removed concept for hyperbolic translaitons; imposed translation type; changed Point_2 to Hyperbolic_point_2; added missing constructor objects

Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/HyperbolicOctagonTranslation.h

@@ -1,145 +0,0 @@
-// Copyright (c) 2016-2017 INRIA Nancy - Grand Est (France).
-// All rights reserved.
-
-/*!
-\ingroup PkgPeriodic4HyperbolicTriangulation2Concepts
-\cgalConcept
-\cgalModifBegin
-The concept `HyperbolicOctagonTranslation` describes the requirements for an object that represents 
-a hyperbolic translation in the fundamental group \f$\mathcal G\f$ of the the Bolza surface. 
-
-Generally, a hyperbolic translation \f$g\f$ is an orientation-preserving isometry acting 
-on the hyperbolic plane, and is specified by two complex numbers \f$\alpha\f$ and \f$\beta\f$:
-\f[
-	g(z) = \frac{\alpha \cdot z + \beta}{\overline{\beta} \cdot z + \overline{\alpha}},
-	\qquad |\alpha|^2 - |\beta|^2 = 1,
-\f]
-where \f$\overline{a}\f$ and \f$\overline{b}\f$ denote the complex conjugates of \f$a\f$
-and \f$b\f$ respectively. A hyperbolic translation is also a word on the generators of the 
-fundamental group of a hyperbolic surface.
-
-Specifically for the group \f$\mathcal G\f$, let \f$[g_0, g_1, \ldots, g_7]\f$ be the set of its 
-generators, ordered counter-clockwise around the origin, with \f$g_k\f$ translating the origin 
-\f$O\f$ along the real axis in the positive direction. The coefficients \f$\alpha_k\f$ and \f$\beta_k\f$ 
-of each generator of this ordered set are given as 
-\f[
-	\alpha_k = 1 + \sqrt{2}, \qquad \beta_k = \exp\left(\tfrac{ik\pi}{4}\right)\sqrt{2}\sqrt{1+\sqrt{2}}.
-\f]
-Note that with the notation given in Section \ref P4HT2_thespace of the User manual, the ordered 
-set of generators can be written also as
-\f[
-	[g_k, k = 0, \ldots, 7] = [ a, \overline{b}, c, \overline{d}, \overline{a}, b, \overline{c}, d ].
-\f] 
-\cgalModifEnd
-
-\cgalHasModel CGAL::Hyperbolic_octagon_translation
-*/
-
-
-class HyperbolicOctagonTranslation {
-
-public:
-	
-	
-	/// \name Types
-	
-	/// Number type of the coefficients of \f$\alpha\f$ and \f$\beta\f$.
-	/// This number type must be compatible with the field type `FT` of the concept 
-	/// `Periodic_4HyperbolicDelaunayTriangulationTraits_2`.
-	typedef unspecified_type 			NT;
-
-	/// \cgalModifBegin Represents a single letter of the word corresponding to the translation. \cgalModifEnd
-	typedef unsigned short int 			Word_letter;
-
-	/// Word representation of the translation, a sequence of elements of type `Word_letter`.
-	typedef std::vector<Word_letter> 	Word;
-
-	/// \cgalModifBegin Represents a complex number with coefficients of type `NT`.\cgalModifEnd
-	typedef std::pair<NT,NT> 			Complex;
-
-	/// \cgalModifBegin Represents the coefficients \f$\alpha\f$ and \f$\beta\f$ of a hyperbolic translation.\cgalModifEnd
-	typedef std::pair<Complex,Complex> 	Coefficients;
-
-	/// \name Creation
-
-	/// Default constructor. Creates the identity translation.
-	HyperbolicOctagonTranslation();
-
-	/// Creates the translation described by the word `w`.
-	HyperbolicOctagonTranslation(Word w);
-
-	/// Creates the translation described by the one-letter word `l`.
-	HyperbolicOctagonTranslation(Word_letter l);
-
-	/// Creates the translation described by the two-letter word `lm`.
-	HyperbolicOctagonTranslation(Word_letter l, Word_letter m);
-
-	/// Creates the translation described by the three-letter word `lmn`.
-	HyperbolicOctagonTranslation(Word_letter l, Word_letter m, Word_letter n);
-
-	/// Creates the translation described by the four-letter word `lmno`.
-	HyperbolicOctagonTranslation(Word_letter l, Word_letter m, Word_letter n, Word_letter o);
-
-
-	/// \name Operations
-	
-	/// Multiplication operator; composes the current translation with `other`. 
-	HyperbolicOctagonTranslation operator*(const HyperbolicOctagonTranslation& other) const;
-
-	///	Difference operator; the difference of two translations \f$v\f$ and \f$w\f$ is defined as \f$v * w^{-1}\f$. 
-  	HyperbolicOctagonTranslation operator-(const HyperbolicOctagonTranslation& other) const;
-
-  	/// Assignment operator; modifying the translation after the assignment leaves `other` unaffected.
-	HyperbolicOctagonTranslation& operator=(const HyperbolicOctagonTranslation& other);
-
-	/// Equality operator.
-	bool operator==(const Hyperbolic_octagon_translation<NT>& other) const;
-
-	/// Inequality operator.
-	bool operator!=(const Hyperbolic_octagon_translation<NT>& other) const;
-
-	/// Comparison operator. 
-	/// The comparison is done on the ordering of the translations around the original domain.
-	bool operator<(const Hyperbolic_octagon_translation<NT>& other) const;
-
-	/// Returns the inverse of the current translation.
-	HyperbolicOctagonTranslation inverse() const;
-
-
-	/// \name Access Functions
-
-	/// Returns the coefficient \f$\alpha\f$ of the translation's matrix. The first element of the returned `pair` 
-	/// contains the real part of \f$\alpha\f$. The second element contains its imaginary part.
-	Complex alpha() const;
-
-	/// Returns the coefficient \f$\beta\f$ of the translation's matrix. The first element of the returned `pair` 
-	/// contains the real part of \f$\beta\f$. The second element contains its imaginary part.
-	Complex beta() const;
-
-	/// Returns `true` if the current translation represents the identity element of the group.
-	bool is_identity();
-
-
-	/// \name Static Access Functions
-
-	/*!
-		\cgalModifBegin
-		Returns a vector containing the coefficients of the generators of \f$\mathcal G\f$ and of their inverses.
-		The translations must be given in the order:
-		\f[ [g_0, g_1, \ldots, g_7]. \f]
-		\cgalModifEnd
- 	*/
-	static void get_generator_coefficients(std::vector< Coefficients >& gens);
-
-
-	/*!
-		\cgalModifBegin
-		Returns a vector containing the generators of \f$\mathcal G\f$ and their inverses.
-		The translations must be given in the order:
-		\f[ [g_0, g_1, \ldots, g_7]. \f]
-		\cgalModifEnd
- 	*/
-	static void get_generators(std::vector<HyperbolicOctagonTranslation>& gens);
-
-}; // end of class HyperbolicOctagonTranslation
-

Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicDelaunayTriangulationTraits_2.h

@@ -7,23 +7,13 @@
 
 \cgalRefines Periodic_4HyperbolicTriangulationTraits_2
 
-The concept `Periodic_4HyperbolicDelaunayTriangulationTraits_2` refines the concept 
+The concept `Periodic_4HyperbolicDelaunayTriangulationTraits_2` adds a requirement 
-`Periodic_4HyperbolicDelaunayTriangulationTraits_2`. It adds a requirement that needs
+to `Periodic_4HyperbolicDelaunayTriangulationTraits_2` that needs to be fulfilled 
-to be fulfilled by any class used to instantiate the first template parameter of the class 
+by any class used to instantiate the first template parameter of the class 
 `CGAL::Periodic_4_hyperbolic_Delaunay_triangulation_2`. The added requirement is 
 essential for the removal of existing vertices in a Delaunay triangulation of the
 Bolza surface.
 
-\cgalModifBegin
-	The concept requires that two nested types are provided:
-	<ul>
-		<li> A field number type `FT` that must support exact computations with algebraic 
-			 numbers, in particular with nested square roots;
-		<li> A `Hyperbolic_translation` type, which satisfies the requirements described 
-			 in the concept `HyperbolicOctagonTranslation`.
-	</ul>
-\cgalModifEnd
-
 \cgalHasModel CGAL::Periodic_4_hyperbolic_Delaunay_triangulation_traits_2
 */
 
@@ -36,13 +26,15 @@ public:
 	/// \name Computation Types
 	/// @{
 		/*!
+			\cgalModifBegin
 			Type that permits to compute the hyperbolic diameter of a circle.
 			Must provide the function operator
 
-			`double operator()(Circle_2 c),`
+			`double operator()(Hyperbolic_point_2 p1, Hyperbolic_point_2 p2, Hyperbolic_point_2 p3),`
 
 			which returns a floating-point approximation of the hyperbolic diameter
-			of the circle `c`.
+			of the circle defined by the points `p1, p2,` and `p3`.
+			\cgalModifEnd
 		*/
 		typedef unspecified_type 				Compute_approximate_hyperbolic_diameter;
 	/// @}

Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationFaceBase_2.h

@@ -16,9 +16,11 @@ Compare with Section \ref Section_2D_Triangulations_Software_Design of the 2D Tr
 package. The vertices and neighbors are indexed counter-clockwise 0, 1, and 2. Neighbor `i` lies
 opposite to vertex `i`. 
 
-For periodic hyperbolic triangulations, the face base class needs to store three hyperbolic translations, 
+For periodic hyperbolic triangulations, the face base class needs to store three hyperbolic 
-one for each vertex. Applying each translation to the point stored in the corresponding vertex produces 
+translations, one for each vertex. Applying each translation to the point stored in the 
-the canonical representative of the face in the hyperbolic plane.
+corresponding vertex produces the canonical representative of the face in the hyperbolic plane. 
+Hyperbolic translations are represented by a nested type which is provided by the concept 
+`Periodic_4HyperbolicDelaunayTriangulationTraits_2`.
 
 \cgalHasModel CGAL::Periodic_4_hyperbolic_triangulation_face_base_2
 
@@ -33,11 +35,8 @@ public:
 
 	/// \name Types
 	/// @{		
-
+		typedef Periodic_4HyperbolicDelaunayTriangulationTraits_2 		Geometric_traits;
-		/*!
+		typedef Geometric_traits::Hyperbolic_translation 				Hyperbolic_translation;
-			This must be a model of the concept HyperbolicOctagonTranslation.
-		*/
-		typedef undefined_type 						Hyperbolic_translation;
 	///@}
 
 

Periodic_4_hyperbolic_triangulation_2/doc/Periodic_4_hyperbolic_triangulation_2/Concepts/Periodic_4HyperbolicTriangulationTraits_2.h

@@ -7,22 +7,16 @@
 
 \cgalRefines HyperbolicDelaunayTriangulationTraits_2
 
-The concept `Periodic_4HyperbolicTriangulationTraits_2` refines the concept 
+The concept `Periodic_4HyperbolicTriangulationTraits_2` describes the set of requirements 
-`HyperbolicDelaunayTriangulationTraits_2`. It describes the set of requirements to be 
+to be fulfilled by any class used to instantiate the first template parameter of the class 
-fulfilled by any class used to instantiate the first template parameter of the class 
+`CGAL::Periodic_4_hyperbolic_triangulation_2`. In addition to the geometric types and the 
-`CGAL::Periodic_4_hyperbolic_triangulation_2`. In addition to the geometric 
+operations defined on them in `HyperbolicDelaunayTriangulationTraits_2`, it defines the 
-types and the operations defined on them in `HyperbolicDelaunayTriangulationTraits_2`, 
+hyperbolic translations that allow to encode the periodicity of the triangulation.
-it defines the hyperbolic translations that allow to encode the periodicity of the 
-triangulation.
 
 \cgalModifBegin
-	The concept requires that two nested types are provided:
+The concept requires that a nested field number type `FT` is provided. The type `FT`  
-	<ul>
+must support exact computations with algebraic numbers, in particular with nested 
-		<li> A field number type `FT` that must support exact computations with algebraic 
+square roots.
-			 numbers, in particular with nested square roots;
-		<li> A `Hyperbolic_translation` type, which satisfies the requirements described 
-			 in the concept `HyperbolicOctagonTranslation`.
-	</ul>
 \cgalModifEnd
 
 */
@@ -37,18 +31,10 @@ public:
 	/// \name Types
 	/// @{
 
-		/*!
-			\cgalModifBegin
-			Represents a hyperbolic circle, i.e., a circle contained in the unit disk.
-			\cgalModifEnd
-		*/
-		typedef unspecified_type 				Circle_2;
-
 		/*!
 			Represents a hyperbolic translation. 
-			Must be a model of the concept `HyperbolicOctagonTranslation`. 
 		*/
-		typedef unspecified_type 				Hyperbolic_translation;
+		typedef CGAL::Hyperbolic_octagon_translation<FT> 		Hyperbolic_translation;
 	/// @}
 
 
@@ -57,7 +43,7 @@ public:
 		/*!
 			Predicate type. Must provide the function operator
 
-			`Bounded_side operator()(Point_2 p),`
+			`Bounded_side operator()(Hyperbolic_point_2 p),`
 
 			which returns the position of point `p` relative to the half-open
 			regular hyperbolic octagon.
@@ -71,12 +57,12 @@ public:
 		/*!
 			Construction type. Must provide the function operator
 
-			`Point_2 operator() ( const Point_2& pt, const HyperbolicOctagonTranslation& tr ) const,`
+			`Hyperbolic_point_2 operator() ( const Hyperbolic_point_2& pt, const Hyperbolic_translation& tr ) const,`
 
 			which returns the image of the point `pt` under the action of the 
 			hyperbolic translation `tr`.
 		*/
-		typedef unspecified_type		      	Construct_point_2;
+		typedef unspecified_type		      	Construct_hyperbolic_point_2;
 	/// @}
 	
 
@@ -92,8 +78,8 @@ public:
 	/// \name
 	/// The following functions give access to the construction objects:
 	/// @{
-		Construct_point_2 
+		Construct_hyperbolic_point_2 
-		construct_point_2_object() const;
+		construct_hyperbolic_point_2_object() const;
 	/// @}
 
 };