diff --git a/Kernel_d/doc/Kernel_d/Concepts/Kernel_d.h b/Kernel_d/doc/Kernel_d/Concepts/Kernel_d.h index 974753909b1..76086be5b9d 100644 --- a/Kernel_d/doc/Kernel_d/Concepts/Kernel_d.h +++ b/Kernel_d/doc/Kernel_d/Concepts/Kernel_d.h @@ -18,8 +18,8 @@ predicates. The former replace constructors of the kernel classes and constructive procedures in the kernel. There are also function objects replacing operators, especially for equality testing. -\hasModel `Cartesian_d` -\hasModel `Homogeneous_d` +\hasModel `CGAL::Cartesian_d` +\hasModel `CGAL::Homogeneous_d` */ class Kernel_d { public: diff --git a/Kernel_d/doc/Kernel_d/Kernel_d.txt b/Kernel_d/doc/Kernel_d/Kernel_d.txt index 535f816f5db..709e9a83810 100644 --- a/Kernel_d/doc/Kernel_d/Kernel_d.txt +++ b/Kernel_d/doc/Kernel_d/Kernel_d.txt @@ -1,7 +1,7 @@ namespace CGAL { /*! -\mainpage dD Geometry Kernel +\mainpage dD Geometry %Kernel \anchor Chapter_dD_Geometry_Kernel \autotoc \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 \f$ ++^{(d+1)}\mathit{first} = \mathit{last}\f$. -# Kernel Representations # +# %Kernel Representations # Our object of study is the \f$ d\f$-dimensional affine Euclidean space, where \f$ 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 possible homogeneous representation is \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$. In \cgal, we do not compute in projective geometry. Rather, we use 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 should fulfill \cgal's requirements on a number type. -## Cartesian Kernel ## +## %Cartesian %Kernel ## With `Cartesian_d` you can choose Cartesian representation of coordinates. The type @@ -170,7 +170,7 @@ and `Cartesian::RT` are mapped to number type type `LinearAlgebra`. `Cartesian` uses reference counting internally to save copying costs. -## Homogeneous Kernel ## +## %Homogeneous %Kernel ## As we mentioned before, homogeneous coordinates permit to avoid division operations in numerical computations, since the additional @@ -222,7 +222,7 @@ parameterized with a number type, such as `Cartesian_d` or `Homogeneous_d`. -## Kernel as a Traits Class ## +## %Kernel as a Traits Class ## Algorithms and data structures in the basic library of \cgal are 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 not be used as a traits class. -## Choosing a Kernel ## +## Choosing a %Kernel ## If you start with integral Cartesian coordinates, 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 `CGAL/Homogeneous_d.h` -# Kernel Geometry # +# %Kernel Geometry # ## 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 classes. -## Kernel Objects ## +## %Kernel Objects ## Besides points (`Point_d`), vectors (`Vector_d`), and directions (`Direction_d`), \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 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 predicates to compare distances.