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Andreas Fabri 2012-09-21 08:12:58 +00:00
parent 5d659a6c71
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2 changed files with 12 additions and 12 deletions
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4
Kernel_d/doc/Kernel_d/Concepts/Kernel_d.h
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@ -18,8 +18,8 @@ predicates. The former replace constructors of the kernel classes and
constructive procedures in the kernel. There are also function objects constructive procedures in the kernel. There are also function objects
replacing operators, especially for equality testing. replacing operators, especially for equality testing.
\hasModel `Cartesian_d<FieldNumberType>` \hasModel `CGAL::Cartesian_d<FieldNumberType>`
\hasModel `Homogeneous_d<RingNumberType>` \hasModel `CGAL::Homogeneous_d<RingNumberType>`
*/ */
class Kernel_d { class Kernel_d {
public: public:

20
Kernel_d/doc/Kernel_d/Kernel_d.txt
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@ -1,7 +1,7 @@
namespace CGAL { namespace CGAL {
/*! /*!
\mainpage dD Geometry Kernel \mainpage dD Geometry %Kernel
\anchor Chapter_dD_Geometry_Kernel \anchor Chapter_dD_Geometry_Kernel
\autotoc \autotoc
\authors Michael Seel \authors Michael Seel
@ -69,7 +69,7 @@ This extends the syntax of random access iterators to input iterators.
If we index the tuple as above then we require that If we index the tuple as above then we require that
\f$ ++^{(d+1)}\mathit{first} = \mathit{last}\f$. \f$ ++^{(d+1)}\mathit{first} = \mathit{last}\f$.
# Kernel Representations # # %Kernel Representations #
Our object of study is the \f$ d\f$-dimensional affine Euclidean space, Our object of study is the \f$ d\f$-dimensional affine Euclidean space,
where \f$ d\f$ is a parameter of our geometry. Objects in that space are where \f$ d\f$ is a parameter of our geometry. Objects in that space are
@ -94,7 +94,7 @@ For a point with Cartesian coordinates
\f$ (c_0,c_1,\ldots,c_{d-1})\f$ a \f$ (c_0,c_1,\ldots,c_{d-1})\f$ a
possible homogeneous representation is possible homogeneous representation is
\f$ (c_0,c_1,\ldots,c_{d-1},1)\f$. \f$ (c_0,c_1,\ldots,c_{d-1},1)\f$.
Homogeneous coordinates in fact allow to represent %Homogeneous coordinates in fact allow to represent
objects in a more general space, the projective space \f$ \mathbb{P}^d\f$. objects in a more general space, the projective space \f$ \mathbb{P}^d\f$.
In \cgal, we do not compute in projective geometry. Rather, we use In \cgal, we do not compute in projective geometry. Rather, we use
homogeneous coordinates to avoid division operations, homogeneous coordinates to avoid division operations,
@ -150,7 +150,7 @@ must be available as well. It must work for exact (i.e., no
remainder) integer divisions only. Furthermore, both number types remainder) integer divisions only. Furthermore, both number types
should fulfill \cgal's requirements on a number type. should fulfill \cgal's requirements on a number type.
## Cartesian Kernel ## ## %Cartesian %Kernel ##
With `Cartesian_d<FieldNumberType,LinearAlgebra>` you can choose With `Cartesian_d<FieldNumberType,LinearAlgebra>` you can choose
Cartesian representation of coordinates. The type Cartesian representation of coordinates. The type
@ -170,7 +170,7 @@ and `Cartesian<FieldNumberType>::RT` are mapped to number type
type `LinearAlgebra`. `Cartesian<FieldNumberType>` uses type `LinearAlgebra`. `Cartesian<FieldNumberType>` uses
reference counting internally to save copying costs. reference counting internally to save copying costs.
## Homogeneous Kernel ## ## %Homogeneous %Kernel ##
As we mentioned before, homogeneous coordinates permit to avoid As we mentioned before, homogeneous coordinates permit to avoid
division operations in numerical computations, since the additional division operations in numerical computations, since the additional
@ -222,7 +222,7 @@ parameterized with a number type, such as
`Cartesian_d<double>` or `Homogeneous_d<leda_integer>`. `Cartesian_d<double>` or `Homogeneous_d<leda_integer>`.
</OL> </OL>
## Kernel as a Traits Class ## ## %Kernel as a Traits Class ##
Algorithms and data structures in the basic library of \cgal are Algorithms and data structures in the basic library of \cgal are
parameterized by a traits class that subsumes the objects on which the parameterized by a traits class that subsumes the objects on which the
@ -235,7 +235,7 @@ algorithm. In some other cases, the algorithms or data structures
needs more than is provided by a kernel. In these cases, a kernel can needs more than is provided by a kernel. In these cases, a kernel can
not be used as a traits class. not be used as a traits class.
## Choosing a Kernel ## ## Choosing a %Kernel ##
If you start with integral Cartesian coordinates, If you start with integral Cartesian coordinates,
many geometric computations will involve integral numerical values many geometric computations will involve integral numerical values
@ -274,7 +274,7 @@ geometric objects of the kernel that you would like to use with the
representation class, i.e., `CGAL/Cartesian_d.h` or representation class, i.e., `CGAL/Cartesian_d.h` or
`CGAL/Homogeneous_d.h` `CGAL/Homogeneous_d.h`
# Kernel Geometry # # %Kernel Geometry #
## Points and Vectors ## ## Points and Vectors ##
@ -317,7 +317,7 @@ Note that these constructions do not involve any performance overhead
for the conversion with the currently available representation for the conversion with the currently available representation
classes. classes.
## Kernel Objects ## ## %Kernel Objects ##
Besides points (`Point_d<R>`), vectors (`Vector_d<R>`), and Besides points (`Point_d<R>`), vectors (`Vector_d<R>`), and
directions (`Direction_d<R>`), \cgal provides lines, rays, directions (`Direction_d<R>`), \cgal provides lines, rays,
@ -384,7 +384,7 @@ objects (also called functors and provided by a kernel class).
\cgal provides predicates for the orientation of \cgal provides predicates for the orientation of
point sets (`orientation`), for comparing points according to some point sets (`orientation`), for comparing points according to some
given order, especially for comparing Cartesian coordinates given order, especially for comparing %Cartesian coordinates
(e.g. `lexicographically_xy_smaller`), in-sphere tests, and (e.g. `lexicographically_xy_smaller`), in-sphere tests, and
predicates to compare distances. predicates to compare distances.