mirror of https://github.com/CGAL/cgal
Merge pull request #7660 from afabri/Arrangement-typo-GF
Arrangement: small doc fixes
This commit is contained in:
commit
6ce966767b
|
|
@ -169,8 +169,8 @@ Every \cgal `Kernel` comes with two <I>real number types</I>
|
||||||
(number types embeddable into the real numbers). One of them is a
|
(number types embeddable into the real numbers). One of them is a
|
||||||
`FieldNumberType`, and the other a `RingNumberType`. The
|
`FieldNumberType`, and the other a `RingNumberType`. The
|
||||||
coordinates of the basic kernel objects (points, vectors, etc.) come
|
coordinates of the basic kernel objects (points, vectors, etc.) come
|
||||||
from one of these types (the `FieldNumberType` in case of Cartesian
|
from one of these types (the `FieldNumberType` in case of %Cartesian
|
||||||
kernels, and the `RingNumberType` for Homogeneous kernels).
|
kernels, and the `RingNumberType` for %Homogeneous kernels).
|
||||||
|
|
||||||
The concept `FieldNumberType` combines the requirements of the
|
The concept `FieldNumberType` combines the requirements of the
|
||||||
concepts `Field` and `RealEmbeddable`, while
|
concepts `Field` and `RealEmbeddable`, while
|
||||||
|
|
@ -277,4 +277,3 @@ subsequent chapters.
|
||||||
|
|
||||||
*/
|
*/
|
||||||
} /* namespace CGAL */
|
} /* namespace CGAL */
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -5,7 +5,7 @@
|
||||||
The concept `FieldNumberType` combines the requirements of the concepts
|
The concept `FieldNumberType` combines the requirements of the concepts
|
||||||
`Field` and `RealEmbeddable`.
|
`Field` and `RealEmbeddable`.
|
||||||
A model of `FieldNumberType` can be used as a template parameter
|
A model of `FieldNumberType` can be used as a template parameter
|
||||||
for Cartesian kernels.
|
for %Cartesian kernels.
|
||||||
|
|
||||||
\cgalRefines{Field,RealEmbeddable}
|
\cgalRefines{Field,RealEmbeddable}
|
||||||
|
|
||||||
|
|
@ -32,4 +32,3 @@ public:
|
||||||
/// @}
|
/// @}
|
||||||
|
|
||||||
}; /* end FieldNumberType */
|
}; /* end FieldNumberType */
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -6,7 +6,7 @@
|
||||||
The concept `RingNumberType` combines the requirements of the concepts
|
The concept `RingNumberType` combines the requirements of the concepts
|
||||||
`IntegralDomainWithoutDivision` and `RealEmbeddable`.
|
`IntegralDomainWithoutDivision` and `RealEmbeddable`.
|
||||||
A model of `RingNumberType` can be used as a template parameter
|
A model of `RingNumberType` can be used as a template parameter
|
||||||
for Homogeneous kernels.
|
for homogeneous kernels.
|
||||||
|
|
||||||
\cgalRefines{IntegralDomainWithoutDivision,RealEmbeddable}
|
\cgalRefines{IntegralDomainWithoutDivision,RealEmbeddable}
|
||||||
|
|
||||||
|
|
@ -32,4 +32,3 @@ class RingNumberType {
|
||||||
public:
|
public:
|
||||||
|
|
||||||
}; /* end RingNumberType */
|
}; /* end RingNumberType */
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -117,8 +117,8 @@ special type of objects. They must, however, supply the relevant
|
||||||
traits class, which mainly involves algebraic computations. A traits
|
traits class, which mainly involves algebraic computations. A traits
|
||||||
class also encapsulates the number types used to represent coordinates
|
class also encapsulates the number types used to represent coordinates
|
||||||
of geometric objects and to carry out algebraic operations on them. It
|
of geometric objects and to carry out algebraic operations on them. It
|
||||||
encapsulates the type of coordinate system used (e.g., Cartesian and
|
encapsulates the type of coordinate system used (e.g., %Cartesian and
|
||||||
Homogeneous), and the geometric or algebraic computation methods
|
homogeneous), and the geometric or algebraic computation methods
|
||||||
themselves. The precise minimal sets of requirements the actual traits
|
themselves. The precise minimal sets of requirements the actual traits
|
||||||
classes must conform to are organized as a hierarchy of concepts; see
|
classes must conform to are organized as a hierarchy of concepts; see
|
||||||
Section \ref aos_sec-geom_traits.
|
Section \ref aos_sec-geom_traits.
|
||||||
|
|
@ -4780,7 +4780,7 @@ or line segments. The \link Arr_conic_traits_2::Curve_2
|
||||||
`Curve_2`\endlink and the derived \link
|
`Curve_2`\endlink and the derived \link
|
||||||
Arr_conic_traits_2::X_monotone_curve_2 `X_monotone_curve_2`\endlink
|
Arr_conic_traits_2::X_monotone_curve_2 `X_monotone_curve_2`\endlink
|
||||||
classes also support basic access functions such as `source()`,
|
classes also support basic access functions such as `source()`,
|
||||||
`target()`, and `orientation()`.
|
`target()`, and `%orientation()`.
|
||||||
|
|
||||||
<!-- ------------------------------------------------------------------------- -->
|
<!-- ------------------------------------------------------------------------- -->
|
||||||
\cgalFigureBegin{aos_fig-conics,conics.png}
|
\cgalFigureBegin{aos_fig-conics,conics.png}
|
||||||
|
|
@ -5067,7 +5067,7 @@ substitute the template parameters `RatKernel`, `AlgKernel`, and
|
||||||
the same requirements of the corresponding types used to instantiate
|
the same requirements of the corresponding types used to instantiate
|
||||||
the `Arr_conic_traits_2` class template. Here, the use of the
|
the `Arr_conic_traits_2` class template. Here, the use of the
|
||||||
`CORE_algebraic_number_traits` class is also recommended with
|
`CORE_algebraic_number_traits` class is also recommended with
|
||||||
Cartesian kernels instantiated with the `Rational` and `Algebraic`
|
%Cartesian kernels instantiated with the `Rational` and `Algebraic`
|
||||||
number types defined by this class. The examples given in this manual
|
number types defined by this class. The examples given in this manual
|
||||||
use the type definitions listed below. These types are defined in the
|
use the type definitions listed below. These types are defined in the
|
||||||
header file `arr_Bezier.h`.
|
header file `arr_Bezier.h`.
|
||||||
|
|
|
||||||
|
|
@ -168,7 +168,7 @@ public:
|
||||||
|
|
||||||
|
|
||||||
/*! The `Point_2` number-type nested within the traits class represents
|
/*! The `Point_2` number-type nested within the traits class represents
|
||||||
* a Cartesian point whose coordinates are algebraic numbers of type
|
* a %Cartesian point whose coordinates are algebraic numbers of type
|
||||||
* `CoordNT`.
|
* `CoordNT`.
|
||||||
*/
|
*/
|
||||||
class Point_2 {
|
class Point_2 {
|
||||||
|
|
|
||||||
|
|
@ -274,7 +274,7 @@ public:
|
||||||
*/
|
*/
|
||||||
Point_2(const Algebraic& hx, const Algebraic& hy, const Algebraic& hz);
|
Point_2(const Algebraic& hx, const Algebraic& hy, const Algebraic& hz);
|
||||||
|
|
||||||
/*! constructs from Cartesian coordinates.
|
/*! constructs from %Cartesian coordinates.
|
||||||
*/
|
*/
|
||||||
Point_2(const Algebraic& x, const Algebraic& y);:
|
Point_2(const Algebraic& x, const Algebraic& y);:
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -159,7 +159,7 @@ typedef unspecified_type Less_xy_2;
|
||||||
|
|
||||||
`Comparison_result operator(const Point_2& p, const Point_2& q)`
|
`Comparison_result operator(const Point_2& p, const Point_2& q)`
|
||||||
|
|
||||||
that compares the Cartesian x-coordinates of the points `p` and `q`.
|
that compares the %Cartesian x-coordinates of the points `p` and `q`.
|
||||||
*/
|
*/
|
||||||
typedef unspecified_type Compare_x_2;
|
typedef unspecified_type Compare_x_2;
|
||||||
|
|
||||||
|
|
@ -168,7 +168,7 @@ typedef unspecified_type Compare_x_2;
|
||||||
|
|
||||||
`Comparison_result operator(const Point_2& p, const Point_2& q)`
|
`Comparison_result operator(const Point_2& p, const Point_2& q)`
|
||||||
|
|
||||||
that compares the Cartesian y-coordinates of the points `p` and `q`.
|
that compares the %Cartesian y-coordinates of the points `p` and `q`.
|
||||||
*/
|
*/
|
||||||
typedef unspecified_type Compare_y_2;
|
typedef unspecified_type Compare_y_2;
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -8,7 +8,7 @@ An object of class `Approximate_min_ellipsoid_d` is an approximation to the
|
||||||
ellipsoid of smallest volume enclosing a finite multiset of points
|
ellipsoid of smallest volume enclosing a finite multiset of points
|
||||||
in \f$ d\f$-dimensional Euclidean space \f$ \E^d\f$, \f$ d\ge 2\f$.
|
in \f$ d\f$-dimensional Euclidean space \f$ \E^d\f$, \f$ d\ge 2\f$.
|
||||||
|
|
||||||
An <I>ellipsoid</I> in \f$ \E^d\f$ is a Cartesian pointset of the form \f$ \{
|
An <I>ellipsoid</I> in \f$ \E^d\f$ is a %Cartesian pointset of the form \f$ \{
|
||||||
x\in\E^d \mid x^T E x + x^T e + \eta\leq 0 \}\f$, where \f$ E\f$ is some
|
x\in\E^d \mid x^T E x + x^T e + \eta\leq 0 \}\f$, where \f$ E\f$ is some
|
||||||
positive definite matrix from the set \f$ \mathbb{R}^{d\times d}\f$, \f$ e\f$ is some
|
positive definite matrix from the set \f$ \mathbb{R}^{d\times d}\f$, \f$ e\f$ is some
|
||||||
real \f$ d\f$-vector, and \f$ \eta\in\mathbb{R}\f$. A pointset \f$ P\subseteq \E^d\f$ is
|
real \f$ d\f$-vector, and \f$ \eta\in\mathbb{R}\f$. A pointset \f$ P\subseteq \E^d\f$ is
|
||||||
|
|
@ -94,7 +94,7 @@ is actually achieved; the performance of the algorithm in this respect
|
||||||
highly depends on the input pointset. Values of at least \f$ 0.01\f$ for
|
highly depends on the input pointset. Values of at least \f$ 0.01\f$ for
|
||||||
\f$ \epsilon\f$ are usually handled without problems.
|
\f$ \epsilon\f$ are usually handled without problems.
|
||||||
|
|
||||||
Internally, the algorithm represents the input points' Cartesian
|
Internally, the algorithm represents the input points' %Cartesian
|
||||||
coordinates as `double`'s. For this conversion to work, the input
|
coordinates as `double`'s. For this conversion to work, the input
|
||||||
point coordinates must be convertible to `double`. Also, in order
|
point coordinates must be convertible to `double`. Also, in order
|
||||||
to compute the achieved epsilon \f$ \epsilon'\f$ mentioned above, the algorithm
|
to compute the achieved epsilon \f$ \epsilon'\f$ mentioned above, the algorithm
|
||||||
|
|
@ -171,7 +171,7 @@ typedef unspecified_type Cartesian_const_iterator;
|
||||||
/*!
|
/*!
|
||||||
A model of STL concept
|
A model of STL concept
|
||||||
`RandomAccessIterator` with value type `double` that is used
|
`RandomAccessIterator` with value type `double` that is used
|
||||||
to iterate over the Cartesian center coordinates of the computed
|
to iterate over the %Cartesian center coordinates of the computed
|
||||||
ellipsoid, see `center_cartesian_begin()`.
|
ellipsoid, see `center_cartesian_begin()`.
|
||||||
*/
|
*/
|
||||||
typedef unspecified_type Center_coordinate_iterator;
|
typedef unspecified_type Center_coordinate_iterator;
|
||||||
|
|
@ -313,7 +313,7 @@ int dimension() const;
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
|
|
||||||
returns an iterator pointing to the first of the \f$ d\f$ Cartesian
|
returns an iterator pointing to the first of the \f$ d\f$ %Cartesian
|
||||||
coordinates of the computed ellipsoid's center.
|
coordinates of the computed ellipsoid's center.
|
||||||
|
|
||||||
The returned point is a floating-point approximation to the
|
The returned point is a floating-point approximation to the
|
||||||
|
|
|
||||||
|
|
@ -46,7 +46,7 @@ bool is_circle();
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
gives a double approximation of the
|
gives a double approximation of the
|
||||||
ellipse's conic equation. If `K` is a Cartesian kernel, the ellipse
|
ellipse's conic equation. If `K` is a %Cartesian kernel, the ellipse
|
||||||
is the set of all points \f$ (x,y)\f$ satisfying \f$ rx^2+sy^2+txy+ux+vy+w=0\f$. In the
|
is the set of all points \f$ (x,y)\f$ satisfying \f$ rx^2+sy^2+txy+ux+vy+w=0\f$. In the
|
||||||
Homogeneous case, the ellipse is the set of points \f$ (hx,hy,hw)\f$ satisfying
|
Homogeneous case, the ellipse is the set of points \f$ (hx,hy,hw)\f$ satisfying
|
||||||
\f$ r(hx)^2+s(hy)^2+t(hx)(hy)+u(hx)(hw)+v(hy)(hw)+w(hw)^2=0\f$.
|
\f$ r(hx)^2+s(hy)^2+t(hx)(hy)+u(hx)(hw)+v(hy)(hw)+w(hw)^2=0\f$.
|
||||||
|
|
|
||||||
|
|
@ -90,7 +90,7 @@ be used in such a case. (For exact number types
|
||||||
Currently, we require `Traits::FT` to be either an exact number
|
Currently, we require `Traits::FT` to be either an exact number
|
||||||
type or `double` or `float`; other inexact number types are
|
type or `double` or `float`; other inexact number types are
|
||||||
not supported at this time. Also, the current implementation only
|
not supported at this time. Also, the current implementation only
|
||||||
handles spheres with Cartesian coordinates; homogeneous representation
|
handles spheres with %Cartesian coordinates; homogeneous representation
|
||||||
is not supported yet.
|
is not supported yet.
|
||||||
|
|
||||||
\cgalHeading{Example}
|
\cgalHeading{Example}
|
||||||
|
|
|
||||||
|
|
@ -21,7 +21,7 @@ we use the function objects `C2E` and `C2F`, which must be of the form
|
||||||
\cgalHeading{Example}
|
\cgalHeading{Example}
|
||||||
|
|
||||||
The following example defines an efficient and exact version of the
|
The following example defines an efficient and exact version of the
|
||||||
orientation predicate over three points using the Cartesian representation
|
orientation predicate over three points using the %Cartesian representation
|
||||||
with double coordinates and without reference counting
|
with double coordinates and without reference counting
|
||||||
(`Simple_cartesian::Point_2`).
|
(`Simple_cartesian::Point_2`).
|
||||||
Of course, the orientation predicate can already be found in the kernel, but
|
Of course, the orientation predicate can already be found in the kernel, but
|
||||||
|
|
|
||||||
|
|
@ -753,7 +753,7 @@ const CGAL::Point_3<Kernel>& r);
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and
|
Compares the %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically in \f$ xy\f$ order: first
|
`q` lexicographically in \f$ xy\f$ order: first
|
||||||
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
||||||
are compared. This is the same function as `compare_xy` and exists for compatibility with `Point_d<Kernel>`.
|
are compared. This is the same function as `compare_xy` and exists for compatibility with `Point_d<Kernel>`.
|
||||||
|
|
@ -763,7 +763,7 @@ Comparison_result
|
||||||
compare_lexicographically(const CGAL::Point_2<Kernel>& p, const CGAL::Point_2<Kernel>& q);
|
compare_lexicographically(const CGAL::Point_2<Kernel>& p, const CGAL::Point_2<Kernel>& q);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and
|
Compares the %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically in \f$ xyz\f$ order: first
|
`q` lexicographically in \f$ xyz\f$ order: first
|
||||||
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
||||||
are compared, and if both \f$ x\f$- and \f$ y\f$- coordinate are equal,
|
are compared, and if both \f$ x\f$- and \f$ y\f$- coordinate are equal,
|
||||||
|
|
@ -1144,7 +1144,7 @@ global function are available.
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and
|
Compares the %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically in \f$ xy\f$ order: first
|
`q` lexicographically in \f$ xy\f$ order: first
|
||||||
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
||||||
are compared.
|
are compared.
|
||||||
|
|
@ -1154,7 +1154,7 @@ Comparison_result
|
||||||
compare_xy(const CGAL::Point_2<Kernel>& p, const CGAL::Point_2<Kernel>& q);
|
compare_xy(const CGAL::Point_2<Kernel>& p, const CGAL::Point_2<Kernel>& q);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and `q`
|
Compares the %Cartesian coordinates of points `p` and `q`
|
||||||
lexicographically in \f$ xy\f$ order: first \f$ x\f$-coordinates are
|
lexicographically in \f$ xy\f$ order: first \f$ x\f$-coordinates are
|
||||||
compared, if they are equal, \f$ y\f$-coordinates are compared.
|
compared, if they are equal, \f$ y\f$-coordinates are compared.
|
||||||
|
|
||||||
|
|
@ -1177,7 +1177,7 @@ compare_xy(const CGAL::Point_3<Kernel>& p, const CGAL::Point_3<Kernel>& q);
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the \f$ x\f$ and \f$ y\f$ Cartesian coordinates of points `p` and
|
Compares the \f$ x\f$ and \f$ y\f$ %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically.
|
`q` lexicographically.
|
||||||
*/
|
*/
|
||||||
template <typename CircularKernel>
|
template <typename CircularKernel>
|
||||||
|
|
@ -1186,7 +1186,7 @@ Comparison_result
|
||||||
const CGAL::Circular_arc_point_2<CircularKernel> &q);
|
const CGAL::Circular_arc_point_2<CircularKernel> &q);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the \f$ x\f$ and \f$ y\f$ Cartesian coordinates of points `p` and
|
Compares the \f$ x\f$ and \f$ y\f$ %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically.
|
`q` lexicographically.
|
||||||
*/
|
*/
|
||||||
template <typename CircularKernel>
|
template <typename CircularKernel>
|
||||||
|
|
@ -1209,7 +1209,7 @@ compare_xy(const CGAL::Circular_arc_point_2<CircularKernel> &p,
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
|
|
||||||
Compares the \f$ x\f$ and \f$ y\f$ Cartesian coordinates of points `p` and
|
Compares the \f$ x\f$ and \f$ y\f$ %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically.
|
`q` lexicographically.
|
||||||
*/
|
*/
|
||||||
template <typename SphericalKernel>
|
template <typename SphericalKernel>
|
||||||
|
|
@ -1218,7 +1218,7 @@ Comparison_result
|
||||||
const CGAL::Circular_arc_point_3<SphericalKernel> &q);
|
const CGAL::Circular_arc_point_3<SphericalKernel> &q);
|
||||||
/*!
|
/*!
|
||||||
|
|
||||||
Compares the \f$ x\f$ and \f$ y\f$ Cartesian coordinates of points `p` and
|
Compares the \f$ x\f$ and \f$ y\f$ %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically.
|
`q` lexicographically.
|
||||||
*/
|
*/
|
||||||
template <typename SphericalKernel>
|
template <typename SphericalKernel>
|
||||||
|
|
@ -1442,13 +1442,13 @@ global function are available.
|
||||||
*/
|
*/
|
||||||
/// @{
|
/// @{
|
||||||
/*!
|
/*!
|
||||||
compares Cartesian \f$ y\f$-coordinates of `p` and `q`.
|
compares %Cartesian \f$ y\f$-coordinates of `p` and `q`.
|
||||||
*/
|
*/
|
||||||
template <typename Kernel>
|
template <typename Kernel>
|
||||||
Comparison_result compare_y(const CGAL::Point_2<Kernel> &p,
|
Comparison_result compare_y(const CGAL::Point_2<Kernel> &p,
|
||||||
const CGAL::Point_2<Kernel> &q);
|
const CGAL::Point_2<Kernel> &q);
|
||||||
/*!
|
/*!
|
||||||
compares Cartesian \f$ y\f$-coordinates of `p` and `q`.
|
compares %Cartesian \f$ y\f$-coordinates of `p` and `q`.
|
||||||
*/
|
*/
|
||||||
template <typename Kernel>
|
template <typename Kernel>
|
||||||
Comparison_result compare_y(const CGAL::Point_3<Kernel> &p,
|
Comparison_result compare_y(const CGAL::Point_3<Kernel> &p,
|
||||||
|
|
@ -1564,7 +1564,7 @@ global function are available.
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and
|
Compares the %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically in \f$ xyz\f$ order: first
|
`q` lexicographically in \f$ xyz\f$ order: first
|
||||||
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
||||||
are compared, and if both \f$ x\f$- and \f$ y\f$- coordinate are equal,
|
are compared, and if both \f$ x\f$- and \f$ y\f$- coordinate are equal,
|
||||||
|
|
@ -1587,7 +1587,7 @@ compare_xyz(const CGAL::Point_3<Kernel>& p, const CGAL::Point_3<Kernel>& q);
|
||||||
*/
|
*/
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*! Compares the Cartesian coordinates of points `p` and `q` lexicographically.
|
/*! Compares the %Cartesian coordinates of points `p` and `q` lexicographically.
|
||||||
*/
|
*/
|
||||||
template <typename SphericalKernel>
|
template <typename SphericalKernel>
|
||||||
Comparison_result
|
Comparison_result
|
||||||
|
|
@ -1595,7 +1595,7 @@ compare_xyz(const CGAL::Circular_arc_point_3<SphericalKernel> &p,
|
||||||
const CGAL::Circular_arc_point_3<SphericalKernel> &q);
|
const CGAL::Circular_arc_point_3<SphericalKernel> &q);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and `q` lexicographically.
|
Compares the %Cartesian coordinates of points `p` and `q` lexicographically.
|
||||||
*/
|
*/
|
||||||
template <typename SphericalKernel>
|
template <typename SphericalKernel>
|
||||||
Comparison_result
|
Comparison_result
|
||||||
|
|
@ -1682,7 +1682,7 @@ compare_z(const CGAL::Circular_arc_point_3<SphericalKernel> &p, const CGAL::Poin
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and
|
Compares the %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically in \f$ yx\f$ order: first
|
`q` lexicographically in \f$ yx\f$ order: first
|
||||||
\f$ y\f$-coordinates are compared, if they are equal, \f$ x\f$-coordinates
|
\f$ y\f$-coordinates are compared, if they are equal, \f$ x\f$-coordinates
|
||||||
are compared.
|
are compared.
|
||||||
|
|
|
||||||
|
|
@ -13,7 +13,7 @@ will explicitly state where you can pass this constant as an argument
|
||||||
instead of a vector initialized with zeros.
|
instead of a vector initialized with zeros.
|
||||||
|
|
||||||
\cgalModels `Kernel::Vector_2`
|
\cgalModels `Kernel::Vector_2`
|
||||||
\cgalModels `Hashable` if `Kernel` is a cartesian kernel and if `Kernel::FT` is `Hashable`
|
\cgalModels `Hashable` if `Kernel` is a %Cartesian kernel and if `Kernel::FT` is `Hashable`
|
||||||
|
|
||||||
*/
|
*/
|
||||||
template< typename Kernel >
|
template< typename Kernel >
|
||||||
|
|
@ -25,7 +25,7 @@ public:
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
An iterator for enumerating the
|
An iterator for enumerating the
|
||||||
Cartesian coordinates of a vector.
|
%Cartesian coordinates of a vector.
|
||||||
*/
|
*/
|
||||||
typedef unspecified_type Cartesian_const_iterator;
|
typedef unspecified_type Cartesian_const_iterator;
|
||||||
|
|
||||||
|
|
@ -119,7 +119,7 @@ Kernel::FT y() const;
|
||||||
|
|
||||||
/// \name Convenience Operators
|
/// \name Convenience Operators
|
||||||
/// The following operations are for convenience and for compatibility
|
/// The following operations are for convenience and for compatibility
|
||||||
/// with higher dimensional vectors. Again they come in a Cartesian
|
/// with higher dimensional vectors. Again they come in a %Cartesian
|
||||||
/// and homogeneous flavor.
|
/// and homogeneous flavor.
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
|
|
@ -131,7 +131,7 @@ returns the i'th homogeneous coordinate of `v`.
|
||||||
Kernel::RT homogeneous(int i) const;
|
Kernel::RT homogeneous(int i) const;
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns the i'th Cartesian coordinate of `v`.
|
returns the i'th %Cartesian coordinate of `v`.
|
||||||
\pre `0 <= i <= 1`.
|
\pre `0 <= i <= 1`.
|
||||||
*/
|
*/
|
||||||
Kernel::FT cartesian(int i) const;
|
Kernel::FT cartesian(int i) const;
|
||||||
|
|
@ -143,13 +143,13 @@ returns `cartesian(i)`.
|
||||||
Kernel::FT operator[](int i) const;
|
Kernel::FT operator[](int i) const;
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns an iterator to the Cartesian coordinates
|
returns an iterator to the %Cartesian coordinates
|
||||||
of `v`, starting with the 0th coordinate.
|
of `v`, starting with the 0th coordinate.
|
||||||
*/
|
*/
|
||||||
Cartesian_const_iterator cartesian_begin() const;
|
Cartesian_const_iterator cartesian_begin() const;
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns an off the end iterator to the Cartesian
|
returns an off the end iterator to the %Cartesian
|
||||||
coordinates of `v`.
|
coordinates of `v`.
|
||||||
*/
|
*/
|
||||||
Cartesian_const_iterator cartesian_end() const;
|
Cartesian_const_iterator cartesian_end() const;
|
||||||
|
|
|
||||||
|
|
@ -478,7 +478,7 @@ public:
|
||||||
\ingroup PkgKernel23ConceptsFunctionObjects
|
\ingroup PkgKernel23ConceptsFunctionObjects
|
||||||
\cgalConcept
|
\cgalConcept
|
||||||
|
|
||||||
A type representing an iterator to the Cartesian coordinates of a point
|
A type representing an iterator to the %Cartesian coordinates of a point
|
||||||
in two dimensions.
|
in two dimensions.
|
||||||
|
|
||||||
\cgalRefines{CopyConstructible,Assignable,DefaultConstructible}
|
\cgalRefines{CopyConstructible,Assignable,DefaultConstructible}
|
||||||
|
|
@ -495,7 +495,7 @@ public:
|
||||||
\ingroup PkgKernel23ConceptsFunctionObjects
|
\ingroup PkgKernel23ConceptsFunctionObjects
|
||||||
\cgalConcept
|
\cgalConcept
|
||||||
|
|
||||||
A type representing an iterator to the Cartesian coordinates of a point
|
A type representing an iterator to the %Cartesian coordinates of a point
|
||||||
in three dimensions.
|
in three dimensions.
|
||||||
|
|
||||||
\cgalRefines{CopyConstructible,Assignable,DefaultConstructible}
|
\cgalRefines{CopyConstructible,Assignable,DefaultConstructible}
|
||||||
|
|
@ -1365,7 +1365,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and
|
Compares the %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically in \f$ xyz\f$ order: first
|
`q` lexicographically in \f$ xyz\f$ order: first
|
||||||
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
||||||
are compared. If they are equal, \f$ z\f$-coordinates are compared.
|
are compared. If they are equal, \f$ z\f$-coordinates are compared.
|
||||||
|
|
@ -1395,7 +1395,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and
|
Compares the %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically in \f$ xy\f$ order: first
|
`q` lexicographically in \f$ xy\f$ order: first
|
||||||
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
||||||
are compared.
|
are compared.
|
||||||
|
|
@ -1425,7 +1425,7 @@ public:
|
||||||
|
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and
|
Compares the %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically in \f$ xy\f$ order: first
|
`q` lexicographically in \f$ xy\f$ order: first
|
||||||
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
\f$ x\f$-coordinates are compared, if they are equal, \f$ y\f$-coordinates
|
||||||
are compared.
|
are compared.
|
||||||
|
|
@ -1458,7 +1458,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
compares the Cartesian \f$ x\f$-coordinates of points `p` and `q`
|
compares the %Cartesian \f$ x\f$-coordinates of points `p` and `q`
|
||||||
*/
|
*/
|
||||||
Comparison_result operator()(const Kernel::Point_2&p,
|
Comparison_result operator()(const Kernel::Point_2&p,
|
||||||
const Kernel::Point_2&q);
|
const Kernel::Point_2&q);
|
||||||
|
|
@ -1514,7 +1514,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian \f$ x\f$-coordinates of points `p` and
|
Compares the %Cartesian \f$ x\f$-coordinates of points `p` and
|
||||||
`q`
|
`q`
|
||||||
*/
|
*/
|
||||||
Comparison_result operator()(const Kernel::Point_3&p,
|
Comparison_result operator()(const Kernel::Point_3&p,
|
||||||
|
|
@ -1633,7 +1633,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian coordinates of points `p` and
|
Compares the %Cartesian coordinates of points `p` and
|
||||||
`q` lexicographically in \f$ yx\f$ order: first
|
`q` lexicographically in \f$ yx\f$ order: first
|
||||||
\f$ y\f$-coordinates are compared, if they are equal, \f$ x\f$-coordinates
|
\f$ y\f$-coordinates are compared, if they are equal, \f$ x\f$-coordinates
|
||||||
are compared.
|
are compared.
|
||||||
|
|
@ -1666,7 +1666,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian \f$ y\f$-coordinates of points `p` and
|
Compares the %Cartesian \f$ y\f$-coordinates of points `p` and
|
||||||
`q`
|
`q`
|
||||||
*/
|
*/
|
||||||
Comparison_result operator()(const Kernel::Point_2&p,
|
Comparison_result operator()(const Kernel::Point_2&p,
|
||||||
|
|
@ -1725,7 +1725,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian \f$ y\f$-coordinates of points `p` and
|
Compares the %Cartesian \f$ y\f$-coordinates of points `p` and
|
||||||
`q`
|
`q`
|
||||||
*/
|
*/
|
||||||
Comparison_result operator()(const Kernel::Point_3&p,
|
Comparison_result operator()(const Kernel::Point_3&p,
|
||||||
|
|
@ -1752,7 +1752,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Compares the Cartesian \f$ z\f$-coordinates of points `p` and
|
Compares the %Cartesian \f$ z\f$-coordinates of points `p` and
|
||||||
`q`
|
`q`
|
||||||
*/
|
*/
|
||||||
Comparison_result operator()(const Kernel::Point_3&p,
|
Comparison_result operator()(const Kernel::Point_3&p,
|
||||||
|
|
@ -3983,25 +3983,25 @@ public:
|
||||||
|
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns an iterator on the 0'th Cartesian coordinate of `p`.
|
returns an iterator on the 0'th %Cartesian coordinate of `p`.
|
||||||
*/
|
*/
|
||||||
Kernel::Cartesian_const_iterator_2 operator()(const Kernel::Point_2
|
Kernel::Cartesian_const_iterator_2 operator()(const Kernel::Point_2
|
||||||
&p);
|
&p);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns the past the end iterator of the Cartesian coordinates of `p`.
|
returns the past the end iterator of the %Cartesian coordinates of `p`.
|
||||||
*/
|
*/
|
||||||
Kernel::Cartesian_const_iterator_2 operator()(const Kernel::Point_2
|
Kernel::Cartesian_const_iterator_2 operator()(const Kernel::Point_2
|
||||||
&p, int);
|
&p, int);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns an iterator on the 0'th Cartesian coordinate of `v`.
|
returns an iterator on the 0'th %Cartesian coordinate of `v`.
|
||||||
*/
|
*/
|
||||||
Kernel::Cartesian_const_iterator_2 operator()(const Kernel::Vector_2
|
Kernel::Cartesian_const_iterator_2 operator()(const Kernel::Vector_2
|
||||||
&v);
|
&v);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns the past the end iterator of the Cartesian coordinates of `v`.
|
returns the past the end iterator of the %Cartesian coordinates of `v`.
|
||||||
*/
|
*/
|
||||||
Kernel::Cartesian_const_iterator_2 operator()(const Kernel::Vector_2
|
Kernel::Cartesian_const_iterator_2 operator()(const Kernel::Vector_2
|
||||||
&v, int);
|
&v, int);
|
||||||
|
|
@ -4028,25 +4028,25 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns an iterator on the 0'th Cartesian coordinate of `p`.
|
returns an iterator on the 0'th %Cartesian coordinate of `p`.
|
||||||
*/
|
*/
|
||||||
Kernel::Cartesian_const_iterator_3 operator()(const Kernel::Point_3
|
Kernel::Cartesian_const_iterator_3 operator()(const Kernel::Point_3
|
||||||
&p);
|
&p);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns the past the end iterator of the Cartesian coordinates of `p`.
|
returns the past the end iterator of the %Cartesian coordinates of `p`.
|
||||||
*/
|
*/
|
||||||
Kernel::Cartesian_const_iterator_3 operator()(const Kernel::Point_3
|
Kernel::Cartesian_const_iterator_3 operator()(const Kernel::Point_3
|
||||||
&p, int);
|
&p, int);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns an iterator on the 0'th Cartesian coordinate of `v`.
|
returns an iterator on the 0'th %Cartesian coordinate of `v`.
|
||||||
*/
|
*/
|
||||||
Kernel::Cartesian_const_iterator_3 operator()(const Kernel::Vector_3
|
Kernel::Cartesian_const_iterator_3 operator()(const Kernel::Vector_3
|
||||||
&v);
|
&v);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns the past the end iterator of the Cartesian coordinates of `v`.
|
returns the past the end iterator of the %Cartesian coordinates of `v`.
|
||||||
*/
|
*/
|
||||||
Kernel::Cartesian_const_iterator_3 operator()(const Kernel::Vector_3
|
Kernel::Cartesian_const_iterator_3 operator()(const Kernel::Vector_3
|
||||||
&v, int);
|
&v, int);
|
||||||
|
|
@ -5992,7 +5992,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
introduces a variable with Cartesian coordinates
|
introduces a variable with %Cartesian coordinates
|
||||||
\f$ (0,0)\f$.
|
\f$ (0,0)\f$.
|
||||||
*/
|
*/
|
||||||
Kernel::Point_2 operator()(const CGAL::Origin &CGAL::ORIGIN);
|
Kernel::Point_2 operator()(const CGAL::Origin &CGAL::ORIGIN);
|
||||||
|
|
@ -6033,7 +6033,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
introduces a point with Cartesian coordinates\f$ (0,0,0)\f$.
|
introduces a point with %Cartesian coordinates\f$ (0,0,0)\f$.
|
||||||
*/
|
*/
|
||||||
Kernel::Point_3 operator()(const CGAL::Origin &CGAL::ORIGIN);
|
Kernel::Point_3 operator()(const CGAL::Origin &CGAL::ORIGIN);
|
||||||
|
|
||||||
|
|
@ -7287,19 +7287,19 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
introduces a weighted point with Cartesian coordinates
|
introduces a weighted point with %Cartesian coordinates
|
||||||
\f$ (0,0)\f$ and weight \f$ 0 \f$.
|
\f$ (0,0)\f$ and weight \f$ 0 \f$.
|
||||||
*/
|
*/
|
||||||
Kernel::Weighted_point_2 operator()(const CGAL::Origin &CGAL::ORIGIN);
|
Kernel::Weighted_point_2 operator()(const CGAL::Origin &CGAL::ORIGIN);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
introduces a weighted point with Cartesian coordinates
|
introduces a weighted point with %Cartesian coordinates
|
||||||
those of \f$ p \f$ and weight \f$ 0 \f$.
|
those of \f$ p \f$ and weight \f$ 0 \f$.
|
||||||
*/
|
*/
|
||||||
Kernel::Weighted_point_2 operator()(const Kernel::Point_2& p);
|
Kernel::Weighted_point_2 operator()(const Kernel::Point_2& p);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
introduces a weighted point with Cartesian coordinates
|
introduces a weighted point with %Cartesian coordinates
|
||||||
those of \f$ p \f$ and weight \f$ w \f$.
|
those of \f$ p \f$ and weight \f$ w \f$.
|
||||||
*/
|
*/
|
||||||
Kernel::Weighted_point_2 operator()(const Kernel::Point_2& p, const Kernel::FT& w);
|
Kernel::Weighted_point_2 operator()(const Kernel::Point_2& p, const Kernel::FT& w);
|
||||||
|
|
@ -7325,19 +7325,19 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
introduces a weighted point with Cartesian coordinates
|
introduces a weighted point with %Cartesian coordinates
|
||||||
\f$ (0,0,0)\f$ and weight \f$ 0 \f$.
|
\f$ (0,0,0)\f$ and weight \f$ 0 \f$.
|
||||||
*/
|
*/
|
||||||
Kernel::Weighted_point_3 operator()(const CGAL::Origin &CGAL::ORIGIN);
|
Kernel::Weighted_point_3 operator()(const CGAL::Origin &CGAL::ORIGIN);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
introduces a weighted point with Cartesian coordinates
|
introduces a weighted point with %Cartesian coordinates
|
||||||
those of \f$ p \f$ and weight \f$ 0 \f$.
|
those of \f$ p \f$ and weight \f$ 0 \f$.
|
||||||
*/
|
*/
|
||||||
Kernel::Weighted_point_3 operator()(const Kernel::Point_3& p);
|
Kernel::Weighted_point_3 operator()(const Kernel::Point_3& p);
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
introduces a weighted point with Cartesian coordinates
|
introduces a weighted point with %Cartesian coordinates
|
||||||
those of \f$ p \f$ and weight \f$ w \f$.
|
those of \f$ p \f$ and weight \f$ w \f$.
|
||||||
*/
|
*/
|
||||||
Kernel::Weighted_point_3 operator()(const Kernel::Point_3& p, const Kernel::FT& w);
|
Kernel::Weighted_point_3 operator()(const Kernel::Point_3& p, const Kernel::FT& w);
|
||||||
|
|
@ -7590,8 +7590,8 @@ public:
|
||||||
|
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns true iff `p` and `q` have the same Cartesian \f$ x\f$-coordinate
|
returns true iff `p` and `q` have the same %Cartesian \f$ x\f$-coordinate
|
||||||
and the same Cartesian \f$ y\f$-coordinate.
|
and the same %Cartesian \f$ y\f$-coordinate.
|
||||||
*/
|
*/
|
||||||
bool operator()(const Kernel::Point_3&p,
|
bool operator()(const Kernel::Point_3&p,
|
||||||
const Kernel::Point_3&q);
|
const Kernel::Point_3&q);
|
||||||
|
|
@ -7617,7 +7617,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns true iff `p` and `q` have the same Cartesian \f$ x\f$-coordinate.
|
returns true iff `p` and `q` have the same %Cartesian \f$ x\f$-coordinate.
|
||||||
*/
|
*/
|
||||||
bool operator()(const Kernel::Point_2&p,
|
bool operator()(const Kernel::Point_2&p,
|
||||||
const Kernel::Point_2&q);
|
const Kernel::Point_2&q);
|
||||||
|
|
@ -7643,7 +7643,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns true iff `p` and `q` have the same Cartesian \f$ x\f$-coordinate.
|
returns true iff `p` and `q` have the same %Cartesian \f$ x\f$-coordinate.
|
||||||
*/
|
*/
|
||||||
bool operator()(const Kernel::Point_3&p,
|
bool operator()(const Kernel::Point_3&p,
|
||||||
const Kernel::Point_3&q);
|
const Kernel::Point_3&q);
|
||||||
|
|
@ -7669,7 +7669,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns true iff `p` and `q` have the same Cartesian \f$ y\f$-coordinate.
|
returns true iff `p` and `q` have the same %Cartesian \f$ y\f$-coordinate.
|
||||||
*/
|
*/
|
||||||
bool operator()(const Kernel::Point_2&p,
|
bool operator()(const Kernel::Point_2&p,
|
||||||
const Kernel::Point_2&q);
|
const Kernel::Point_2&q);
|
||||||
|
|
@ -7695,7 +7695,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns true iff `p` and `q` have the same Cartesian \f$ y\f$-coordinate.
|
returns true iff `p` and `q` have the same %Cartesian \f$ y\f$-coordinate.
|
||||||
*/
|
*/
|
||||||
bool operator()(const Kernel::Point_3&p,
|
bool operator()(const Kernel::Point_3&p,
|
||||||
const Kernel::Point_3&q);
|
const Kernel::Point_3&q);
|
||||||
|
|
@ -7721,7 +7721,7 @@ public:
|
||||||
/// @{
|
/// @{
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
returns true iff `p` and `q` have the same Cartesian \f$ z\f$-coordinate.
|
returns true iff `p` and `q` have the same %Cartesian \f$ z\f$-coordinate.
|
||||||
*/
|
*/
|
||||||
bool operator()(const Kernel::Point_3&p,
|
bool operator()(const Kernel::Point_3&p,
|
||||||
const Kernel::Point_3&q);
|
const Kernel::Point_3&q);
|
||||||
|
|
|
||||||
|
|
@ -79,9 +79,9 @@ Point_d(ForwardIterator first, ForwardIterator end);
|
||||||
\pre `i` is non-negative and less than the dimension. */
|
\pre `i` is non-negative and less than the dimension. */
|
||||||
double operator[](int i)const;
|
double operator[](int i)const;
|
||||||
|
|
||||||
/*! returns an iterator pointing to the zeroth Cartesian coordinate. */
|
/*! returns an iterator pointing to the zeroth %Cartesian coordinate. */
|
||||||
Cartesian_const_iterator_d cartesian_begin()const;
|
Cartesian_const_iterator_d cartesian_begin()const;
|
||||||
/*! returns an iterator pointing beyond the last Cartesian coordinate. */
|
/*! returns an iterator pointing beyond the last %Cartesian coordinate. */
|
||||||
Cartesian_const_iterator_d cartesian_end()const;
|
Cartesian_const_iterator_d cartesian_end()const;
|
||||||
};
|
};
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -3,7 +3,7 @@
|
||||||
\ingroup PkgKernelDKernelConcept
|
\ingroup PkgKernelDKernelConcept
|
||||||
\cgalConcept
|
\cgalConcept
|
||||||
|
|
||||||
A type representing an iterator to the Cartesian coordinates of a point
|
A type representing an iterator to the %Cartesian coordinates of a point
|
||||||
in `d` dimensions.
|
in `d` dimensions.
|
||||||
|
|
||||||
\cgalRefines{CopyConstructible,Assignable,DefaultConstructible}
|
\cgalRefines{CopyConstructible,Assignable,DefaultConstructible}
|
||||||
|
|
@ -18,4 +18,3 @@ class Kernel_d::CartesianConstIterator_d {
|
||||||
public:
|
public:
|
||||||
|
|
||||||
}; /* end Kernel_d::CartesianConstIterator_d */
|
}; /* end Kernel_d::CartesianConstIterator_d */
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -8,7 +8,7 @@ geometry\cgalFootnote{It is called extended geometry for simplicity,
|
||||||
though it is not a real geometry in the classical sense}. Let `K` be
|
though it is not a real geometry in the classical sense}. Let `K` be
|
||||||
an instance of the data type `ExtendedKernelTraits_2`. The central
|
an instance of the data type `ExtendedKernelTraits_2`. The central
|
||||||
notion of extended geometry are extended points. An extended point
|
notion of extended geometry are extended points. An extended point
|
||||||
represents either a standard affine point of the Cartesian plane or a
|
represents either a standard affine point of the %Cartesian plane or a
|
||||||
non-standard point representing the equivalence class of rays where
|
non-standard point representing the equivalence class of rays where
|
||||||
two rays are equivalent if one is contained in the other.
|
two rays are equivalent if one is contained in the other.
|
||||||
|
|
||||||
|
|
@ -353,4 +353,3 @@ const char* output_identifier() ;
|
||||||
/// @}
|
/// @}
|
||||||
|
|
||||||
}; /* end ExtendedKernelTraits_2 */
|
}; /* end ExtendedKernelTraits_2 */
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -448,7 +448,7 @@ We recommend the use of the \cgal kernels `Homogeneous`,
|
||||||
The homogeneous kernel provides reliable fast performance. In combination with
|
The homogeneous kernel provides reliable fast performance. In combination with
|
||||||
`leda_integer` it is the fastest kernel for `Nef_polyhedron_3`. The
|
`leda_integer` it is the fastest kernel for `Nef_polyhedron_3`. The
|
||||||
`Exact_predicates_exact_constructions_kernel` uses filtering. In non-degenerate
|
`Exact_predicates_exact_constructions_kernel` uses filtering. In non-degenerate
|
||||||
scenarios it's faster than the Homogeneous kernel. The most
|
scenarios it's faster than the homogeneous kernel. The most
|
||||||
important advantage of the filtered kernel is that it is a %Cartesian
|
important advantage of the filtered kernel is that it is a %Cartesian
|
||||||
kernel, which allows the proper handling of OFF files using
|
kernel, which allows the proper handling of OFF files using
|
||||||
floating-point coordinates.
|
floating-point coordinates.
|
||||||
|
|
|
||||||
|
|
@ -120,7 +120,7 @@ To use these classes, \gmp and \mpfr must be installed.
|
||||||
\anchor ledant
|
\anchor ledant
|
||||||
|
|
||||||
\leda provides number types that can be used for exact computation
|
\leda provides number types that can be used for exact computation
|
||||||
with both Cartesian and homogeneous representations. If you are using
|
with both %Cartesian and homogeneous representations. If you are using
|
||||||
homogeneous representation with the built-in integer types
|
homogeneous representation with the built-in integer types
|
||||||
`short`, `int`, and `long` as ring type, exactness of
|
`short`, `int`, and `long` as ring type, exactness of
|
||||||
computations can be guaranteed only if your input data come from a
|
computations can be guaranteed only if your input data come from a
|
||||||
|
|
@ -130,7 +130,7 @@ integers of arbitrary length. (Of course the length is
|
||||||
somehow bounded by the resources of your computer.) It can be used as
|
somehow bounded by the resources of your computer.) It can be used as
|
||||||
ring type in homogeneous kernels and leads to exact
|
ring type in homogeneous kernels and leads to exact
|
||||||
computation as long as all intermediate results are rational. For the
|
computation as long as all intermediate results are rational. For the
|
||||||
same kind of problems, Cartesian representation with number type
|
same kind of problems, %Cartesian representation with number type
|
||||||
`leda_rational` leads to exact computation as well.
|
`leda_rational` leads to exact computation as well.
|
||||||
The number type `leda_bigfloat` in \leda is a variable precision
|
The number type `leda_bigfloat` in \leda is a variable precision
|
||||||
floating-point type. Rounding mode and precision (i.e.\ mantissa length) of
|
floating-point type. Rounding mode and precision (i.e.\ mantissa length) of
|
||||||
|
|
|
||||||
|
|
@ -19,7 +19,7 @@ public:
|
||||||
/*! 3D point type
|
/*! 3D point type
|
||||||
* It must be default constructible, and can be constructed from 3 objects of type `FT`.
|
* It must be default constructible, and can be constructed from 3 objects of type `FT`.
|
||||||
* `bool operator<(Point_3, Point_3)` to lexicographically compare two points must be available.
|
* `bool operator<(Point_3, Point_3)` to lexicographically compare two points must be available.
|
||||||
* Access to Cartesian coordinates must be possible using `Point_3::x()`, `Point_3::y(), Point_3::z()` and
|
* Access to %Cartesian coordinates must be possible using `Point_3::x()`, `Point_3::y(), Point_3::z()` and
|
||||||
* `FT operator[](int i)` with `0 <= i < 3`.
|
* `FT operator[](int i)` with `0 <= i < 3`.
|
||||||
*
|
*
|
||||||
* There must be a specialization of `CGAL::Kernel_traits` such that
|
* There must be a specialization of `CGAL::Kernel_traits` such that
|
||||||
|
|
|
||||||
|
|
@ -4,7 +4,7 @@
|
||||||
\cgalConcept
|
\cgalConcept
|
||||||
|
|
||||||
This `AdaptableFunctor` returns whether a
|
This `AdaptableFunctor` returns whether a
|
||||||
`PolynomialTraits_d::Polynomial_d` \f$ p\f$ is zero at a given Cartesian point,
|
`PolynomialTraits_d::Polynomial_d` \f$ p\f$ is zero at a given %Cartesian point,
|
||||||
which is represented as an iterator range.
|
which is represented as an iterator range.
|
||||||
|
|
||||||
\cgalRefines{AdaptableFunctor,CopyConstructible,DefaultConstructible}
|
\cgalRefines{AdaptableFunctor,CopyConstructible,DefaultConstructible}
|
||||||
|
|
@ -32,7 +32,7 @@ typedef bool result_type;
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
|
|
||||||
Computes whether \f$ p\f$ is zero at the Cartesian point given by the iterator range,
|
Computes whether \f$ p\f$ is zero at the %Cartesian point given by the iterator range,
|
||||||
where `begin` is referring to the innermost variable.
|
where `begin` is referring to the innermost variable.
|
||||||
|
|
||||||
\pre (end-begin == `PolynomialTraits_d::d`)
|
\pre (end-begin == `PolynomialTraits_d::d`)
|
||||||
|
|
@ -47,4 +47,3 @@ InputIterator end );
|
||||||
/// @}
|
/// @}
|
||||||
|
|
||||||
}; /* end PolynomialTraits_d::IsZeroAt */
|
}; /* end PolynomialTraits_d::IsZeroAt */
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -4,7 +4,7 @@
|
||||||
\cgalConcept
|
\cgalConcept
|
||||||
|
|
||||||
This `AdaptableFunctor` returns the sign of a
|
This `AdaptableFunctor` returns the sign of a
|
||||||
`PolynomialTraits_d::Polynomial_d` \f$ p\f$ at given Cartesian point represented
|
`PolynomialTraits_d::Polynomial_d` \f$ p\f$ at given %Cartesian point represented
|
||||||
as an iterator range.
|
as an iterator range.
|
||||||
|
|
||||||
This functor is well defined if `PolynomialTraits_d::Innermost_coefficient_type` is
|
This functor is well defined if `PolynomialTraits_d::Innermost_coefficient_type` is
|
||||||
|
|
@ -35,7 +35,7 @@ typedef CGAL::Sign result_type;
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
|
|
||||||
Returns the sign of \f$ p\f$ at the given Cartesian point, where `begin` is referring
|
Returns the sign of \f$ p\f$ at the given %Cartesian point, where `begin` is referring
|
||||||
to the innermost variable.
|
to the innermost variable.
|
||||||
\pre (`end-begin` == `PolynomialTraits_d::d`)
|
\pre (`end-begin` == `PolynomialTraits_d::d`)
|
||||||
\pre `std::iterator_traits< InputIterator >::%value_type` is `ExplicitInteroperable` with `PolynomialTraits_d::Innermost_coefficient_type`.
|
\pre `std::iterator_traits< InputIterator >::%value_type` is `ExplicitInteroperable` with `PolynomialTraits_d::Innermost_coefficient_type`.
|
||||||
|
|
@ -49,4 +49,3 @@ InputIterator end );
|
||||||
/// @}
|
/// @}
|
||||||
|
|
||||||
}; /* end PolynomialTraits_d::SignAt */
|
}; /* end PolynomialTraits_d::SignAt */
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -39,7 +39,7 @@ public:
|
||||||
/// The 2D vector type, only required if you want to detect tori
|
/// The 2D vector type, only required if you want to detect tori
|
||||||
typedef unspecified_type Vector_2;
|
typedef unspecified_type Vector_2;
|
||||||
|
|
||||||
/// The number type of the Cartesian coordinates of types Point_3
|
/// The number type of the %Cartesian coordinates of types Point_3
|
||||||
typedef unspecified_type FT;
|
typedef unspecified_type FT;
|
||||||
|
|
||||||
/// A model of the concept `Range` with random access iterators, providing input points and normals
|
/// A model of the concept `Range` with random access iterators, providing input points and normals
|
||||||
|
|
@ -63,9 +63,9 @@ public:
|
||||||
/*!
|
/*!
|
||||||
* Function object type that provides
|
* Function object type that provides
|
||||||
* `Point_3 operator()(Origin p)`
|
* `Point_3 operator()(Origin p)`
|
||||||
* returning the point with 0, 0, 0 as Cartesian coordinates
|
* returning the point with 0, 0, 0 as %Cartesian coordinates
|
||||||
* and `Point_3 operator()(FT x, FT y, FT z)`
|
* and `Point_3 operator()(FT x, FT y, FT z)`
|
||||||
* returning the point with `x`, `y` and `z` as Cartesian coordinates.
|
* returning the point with `x`, `y` and `z` as %Cartesian coordinates.
|
||||||
*/
|
*/
|
||||||
typedef unspecified_type Construct_point_3;
|
typedef unspecified_type Construct_point_3;
|
||||||
|
|
||||||
|
|
@ -106,7 +106,7 @@ public:
|
||||||
/*!
|
/*!
|
||||||
* Function object type that provides
|
* Function object type that provides
|
||||||
* `Point_2 operator()(FT x, FT y)`
|
* `Point_2 operator()(FT x, FT y)`
|
||||||
* returning the 2D point with `x` and `y` as Cartesian coordinates.
|
* returning the 2D point with `x` and `y` as %Cartesian coordinates.
|
||||||
* Only required if you want to detect tori.
|
* Only required if you want to detect tori.
|
||||||
*/
|
*/
|
||||||
typedef unspecified_type Construct_point_2;
|
typedef unspecified_type Construct_point_2;
|
||||||
|
|
|
||||||
|
|
@ -76,7 +76,7 @@ less than \f$ r\f$.
|
||||||
bool contains(const Point_d& p) const;
|
bool contains(const Point_d& p) const;
|
||||||
|
|
||||||
/*!
|
/*!
|
||||||
Test whether the fuzzy sphere contains the point whose Cartesian coordinates
|
Test whether the fuzzy sphere contains the point whose %Cartesian coordinates
|
||||||
are contained in the range [`begin`, `end`).
|
are contained in the range [`begin`, `end`).
|
||||||
*/
|
*/
|
||||||
template <typename Coord_iterator>
|
template <typename Coord_iterator>
|
||||||
|
|
|
||||||
|
|
@ -43,7 +43,7 @@ bool contains(Point_d p) const;
|
||||||
/*!
|
/*!
|
||||||
\note Optional: must be defined when used with a `Kd_tree` where `EnablePointsCache` is set to `Tag_true`.
|
\note Optional: must be defined when used with a `Kd_tree` where `EnablePointsCache` is set to `Tag_true`.
|
||||||
|
|
||||||
tests whether the query item contains the point whose Cartesian coordinates
|
tests whether the query item contains the point whose %Cartesian coordinates
|
||||||
are contained in the range [`begin`, `end`).
|
are contained in the range [`begin`, `end`).
|
||||||
*/
|
*/
|
||||||
template <typename Coord_iterator>
|
template <typename Coord_iterator>
|
||||||
|
|
|
||||||
|
|
@ -69,7 +69,7 @@ as a sequence of four byte. The format depends on the machine.
|
||||||
The mode `PRETTY`
|
The mode `PRETTY`
|
||||||
serves mainly for debugging as the type of the geometric
|
serves mainly for debugging as the type of the geometric
|
||||||
object is written, as well as the data defining the object. For example
|
object is written, as well as the data defining the object. For example
|
||||||
for a point at the origin with Cartesian double coordinates, the output
|
for a point at the origin with %Cartesian double coordinates, the output
|
||||||
would be `PointC2(0.0, 0.0)`. At the moment \cgal does not
|
would be `PointC2(0.0, 0.0)`. At the moment \cgal does not
|
||||||
provide input operations for pretty printed data. By default a stream
|
provide input operations for pretty printed data. By default a stream
|
||||||
is in \ascii mode.
|
is in \ascii mode.
|
||||||
|
|
@ -519,4 +519,3 @@ which might look as follows:
|
||||||
|
|
||||||
*/
|
*/
|
||||||
} /* namespace CGAL */
|
} /* namespace CGAL */
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -9,7 +9,7 @@ class RawPoint_3
|
||||||
public:
|
public:
|
||||||
/// \name Creation
|
/// \name Creation
|
||||||
/// @{
|
/// @{
|
||||||
/// constructor from Cartesian coordinates
|
/// constructor from %Cartesian coordinates
|
||||||
RawPoint_3(double x, double y, double z);
|
RawPoint_3(double x, double y, double z);
|
||||||
/// @}
|
/// @}
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -28,7 +28,7 @@ typedef unspecified_type FT;
|
||||||
/*!
|
/*!
|
||||||
* Function object type that provides
|
* Function object type that provides
|
||||||
* `Point_3 operator()(FT x, FT y, FT z) const`
|
* `Point_3 operator()(FT x, FT y, FT z) const`
|
||||||
* returning the point with `x`, `y` and `z` as Cartesian coordinates.
|
* returning the point with `x`, `y` and `z` as %Cartesian coordinates.
|
||||||
*/
|
*/
|
||||||
typedef unspecified_type Construct_point_3;
|
typedef unspecified_type Construct_point_3;
|
||||||
|
|
||||||
|
|
@ -186,4 +186,3 @@ compute_z_3_object();
|
||||||
/// @}
|
/// @}
|
||||||
|
|
||||||
}; /* end DelaunayTriangulationTraits_2 */
|
}; /* end DelaunayTriangulationTraits_2 */
|
||||||
|
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue