mirror of https://github.com/CGAL/cgal
274 lines
5.5 KiB
C++
274 lines
5.5 KiB
C++
namespace CGAL {
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/*!
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\ingroup kernel_classes3
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An object of the class `Point_3` is a point in the three-dimensional
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Euclidean space \f$ \E^3\f$.
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Remember that `Kernel::RT` and `Kernel::FT` denote a
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`RingNumberType` and a `FieldNumberType`, respectively. For the kernel
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model `Cartesian<NT>`, the two types are the same. For the
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kernel model `Homogeneous<NT>`, `Kernel::RT` is equal
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to `NT`, and `Kernel::FT` is equal to `Quotient<NT>`.
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\cgalHeading{Operators}
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The following operations can be applied on points:
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\cgalModels `Kernel::Point_3`
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\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
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*/
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template< typename Kernel >
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class Point_3 {
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public:
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/// \name Types
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/// @{
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/*!
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An iterator for enumerating the
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%Cartesian coordinates of a point.
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*/
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typedef unspecified_type Cartesian_const_iterator;
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/// @}
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/// \name Creation
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/// @{
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/*!
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introduces a point with %Cartesian coordinates\f$ (0,0,0)\f$.
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*/
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Point_3(const Origin &ORIGIN);
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/*!
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introduces a point `p` initialized to `(x,y,z)`.
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*/
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Point_3(int x, int y, int z);
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/*!
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introduces a point `p` initialized to `(x,y,z)`
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provided `RT` supports it.
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*/
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Point_3(double x, double y, double z);
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/*!
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introduces a point `p` initialized to `(hx/hw,hy/hw, hz/hw)`.
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\pre `hw != 0`.
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*/
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Point_3(const Kernel::RT &hx, const Kernel::RT &hy, const Kernel::RT &hz, const Kernel::RT &hw = RT(1));
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/*!
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introduces a point `p` initialized to `(x,y,z)`.
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*/
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Point_3(const Kernel::FT &x, const Kernel::FT &y, const Kernel::FT &z);
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/*!
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introduces a point from a weighted point.
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\warning The `explicit` keyword is used to avoid accidental implicit conversions
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between Point_3 and Weighted_point_3.
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*/
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explicit Point_3(const Kernel::Weighted_point_3 &wp);
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/// @}
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/// \name Operations
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/// @{
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/*!
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Test for equality: Two points are equal, iff their \f$ x\f$, \f$ y\f$ and \f$ z\f$
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coordinates are equal.
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*/
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bool operator==(const Point_3<Kernel> &q) const;
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/*!
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Test for inequality.
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*/
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bool operator!=(const Point_3<Kernel> &q) const;
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/*!
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translates the point by the vector `v`.
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*/
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Point_3<Kernel>& operator+=(const Vector_3<Kernel> &v);
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/*!
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translates the point by the vector -`v`.
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*/
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Point_3<Kernel>& operator-=(const Vector_3<Kernel> &v);
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/// @}
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/// \name Coordinate Access
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/// There are two sets of coordinate access functions, namely to the
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/// homogeneous and to the %Cartesian coordinates. They can be used
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/// independently from the chosen kernel model. Note that you do not
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/// lose information with the homogeneous representation, because the
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/// FieldNumberType is a quotient.
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/// @{
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/*!
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returns the homogeneous \f$ x\f$ coordinate.
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*/
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Kernel::RT hx() const;
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/*!
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returns the homogeneous \f$ y\f$ coordinate.
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*/
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Kernel::RT hy() const;
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/*!
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returns the homogeneous \f$ z\f$ coordinate.
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*/
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Kernel::RT hz() const;
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/*!
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returns the homogenizing coordinate.
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*/
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Kernel::RT hw() const;
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/*!
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returns the %Cartesian \f$ x\f$ coordinate, that is `hx()`/`hw()`.
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*/
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Kernel::FT x() const;
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/*!
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returns the %Cartesian \f$ y\f$ coordinate, that is `hy()`/`hw()`.
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*/
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Kernel::FT y() const;
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/*!
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returns the %Cartesian \f$ z\f$ coordinate, that is `hz()`/`hw()`.
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*/
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Kernel::FT z() const;
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/// @}
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/// \name Convenience Operators
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/// The following operations are for convenience and for compatibility
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/// with code for higher dimensional points. Again they come in a
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/// %Cartesian and in a homogeneous flavor.
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/// @{
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/*!
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returns the i'th homogeneous coordinate of `p`.
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\pre `0 <= i <= 3`.
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*/
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Kernel::RT homogeneous(int i) const;
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/*!
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returns the i'th %Cartesian coordinate of `p`.
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\pre `0 <= i <= 2`.
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*/
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Kernel::FT cartesian(int i) const;
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/*!
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returns `cartesian(i)`.
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\pre `0 <= i <= 2`.
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*/
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Kernel::FT operator[](int i) const;
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/*!
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returns an iterator to the %Cartesian coordinates
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of `p`, starting with the 0th coordinate.
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*/
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Cartesian_const_iterator cartesian_begin() const;
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/*!
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returns an off the end iterator to the %Cartesian
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coordinates of `p`.
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*/
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Cartesian_const_iterator cartesian_end() const;
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/*!
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returns the dimension (the constant 3).
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*/
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int dimension() const;
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/*!
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returns a bounding box containing `p`.
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*/
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Bbox_3 bbox() const;
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/*!
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returns the point obtained by applying `t` on `p`.
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*/
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Point_3<Kernel> transform(const Aff_transformation_3<Kernel> &t) const;
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/// @}
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}; /* end Point_3 */
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/*!
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returns true iff `p` is lexicographically smaller than `q`
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(the lexicographical order being defined on the %Cartesian
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coordinates).
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\relates Point_3
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*/
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bool operator<(const Point_3<Kernel> &p,
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const Point_3<Kernel> &q);
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/*!
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returns true iff `p` is lexicographically greater than `q`.
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\relates Point_3
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*/
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bool operator>(const Point_3<Kernel> &p,
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const Point_3<Kernel> &q);
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/*!
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returns true iff `p` is lexicographically smaller or equal to
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`q`.
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\relates Point_3
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*/
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bool operator<=(const Point_3<Kernel> &p,
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const Point_3<Kernel> &q);
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/*!
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returns true iff `p` is lexicographically greater or equal to
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`q`.
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\relates Point_3
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*/
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bool operator>=(const Point_3<Kernel> &p,
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const Point_3<Kernel> &q);
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/*!
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returns the difference vector between `q` and `p`.
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You can substitute `ORIGIN` for either `p` or `q`,
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but not for both.
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\relates Point_3
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*/
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Vector_3<Kernel> operator-(const Point_3<Kernel> &p,
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const Point_3<Kernel> &q);
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/// \ingroup Kernel_operator_plus
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///@{
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/*!
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returns the point obtained by translating `p` by the
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vector `v`.
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\relates Point_3
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*/
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Point_3<Kernel> operator+(const Point_3<Kernel> &p,
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const Vector_3<Kernel> &v);
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/// @}
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/// \ingroup Kernel_operator_minus
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///@{
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/*!
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returns the point obtained by translating `p` by the
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vector -`v`.
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\relates Point_3
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*/
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Point_3<Kernel> operator-(const Point_3<Kernel> &p,
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const Vector_3<Kernel> &v);
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/// @}
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} /* end namespace CGAL */
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