction opposite to \ccVar.}
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\ccMethod{Vector_3<R> vector() const;}
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{returns a vector that has the same direction as \ccVar.}
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\ccMethod{Direction_3<R> transform(const Aff_transformation_3<R> &t) const;}
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{returns the direction obtained by applying $t$ on \ccVar.}
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\end{ccRefClass}
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