diff --git a/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_2.h b/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_2.h index d10c2d4a67d..c901b137ef8 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_2.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_2.h @@ -94,14 +94,14 @@ introduces an identity transformation. Aff_transformation_2(const Identity_transformation& ); /*! -introduces a translation by a vector \f$ v\f$. +introduces a translation by a vector `v`. */ Aff_transformation_2(const Translation, const Vector_2 &v); /*! approximates the rotation over the angle indicated by direction -\f$ d\f$, such that the differences between the sines and cosines +`d`, such that the differences between the sines and cosines of the rotation given by d and the approximating rotation are at most \f$ num/den\f$ each. \pre \f$ num/den>0\f$ and \f$ d != 0\f$. diff --git a/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_3.h b/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_3.h index 004512dd39e..27a3b88965d 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Aff_transformation_3.h @@ -50,7 +50,7 @@ introduces an identity transformation. Aff_transformation_3(const Identity_transformation& ); /*! -introduces a translation by a vector \f$ v\f$. +introduces a translation by a vector `v`. */ Aff_transformation_3(const Translation, const Vector_3 &v); diff --git a/Kernel_23/doc/Kernel_23/CGAL/Direction_2.h b/Kernel_23/doc/Kernel_23/CGAL/Direction_2.h index bd9ee8c53ea..ba4202b6fb6 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Direction_2.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Direction_2.h @@ -25,22 +25,22 @@ public: /// @{ /*! -introduces the direction `d` of vector \f$ v\f$. +introduces the direction `d` of vector `v`. */ Direction_2(const Vector_2 &v); /*! -introduces the direction `d` of line \f$ l\f$. +introduces the direction `d` of line `l`. */ Direction_2(const Line_2 &l); /*! -introduces the direction `d` of ray \f$ r\f$. +introduces the direction `d` of ray `r`. */ Direction_2(const Ray_2 &r); /*! -introduces the direction `d` of segment \f$ s\f$. +introduces the direction `d` of segment `s`. */ Direction_2(const Segment_2 &s); @@ -131,7 +131,7 @@ returns a vector that has the same direction as `d`. Vector_2 vector() const; /*! -returns the direction obtained by applying \f$ t\f$ on `d`. +returns the direction obtained by applying `t` on `d`. */ Direction_2 transform(const Aff_transformation_2 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Direction_3.h b/Kernel_23/doc/Kernel_23/CGAL/Direction_3.h index 901d911d9aa..385d72e9a85 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Direction_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Direction_3.h @@ -25,22 +25,22 @@ public: /*! introduces a direction `d` initialized with the -direction of vector \f$ v\f$. +direction of vector `v`. */ Direction_3(const Vector_3 &v); /*! -introduces the direction `d` of line \f$ l\f$. +introduces the direction `d` of line `l`. */ Direction_3(const Line_3 &l); /*! -introduces the direction `d` of ray \f$ r\f$. +introduces the direction `d` of ray `r`. */ Direction_3(const Ray_3 &r); /*! -introduces the direction `d` of segment \f$ s\f$. +introduces the direction `d` of segment `s`. */ Direction_3(const Segment_3 &s); @@ -97,7 +97,7 @@ returns a vector that has the same direction as `d`. Vector_3 vector() const; /*! -returns the direction obtained by applying \f$ t\f$ on `d`. +returns the direction obtained by applying `t` on `d`. */ Direction_3 transform(const Aff_transformation_3 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Iso_cuboid_3.h b/Kernel_23/doc/Kernel_23/CGAL/Iso_cuboid_3.h index 1e4b8664eb7..ecfa3d11d99 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Iso_cuboid_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Iso_cuboid_3.h @@ -28,7 +28,7 @@ public: /*! introduces an iso-oriented cuboid `c` with diagonal -opposite vertices \f$ p\f$ and \f$ q\f$. Note that the object is +opposite vertices `p` and `q`. Note that the object is brought in the canonical form. */ Iso_cuboid_3(const Point_3 &p, @@ -36,7 +36,7 @@ const Point_3 &q); /*! introduces an iso-oriented cuboid `c` with diagonal -opposite vertices \f$ p\f$ and \f$ q\f$. The `int` argument value +opposite vertices `p` and `q`. The `int` argument value is only used to distinguish the two overloaded functions. \pre \f$ p.x()<=q.x()\f$, \f$ p.y()<=q.y()\f$ and \f$ p.z()<=q.z()\f$. */ @@ -146,14 +146,14 @@ returns largest %Cartesian Kernel::FT zmax() const; /*! -returns \f$ i\f$-th %Cartesian coordinate of +returns `i`-th %Cartesian coordinate of the smallest vertex of `c`. \pre \f$ 0 \leq i \leq2\f$. */ Kernel::FT min_coord(int i) const; /*! -returns \f$ i\f$-th %Cartesian coordinate of +returns `i`-th %Cartesian coordinate of the largest vertex of `c`. \pre \f$ 0 \leq i \leq2\f$. */ @@ -174,7 +174,7 @@ bool is_degenerate() const; returns either \ref ON_UNBOUNDED_SIDE, \ref ON_BOUNDED_SIDE, or the constant \ref ON_BOUNDARY, -depending on where point \f$ p\f$ is. +depending on where point `p` is. */ Bounded_side bounded_side(const Point_3 &p) const; @@ -209,7 +209,7 @@ returns a bounding box containing `c`. Bbox_3 bbox() const; /*! -returns the iso-oriented cuboid obtained by applying \f$ t\f$ on +returns the iso-oriented cuboid obtained by applying `t` on the smallest and the largest of `c`. \pre The angle at a rotation must be a multiple of \f$ \pi/2\f$, otherwise the resulting cuboid does not have the same size. Note that rotating about an arbitrary angle can even result in a degenerate iso-oriented cuboid. */ diff --git a/Kernel_23/doc/Kernel_23/CGAL/Iso_rectangle_2.h b/Kernel_23/doc/Kernel_23/CGAL/Iso_rectangle_2.h index 38ea05c0fba..87039ef40ef 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Iso_rectangle_2.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Iso_rectangle_2.h @@ -29,7 +29,7 @@ public: /*! introduces an iso-oriented rectangle `r` with diagonal -opposite vertices \f$ p\f$ and \f$ q\f$. Note that the object is +opposite vertices `p` and `q`. Note that the object is brought in the canonical form. */ Iso_rectangle_2(const Point_2 &p, @@ -37,7 +37,7 @@ const Point_2 &q); /*! introduces an iso-oriented rectangle `r` with diagonal -opposite vertices \f$ p\f$ and \f$ q\f$. The `int` argument value +opposite vertices `p` and `q`. The `int` argument value is only used to distinguish the two overloaded functions. \pre \f$ p.x()<=q.x()\f$ and \f$ p.y()<=q.y()\f$. */ @@ -125,14 +125,14 @@ returns the \f$ y\f$ coordinate of upper right vertex of `r`. Kernel::FT ymax() const; /*! -returns the \f$ i\f$'th %Cartesian coordinate of the +returns the `i`'th %Cartesian coordinate of the lower left vertex of `r`. \pre \f$ 0 \leq i \leq1\f$. */ Kernel::FT min_coord(int i) const; /*! -returns the \f$ i\f$'th %Cartesian coordinate of the +returns the `i`'th %Cartesian coordinate of the upper right vertex of `r`. \pre \f$ 0 \leq i \leq1\f$. */ @@ -153,7 +153,7 @@ bool is_degenerate() const; returns either \ref ON_UNBOUNDED_SIDE, \ref ON_BOUNDED_SIDE, or the constant \ref ON_BOUNDARY, -depending on where point \f$ p\f$ is. +depending on where point `p` is. */ Bounded_side bounded_side(const Point_2 &p) const; @@ -188,7 +188,7 @@ returns a bounding box containing `r`. Bbox bbox() const; /*! -returns the iso-oriented rectangle obtained by applying \f$ t\f$ on +returns the iso-oriented rectangle obtained by applying `t` on the lower left and the upper right corner of `r`. \pre The angle at a rotation must be a multiple of \f$ \pi/2\f$, otherwise the resulting rectangle does not have the same side length. Note that rotating about an arbitrary angle can even result in a degenerate iso-oriented rectangle. */ diff --git a/Kernel_23/doc/Kernel_23/CGAL/Kernel_traits.h b/Kernel_23/doc/Kernel_23/CGAL/Kernel_traits.h index d4d8b04c276..5072e007f8e 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Kernel_traits.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Kernel_traits.h @@ -12,11 +12,11 @@ If this type does not exist, a specialization of `Kernel_traits` can be used to provide the desired information. This class is, for example, useful in the following context. Assume -you want to write a generic function that accepts two points \f$ p\f$ and -\f$ q\f$ as argument and constructs the line segment between \f$ p\f$ and \f$ q\f$. +you want to write a generic function that accepts two points `p` and +`q` as argument and constructs the line segment between `p` and `q`. In order to specify the return type of this function, you need to know what is the segment type corresponding to the Point type representing -\f$ p\f$ and \f$ q\f$. Using `Kernel_traits`, this can be done as follows. +`p` and `q`. Using `Kernel_traits`, this can be done as follows. \code template < class Point > diff --git a/Kernel_23/doc/Kernel_23/CGAL/Line_2.h b/Kernel_23/doc/Kernel_23/CGAL/Line_2.h index 4ea8ddfce91..7786f366ba7 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Line_2.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Line_2.h @@ -10,7 +10,7 @@ that satisfy the equation \f[ l:\; a\, x +b\, y +c = 0. \f] The line splits \f$ \E^2\f$ in a positive and a negative -side. A point \f$ p\f$ with %Cartesian coordinates +side. A point `p` with %Cartesian coordinates \f$ (px, py)\f$ is on the positive side of `l`, iff \f$ a\, px + b\, py +c > 0\f$, it is on the negative side of `l`, iff @@ -28,7 +28,7 @@ the suffix `_2` and the representation type `Cartesian`. Point_2< Cartesian > p(1.0,1.0), q(4.0,7.0); \endcode -To define a line \f$ l\f$ we write: +To define a line `l` we write: \code Line_2< Cartesian > l(p,q); @@ -51,31 +51,31 @@ coordinates \f$ ax +by +c = 0\f$. Line_2(const Kernel::RT &a, const Kernel::RT &b, const Kernel::RT &c); /*! -introduces a line `l` passing through the points \f$ p\f$ and \f$ q\f$. -Line `l` is directed from \f$ p\f$ to \f$ q\f$. +introduces a line `l` passing through the points `p` and `q`. +Line `l` is directed from `p` to `q`. */ Line_2(const Point_2 &p, const Point_2 &q); /*! -introduces a line `l` passing through point \f$ p\f$ with -direction \f$ d\f$. +introduces a line `l` passing through point `p` with +direction `d`. */ Line_2(const Point_2 &p, const Direction_2&d); /*! -introduces a line `l` passing through point \f$ p\f$ and -oriented by \f$ v\f$. +introduces a line `l` passing through point `p` and +oriented by `v`. */ Line_2(const Point_2 &p, const Vector_2&v); /*! -introduces a line `l` supporting the segment \f$ s\f$, +introduces a line `l` supporting the segment `s`, oriented from source to target. */ Line_2(const Segment_2 &s); /*! -introduces a line `l` supporting the ray \f$ r\f$, +introduces a line `l` supporting the ray `r`, with same orientation. */ Line_2(const Ray_2 &r); @@ -97,17 +97,17 @@ Test for inequality. bool operator!=(const Line_2 &h) const; /*! -returns the first coefficient of \f$ l\f$. +returns the first coefficient of `l`. */ Kernel::RT a() const; /*! -returns the second coefficient of \f$ l\f$. +returns the second coefficient of `l`. */ Kernel::RT b() const; /*! -returns the third coefficient of \f$ l\f$. +returns the third coefficient of `l`. */ Kernel::RT c() const; @@ -120,7 +120,7 @@ to `point(j)`, for all `i` \f$ <\f$ `j`. Point_2 point(int i) const; /*! -returns the orthogonal projection of \f$ p\f$ onto `l`. +returns the orthogonal projection of `p` onto `l`. */ Point_2 projection(const Point_2 &p) const; @@ -163,7 +163,7 @@ bool is_vertical() const; returns \ref ON_ORIENTED_BOUNDARY, \ref ON_NEGATIVE_SIDE, or the constant \ref ON_POSITIVE_SIDE, -depending on the position of \f$ p\f$ relative to the oriented line `l`. +depending on the position of `p` relative to the oriented line `l`. */ Oriented_side oriented_side(const Point_2 &p) const; @@ -209,14 +209,14 @@ returns the line with opposite direction. Line_2 opposite() const; /*! -returns the line perpendicular to `l` and passing through \f$ p\f$, +returns the line perpendicular to `l` and passing through `p`, where the direction is the direction of `l` rotated counterclockwise by 90 degrees. */ Line_2 perpendicular(const Point_2 &p) const; /*! -returns the line obtained by applying \f$ t\f$ on a point on `l` +returns the line obtained by applying `t` on a point on `l` and the direction of `l`. */ Line_2 transform(const Aff_transformation_2 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Line_3.h b/Kernel_23/doc/Kernel_23/CGAL/Line_3.h index 900de0d6c35..f13dc88dc7b 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Line_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Line_3.h @@ -17,31 +17,31 @@ public: /// @{ /*! -introduces a line `l` passing through the points \f$ p\f$ and \f$ q\f$. -Line `l` is directed from \f$ p\f$ to \f$ q\f$. +introduces a line `l` passing through the points `p` and `q`. +Line `l` is directed from `p` to `q`. */ Line_3(const Point_3 &p, const Point_3 &q); /*! -introduces a line `l` passing through point \f$ p\f$ with -direction \f$ d\f$. +introduces a line `l` passing through point `p` with +direction `d`. */ Line_3(const Point_3 &p, const Direction_3&d); /*! -introduces a line `l` passing through point \f$ p\f$ and -oriented by \f$ v\f$. +introduces a line `l` passing through point `p` and +oriented by `v`. */ Line_3(const Point_3 &p, const Vector_3&v); /*! -returns the line supporting the segment \f$ s\f$, +returns the line supporting the segment `s`, oriented from source to target. */ Line_3(const Segment_3 &s); /*! -returns the line supporting the ray \f$ r\f$, with the +returns the line supporting the ray `r`, with the same orientation. */ Line_3(const Ray_3 &r); @@ -63,7 +63,7 @@ Test for inequality. bool operator!=(const Line_3 &h) const; /*! -returns the orthogonal projection of \f$ p\f$ on `l`. +returns the orthogonal projection of `p` on `l`. */ Point_3 projection(const Point_3 &p) const; @@ -94,7 +94,7 @@ bool has_on(const Point_3 &p) const; /// @{ /*! -returns the plane perpendicular to `l` passing through \f$ p\f$. +returns the plane perpendicular to `l` passing through `p`. */ Plane_3 perpendicular_plane(const Point_3 &p) const; @@ -114,7 +114,7 @@ returns the direction of `l`. Direction_3 direction() const; /*! -returns the line obtained by applying \f$ t\f$ on a point on `l` +returns the line obtained by applying `t` on a point on `l` and the direction of `l`. */ Line_3 transform(const Aff_transformation_3 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Plane_3.h b/Kernel_23/doc/Kernel_23/CGAL/Plane_3.h index da27537057b..70d839dab04 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Plane_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Plane_3.h @@ -10,7 +10,7 @@ the plane equation \f[h :\; a\, x +b\, y +c\, z + d = 0.\f] The plane splits \f$ \E^3\f$ in a positive and a negative side. -A point \f$ p\f$ with %Cartesian coordinates \f$ (px, py, pz)\f$ is on the +A point `p` with %Cartesian coordinates \f$ (px, py, pz)\f$ is on the positive side of `h`, iff \f$ a\, px +b\, py +c\, pz + d > 0\f$. It is on the negative side, iff \f$ a\, px +b\, py\, +c\, pz + d < 0\f$. @@ -131,7 +131,7 @@ the negative to the positive side of `h`. Line_3 perpendicular_line(const Point_3 &p) const; /*! -returns the orthogonal projection of \f$ p\f$ on `h`. +returns the orthogonal projection of `p` on `h`. */ Point_3 projection(const Point_3 &p) const; @@ -187,7 +187,7 @@ under an affine transformation, which maps `h` onto the Point_2 to_2d(const Point_3 &p) const; /*! -returns a point \f$ q\f$, such that `to_2d( to_3d( p ))` +returns a point `q`, such that `to_2d( to_3d( p ))` is equal to `p`. */ Point_3 to_3d(const Point_2 &p) const; @@ -201,7 +201,7 @@ Point_3 to_3d(const Point_2 &p) const; returns either \ref ON_ORIENTED_BOUNDARY, or the constant \ref ON_POSITIVE_SIDE, or the constant \ref ON_NEGATIVE_SIDE, -determined by the position of \f$ p\f$ relative to the oriented plane `h`. +determined by the position of `p` relative to the oriented plane `h`. */ Oriented_side oriented_side(const Point_3 &p) const; @@ -248,7 +248,7 @@ bool is_degenerate() const; /// @{ /*! -returns the plane obtained by applying \f$ t\f$ on a point of `h` +returns the plane obtained by applying `t` on a point of `h` and the orthogonal direction of `h`. */ Plane_3 transform(const Aff_transformation_3 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Point_2.h b/Kernel_23/doc/Kernel_23/CGAL/Point_2.h index d22ff0ac6ac..567471191b8 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Point_2.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Point_2.h @@ -185,7 +185,7 @@ are not parameterized with whatsoever. Bbox_2 bbox() const; /*! -returns the point obtained by applying \f$ t\f$ on `p`. +returns the point obtained by applying `t` on `p`. */ Point_2 transform(const Aff_transformation_2 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Point_3.h b/Kernel_23/doc/Kernel_23/CGAL/Point_3.h index e455ba7a1d3..641883d57bb 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Point_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Point_3.h @@ -175,7 +175,7 @@ returns a bounding box containing `p`. Bbox_3 bbox() const; /*! -returns the point obtained by applying \f$ t\f$ on `p`. +returns the point obtained by applying `t` on `p`. */ Point_3 transform(const Aff_transformation_3 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Ray_2.h b/Kernel_23/doc/Kernel_23/CGAL/Ray_2.h index 30e5c46f8cc..cef640a7412 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Ray_2.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Ray_2.h @@ -19,25 +19,25 @@ public: /*! introduces a ray `r` -with source \f$ p\f$ and passing through point \f$ q\f$. +with source `p` and passing through point `q`. */ Ray_2(const Point_2 &p, const Point_2&q); /*! -introduces a ray `r` starting at source \f$ p\f$ with -direction \f$ d\f$. +introduces a ray `r` starting at source `p` with +direction `d`. */ Ray_2(const Point_2 &p, const Direction_2 &d); /*! -introduces a ray `r` starting at source \f$ p\f$ with -the direction of \f$ v\f$. +introduces a ray `r` starting at source `p` with +the direction of `v`. */ Ray_2(const Point_2 &p, const Vector_2 &v); /*! -introduces a ray `r` starting at source \f$ p\f$ with -the same direction as \f$ l\f$. +introduces a ray `r` starting at source `p` with +the same direction as `l`. */ Ray_2(const Point_2 &p, const Line_2 &l); @@ -117,10 +117,10 @@ of `r`, or if it is in the interior of `r`. bool has_on(const Point_2 &p) const; /*! -checks if point \f$ p\f$ is on `r`. This function is faster +checks if point `p` is on `r`. This function is faster than function `has_on()` if the precondition checking is disabled. -\pre \f$ p\f$ is on the supporting line of `r`. +\pre `p` is on the supporting line of `r`. */ bool collinear_has_on(const Point_2 &p) const; @@ -130,7 +130,7 @@ bool collinear_has_on(const Point_2 &p) const; /// @{ /*! -returns the ray obtained by applying \f$ t\f$ on the source +returns the ray obtained by applying `t` on the source and on the direction of `r`. */ Ray_2 transform(const Aff_transformation_2 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Ray_3.h b/Kernel_23/doc/Kernel_23/CGAL/Ray_3.h index d30f258d86b..f954fbb1a39 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Ray_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Ray_3.h @@ -19,25 +19,25 @@ public: /*! introduces a ray `r` -with source \f$ p\f$ and passing through point \f$ q\f$. +with source `p` and passing through point `q`. */ Ray_3(const Point_3 &p, const Point_3 &q); /*! -introduces a ray `r` with source \f$ p\f$ and with -direction \f$ d\f$. +introduces a ray `r` with source `p` and with +direction `d`. */ Ray_3(const Point_3 &p, const Direction_3 &d); /*! -introduces a ray `r` with source \f$ p\f$ and with -a direction given by \f$ v\f$. +introduces a ray `r` with source `p` and with +a direction given by `v`. */ Ray_3(const Point_3 &p, const Vector_3 &v); /*! -introduces a ray `r` starting at source \f$ p\f$ with -the same direction as \f$ l\f$. +introduces a ray `r` starting at source `p` with +the same direction as `l`. */ Ray_3(const Point_3 &p, const Line_3 &l); @@ -102,7 +102,7 @@ of `r`, or if it is in the interior of `r`. bool has_on(const Point_3 &p) const; /*! -returns the ray obtained by applying \f$ t\f$ on the source +returns the ray obtained by applying `t` on the source and on the direction of `r`. */ Ray_3 transform(const Aff_transformation_3 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Segment_2.h b/Kernel_23/doc/Kernel_23/CGAL/Segment_2.h index 2f86639aee6..94ba98afee3 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Segment_2.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Segment_2.h @@ -7,9 +7,9 @@ An object `s` of the data type `Segment_2` is a directed straight line segment in the two-dimensional Euclidean plane \f$ \E^2\f$, i.e.\ a straight line segment \f$ [p,q]\f$ connecting two points \f$ p,q \in \R^2\f$. The segment is topologically closed, i.e.\ the end -points belong to it. Point \f$ p\f$ is called the source and \f$ q\f$ -is called the target of \f$ s\f$. The length of \f$ s\f$ is the -Euclidean distance between \f$ p\f$ and \f$ q\f$. Note that there is only a function +points belong to it. Point `p` is called the source and `q` +is called the target of `s`. The length of `s` is the +Euclidean distance between `p` and `q`. Note that there is only a function to compute the square of the length, because otherwise we had to perform a square root operation which is not defined for all number types, which is expensive, and may not be exact. @@ -25,8 +25,8 @@ public: /// @{ /*! -introduces a segment `s` with source \f$ p\f$ -and target \f$ q\f$. The segment is directed from the source towards +introduces a segment `s` with source `p` +and target `q`. The segment is directed from the source towards the target. */ Segment_2(const Point_2 &p, const Point_2 &q); @@ -106,7 +106,7 @@ returns a segment with source and target point interchanged. Segment_2 opposite() const; /*! -returns the line \f$ l\f$ passing through `s`. Line \f$ l\f$ has the +returns the line `l` passing through `s`. Line `l` has the same orientation as segment `s`. */ Line_2 supporting_line() const; @@ -138,9 +138,9 @@ of `s`, or if it is in the interior of `s`. bool has_on(const Point_2 &p) const; /*! -checks if point \f$ p\f$ is on segment `s`. This function is faster +checks if point `p` is on segment `s`. This function is faster than function `has_on()`. -\pre \f$ p\f$ is on the supporting line of `s`. +\pre `p` is on the supporting line of `s`. */ bool collinear_has_on(const Point_2 &p) const; @@ -155,7 +155,7 @@ returns a bounding box containing `s`. Bbox_2 bbox() const; /*! -returns the segment obtained by applying \f$ t\f$ on the source +returns the segment obtained by applying `t` on the source and the target of `s`. */ Segment_2 transform(const Aff_transformation_2 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Segment_3.h b/Kernel_23/doc/Kernel_23/CGAL/Segment_3.h index 6245484a04e..4e07cddc757 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Segment_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Segment_3.h @@ -3,13 +3,13 @@ namespace CGAL { /*! \ingroup kernel_classes3 -An object \f$ s\f$ of the data type `Segment_3` is a directed +An object `s` of the data type `Segment_3` is a directed straight line segment in the three-dimensional Euclidean space \f$ \E^3\f$, that is a straight line segment \f$ [p,q]\f$ connecting two points \f$ p,q \in \R^3\f$. The segment is topologically closed, i.e.\ the end -points belong to it. Point \f$ p\f$ is called the source and \f$ q\f$ -is called the target of \f$ s\f$. The length of \f$ s\f$ is the -Euclidean distance between \f$ p\f$ and \f$ q\f$. Note that there is only a function +points belong to it. Point `p` is called the source and `q` +is called the target of `s`. The length of `s` is the +Euclidean distance between `p` and `q`. Note that there is only a function to compute the square of the length, because otherwise we had to perform a square root operation which is not defined for all number types, which is expensive, and may not be exact. @@ -25,8 +25,8 @@ public: /// @{ /*! -introduces a segment `s` with source \f$ p\f$ -and target \f$ q\f$. It is directed from the source towards +introduces a segment `s` with source `p` +and target `q`. It is directed from the source towards the target. */ Segment_3(const Point_3 &p, const Point_3 &q); @@ -106,7 +106,7 @@ returns a segment with source and target interchanged. Segment_3 opposite() const; /*! -returns the line \f$ l\f$ passing through `s`. Line \f$ l\f$ has the +returns the line `l` passing through `s`. Line `l` has the same orientation as segment `s`, that is from the source to the target of `s`. */ @@ -129,7 +129,7 @@ returns a bounding box containing `s`. Bbox_3 bbox() const; /*! -returns the segment obtained by applying \f$ t\f$ on the source +returns the segment obtained by applying `t` on the source and the target of `s`. */ Segment_3 transform(const Aff_transformation_3 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Tetrahedron_3.h b/Kernel_23/doc/Kernel_23/CGAL/Tetrahedron_3.h index 18c542163a6..5d9446bf3c2 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Tetrahedron_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Tetrahedron_3.h @@ -3,7 +3,7 @@ namespace CGAL { /*! \ingroup kernel_classes3 -An object \f$ t\f$ of the class `Tetrahedron_3` is an oriented +An object `t` of the class `Tetrahedron_3` is an oriented tetrahedron in the three-dimensional Euclidean space \f$ \E^3\f$. It is defined by four vertices \f$ p_0\f$, \f$ p_1\f$, \f$ p_2\f$ and \f$ p_3\f$. diff --git a/Kernel_23/doc/Kernel_23/CGAL/Triangle_2.h b/Kernel_23/doc/Kernel_23/CGAL/Triangle_2.h index 231d730bb78..84a25712933 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Triangle_2.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Triangle_2.h @@ -3,9 +3,9 @@ namespace CGAL { /*! \ingroup kernel_classes2 -An object \f$ t\f$ of the class `Triangle_2` is a triangle +An object `t` of the class `Triangle_2` is a triangle in the two-dimensional Euclidean plane \f$ \E^2\f$. -Triangle \f$ t\f$ is oriented, i.e., its boundary has +Triangle `t` is oriented, i.e., its boundary has clockwise or counterclockwise orientation. We call the side to the left of the boundary the positive side and the side to the right of the boundary the negative side. @@ -24,7 +24,7 @@ public: /// @{ /*! -introduces a triangle `t` with vertices \f$ p\f$, \f$ q\f$ and \f$ r\f$. +introduces a triangle `t` with vertices `p`, `q` and `r`. */ Triangle_2(const Point_2 &p, const Point_2 &q, @@ -79,7 +79,7 @@ returns `POSITIVE_SIDE`, or the constant `ON_NEGATIVE_SIDE`, -determined by the position of point \f$ p\f$. +determined by the position of point `p`. \pre `t` is not degenerate. */ Oriented_side oriented_side(const Point_2 &p) const; @@ -88,7 +88,7 @@ Oriented_side oriented_side(const Point_2 &p) const; returns the constant `ON_BOUNDARY`, `ON_BOUNDED_SIDE`, or else `ON_UNBOUNDED_SIDE`, -depending on where point \f$ p\f$ is. +depending on where point `p` is. \pre `t` is not degenerate. */ Bounded_side bounded_side(const Point_2 &p) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Triangle_3.h b/Kernel_23/doc/Kernel_23/CGAL/Triangle_3.h index 1338e862e73..88a797ed342 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Triangle_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Triangle_3.h @@ -3,7 +3,7 @@ namespace CGAL { /*! \ingroup kernel_classes3 -An object \f$ t\f$ of the class `Triangle_3` is a triangle in +An object `t` of the class `Triangle_3` is a triangle in the three-dimensional Euclidean space \f$ \E^3\f$. As the triangle is not a full-dimensional object there is only a test whether a point lies on the triangle or not. @@ -19,7 +19,7 @@ public: /// @{ /*! -introduces a triangle `t` with vertices \f$ p\f$, \f$ q\f$ and \f$ r\f$. +introduces a triangle `t` with vertices `p`, `q` and `r`. */ Triangle_3(const Point_3 &p, const Point_3 &q, diff --git a/Kernel_23/doc/Kernel_23/CGAL/Vector_2.h b/Kernel_23/doc/Kernel_23/CGAL/Vector_2.h index 9b7258d8212..7681736c827 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Vector_2.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Vector_2.h @@ -44,12 +44,12 @@ introduces the vector \f$ s.target()-s.source()\f$. Vector_2(const Segment_2 &s); /*! -introduces the vector having the same direction as \f$ r\f$. +introduces the vector having the same direction as `r`. */ Vector_2(const Ray_2 &r); /*! -introduces the vector having the same direction as \f$ l\f$. +introduces the vector having the same direction as `l`. */ Vector_2(const Line_2 &l); @@ -182,7 +182,7 @@ returns the direction which passes through `v`. Direction_2 direction() const; /*! -returns the vector obtained by applying \f$ t\f$ on `v`. +returns the vector obtained by applying `t` on `v`. */ Vector_2 transform(const Aff_transformation_2 &t) const; diff --git a/Kernel_23/doc/Kernel_23/CGAL/Vector_3.h b/Kernel_23/doc/Kernel_23/CGAL/Vector_3.h index b62e8ea96c1..f6d224dde59 100644 --- a/Kernel_23/doc/Kernel_23/CGAL/Vector_3.h +++ b/Kernel_23/doc/Kernel_23/CGAL/Vector_3.h @@ -46,12 +46,12 @@ introduces the vector \f$ s.target()-s.source()\f$. Vector_3(const Segment_3 &s); /*! -introduces a vector having the same direction as \f$ r\f$. +introduces a vector having the same direction as `r`. */ Vector_3(const Ray_3 &r); /*! -introduces a vector having the same direction as \f$ l\f$. +introduces a vector having the same direction as `l`. */ Vector_3(const Line_3 &l); @@ -187,7 +187,7 @@ returns the dimension (the constant 3). int dimension() const; /*! -returns the vector obtained by applying \f$ t\f$ on `v`. +returns the vector obtained by applying `t` on `v`. */ Vector_3 transform(const Aff_transformation_3 &t) const;