- add constructor arc(three Point_3)

- constructors for supporting line/circle/plane
- various bug fixes

Circular_kernel_3/doc_tex/Circular_kernel_3_ref/Circular_arc_3.tex

@@ -12,12 +12,12 @@
 \ccThree{Circular_arc_point_3}{ca.is_x_monotone()}{}
 \ccThreeToTwo
 
-\ccConstructor{Circular_arc_3(const SphericalKernel::Circle_3 &c)}
+\ccConstructor{Circular_arc_3(const Circle_3<SphericalKernel> &c)}
 {Constructs an arc from a full circle.}
 
-\ccConstructor{Circular_arc_3(const SphericalKernel::Circle_3 &c,
+\ccConstructor{Circular_arc_3(const Circle_3<SphericalKernel> &c,
-		const SphericalKernel::Circular_arc_point_3 &p1,
+		const Circular_arc_point_3<SphericalKernel> &p1,
-		const SphericalKernel::Circular_arc_point_3 &p2)}
+		const Circular_arc_point_3<SphericalKernel> &p2)}
 {Constructs the circular arc supported by \ccc{c}, whose source and target 
 are respectively \ccc{p1} and \ccc{p2}.
 \ccPrecond{\ccc{p1} and \ccc{p2} lie on \ccc{c}. \ccc{p1} and \ccc{p2} 
@@ -32,16 +32,29 @@ In this definition, we say that a plane is \textit{positive} if its
 equation is of the form $ax+by+cz+d=0$ with $(a,b,c)>(0,0,0)$
 (i.e. $(a>0) || (a==0) \&\& (b>0) || (a==0)\&\&(b==0)\&\&(c>0)$).
 
+\ccConstructor{Circular_arc_3(const Point_3<SphericalKernel> &p,
+                              const Point_3<SphericalKernel> &q,
+                              const Point_3<SphericalKernel> &r)}
+{Constructs an arc that is supported by the circle of type
+  \ccc{Circle_3<SphericalKernel>} passing through the points \ccc{p},
+  \ccc{q} and \ccc{r}. The source and target are respectively \ccc{p}
+  and \ccc{r}, when traversing the supporting circle in the
+  counterclockwise direction in the \textit{positive} plane containing
+  the circle. 
+  Note that, depending on the orientation of the point triple
+  \ccc{(p,q,r)}, \ccc{q} may not lie on the arc. 
+\ccPrecond{\ccc{p}, \ccc{q}, and \ccc{r} are not collinear.}}
+
 \ccAccessFunctions
 
 \ccThree{SphericalKernel::Circular_arc_point_3}{ca.is_x_monotone()}{}
 \ccThreeToTwo
 
-\ccMethod{SphericalKernel::Circle_3 supporting_circle();}{}
+\ccMethod{Circle_3<SphericalKernel> supporting_circle();}{}
 
-\ccMethod{SphericalKernel::Circular_arc_point_3 source();}{}
+\ccMethod{Circular_arc_point_3<SphericalKernel> source();}{}
 \ccGlue
-\ccMethod{SphericalKernel::Circular_arc_point_3 target();}{}
+\ccMethod{Circular_arc_point_3<SphericalKernel> target();}{}
 
 When the methods \ccc{source} and \ccc{target} return the same point, then 
 the arc is in fact a full circle. %\footnote{so far, arcs of zero length are

Circular_kernel_3/doc_tex/Circular_kernel_3_ref/Circular_arc_point_3.tex

@@ -12,7 +12,7 @@
 \ccThree{Circular_arc_point_3}{ca.is_x_monotone()}{}
 \ccThreeToTwo
 
-\ccConstructor{Circular_arc_point_3(const SphericalKernel::Point_3 &q)}{}
+\ccConstructor{Circular_arc_point_3(const Point_3<SphericalKernel> &q)}{}
 
 \ccConstructor{Circular_arc_point_3(const SphericalKernel::Root_for_spheres_2_3 &r)}{}
 

Circular_kernel_3/doc_tex/Circular_kernel_3_ref/GeomFunctorsConstructors.tex

@@ -9,7 +9,11 @@
 A model \ccVar\ of this type must provide:
 
 \ccMemberFunction{SphericalKernel::Plane_3 operator()
-	(SphericalKernel::Polynomial_1_3);}
+	(const SphericalKernel::Circular_arc_3 &a);}
+{Constructs the plane containing the arc.}
+
+\ccMemberFunction{SphericalKernel::Plane_3 operator()
+	(const SphericalKernel::Polynomial_1_3 &p);}
 {Constructs a plane from an equation.}
 
 \ccSeeAlso
@@ -27,8 +31,8 @@ A model \ccVar\ of this type must provide:
 A model \ccVar\ of this type must provide:
 
 \ccMemberFunction{SphericalKernel::Sphere_3 operator()
-	(SphericalKernel::Polynomial_2_3);}
+	(const SphericalKernel::Polynomial_2_3 &p);}
-{Constructs a circle from an equation.}
+{Constructs a sphere from an equation.}
 
 \ccSeeAlso
 
@@ -45,7 +49,11 @@ A model \ccVar\ of this type must provide:
 A model \ccVar\ of this type must provide:
 
 \ccMemberFunction{SphericalKernel::Line_3 operator()
-	(SphericalKernel::Polynomials_for_lines_3);}
+	(const SphericalKernel::Line_arc_3 &s);}
+{Constructs the line containing the segment.}
+
+\ccMemberFunction{SphericalKernel::Line_3 operator()
+	(const SphericalKernel::Polynomials_for_lines_3 &p);}
 {Constructs a line from an equation.}
 
 \ccSeeAlso
@@ -59,7 +67,11 @@ A model \ccVar\ of this type must provide:
 A model \ccVar\ of this type must provide:
 
 \ccMemberFunction{SphericalKernel::Circle_3 operator()
-	(SphericalKernel::Polynomials_for_circles_3);}
+	(const SphericalKernel::Circular_arc_3 &a);}
+{Constructs the circle containing the arc.}
+
+\ccMemberFunction{SphericalKernel::Circle_3 operator()
+	(const SphericalKernel::Polynomials_for_circles_3 &p);}
 {Constructs a circle from an equation.}
 
 \ccSeeAlso
@@ -88,12 +100,11 @@ A model \ccVar\ of this type must provide:
 
 \ccMemberFunction{SphericalKernel::Line_arc_3 operator()
 	(const SphericalKernel::Line_3 &l,
-	const SphericalKernel::Circular_arc_point_3 &p1,
+	const SphericalKernel::Circular_arc_point_3 &p,
-	const SphericalKernel::Circular_arc_point_3 &p2);}
+	const SphericalKernel::Circular_arc_point_3 &q);}
 {Constructs the line segment supported by \ccc{l}, whose source 
-is \ccc{p1} and whose target is \ccc{p2}.
+is \ccc{p} and whose target is \ccc{q}.
-\ccPrecond{\ccc{p1} and \ccc{p2} lie on \ccc{l}. 
+\ccPrecond{\ccc{p} and \ccc{q} lie on \ccc{l} and are different.}}
-\ccc{p1} and \ccc{p2} are different.}}
 
 %\ccMemberFunction{SphericalKernel::Line_arc_3 operator()
 %	(const SphericalKernel::Line_3 &l,
@@ -106,8 +117,8 @@ is \ccc{p1} and whose target is \ccc{p2}.
 {}
 
 \ccMemberFunction{SphericalKernel::Line_arc_3 operator()
-	(const SphericalKernel::Point_3 &p1,
+	(const SphericalKernel::Point_3 &p,
-	const SphericalKernel::Point_3 &p2);}
+	const SphericalKernel::Point_3 &q);}
 {}
 
 \end{ccRefFunctionObjectConcept}
@@ -122,12 +133,11 @@ A model \ccVar\ of this type must provide:
 
 \ccMemberFunction{SphericalKernel::Circular_arc_3 operator()
 	(const SphericalKernel::Circle_3 &c,
-	const SphericalKernel::Circular_arc_point_3 &p1,
+	const SphericalKernel::Circular_arc_point_3 &p,
-	const SphericalKernel::Circular_arc_point_3 &p2);}
+	const SphericalKernel::Circular_arc_point_3 &q);}
 {Constructs the circular arc supported by \ccc{c}, whose source and target 
-are respectively \ccc{p1} and \ccc{p2}.
+are respectively \ccc{p} and \ccc{q}.
-\ccPrecond{\ccc{p1} and \ccc{p2} lie on \ccc{c}. \ccc{p1} and \ccc{p2} 
+\ccPrecond{\ccc{p} and \ccc{q} lie on \ccc{c} and they are different.}}
-are different.}}
 
 The circular arc constructed from a circle, a source, and a target, is
 defined as the set of points of the circle that lie between the source
@@ -138,6 +148,20 @@ In this definition, we say that a plane is \textit{positive} if its
 equation is of the form $ax+by+cz+d=0$ with $(a,b,c)>(0,0,0)$
 (i.e. $(a>0) || (a==0) \&\& (b>0) || (a==0)\&\&(b==0)\&\&(c>0)$).
 
+\ccConstructor{SphericalKernel::Circular_arc_3 operator()
+                 (const SphericalKernel::Point_3 &p,
+                 const SphericalKernel::Point_3 &q,
+                 const SphericalKernel::Point_3 &r);}
+{Constructs an arc that is supported by the circle of type
+  \ccc{SphericalKernel::Circle_3} passing through the points \ccc{p},
+  \ccc{q} and \ccc{r}. The source and target are respectively \ccc{p}
+  and \ccc{r}, when traversing the supporting circle in the
+  counterclockwise direction in the \textit{positive} plane containing
+  the circle. 
+  Note that, depending on the orientation of the point triple
+  \ccc{(p,q,r)}, \ccc{q} may not lie on the arc. 
+\ccPrecond{\ccc{p}, \ccc{q}, and \ccc{r} are not collinear.}}
+
 \end{ccRefFunctionObjectConcept}
 \begin{ccRefFunctionObjectConcept}{SphericalKernel::ConstructCircularMinVertex_3} 
 

Circular_kernel_3/doc_tex/Circular_kernel_3_ref/GeomFunctorsOtherConstructions.tex

@@ -14,36 +14,3 @@ In addition, an object \ccVar\ of this type must provide:
 {Returns the sphere having the supporting circle of \ccc{a} as diameter.}
 
 \end{ccRefFunctionObjectConcept}
-\begin{ccRefFunctionObjectConcept}{SphericalKernel::ConstructSupportingPlane_3}
-
-\ccCreationVariable{fo}
-
-An object \ccVar\ of this type must provide:
-
-\ccMemberFunction{SphericalKernel::Plane_3
-	operator()(const SphericalKernel::Circular_arc_3 & c);}
-{Returns the plane containing the arc.}
-
-\end{ccRefFunctionObjectConcept}
-\begin{ccRefFunctionObjectConcept}{SphericalKernel::ConstructSupportingLine_3}
-
-\ccCreationVariable{fo}
-
-An object \ccVar\ of this type must provide:
-
-\ccMemberFunction{SphericalKernel::Line_3
-	operator()(const SphericalKernel::Line_arc_3 & l);}
-{Returns the line containing the segment.}
-
-\end{ccRefFunctionObjectConcept}
-\begin{ccRefFunctionObjectConcept}{SphericalKernel::ConstructSupportingCircle_3}
-
-\ccCreationVariable{fo}
-
-An object \ccVar\ of this type must provide:
-
-\ccMemberFunction{SphericalKernel::Circle_3
-	operator()(const SphericalKernel::Circular_arc_3 & c);}
-{Returns the circle containing the arc.}
-
-\end{ccRefFunctionObjectConcept}

Circular_kernel_3/doc_tex/Circular_kernel_3_ref/Line_arc_3.tex

@@ -12,38 +12,38 @@
 \ccThree{Circular_arc_point_3}{ca.is_x_monotone()}{}
 \ccThreeToTwo
 
-\ccConstructor{Line_arc_3(const SphericalKernel::Line_3 &l,
+\ccConstructor{Line_arc_3(const Line_3<SphericalKernel> &l,
-		const SphericalKernel::Circular_arc_point_3 &p1,
+		const Circular_arc_point_3<SphericalKernel> &p1,
-		const SphericalKernel::Circular_arc_point_3 &p2)}
+		const Circular_arc_point_3<SphericalKernel> &p2)}
 {Construct the line segment supported by \ccc{l}, whose source 
 is \ccc{p1}, and whose target is \ccc{p2}.
 \ccPrecond{\ccc{p1} and \ccc{p2} lie on \ccc{l}. 
 \ccc{p1} and \ccc{p2} are different.}}
 
-\ccConstructor{Line_arc_3(const SphericalKernel::Line_3 &l,
+\ccConstructor{Line_arc_3(const Line_3<SphericalKernel> &l,
-		const SphericalKernel::Point_3 &p1,
+		const Point_3<SphericalKernel> &p1,
-		const SphericalKernel::Point_3 &p2)}
+		const Point_3<SphericalKernel> &p2)}
 {Same.}
 
-\ccConstructor{Line_arc_3(const SphericalKernel::Segment_3 &s)}
+\ccConstructor{Line_arc_3(const Segment_3<SphericalKernel> &s)}
 {}
 
 \ccAccessFunctions
 
-\ccThree{SphericalKernel::Circular_arc_point_3}{ca.is_x_monotone()}{}
+\ccThree{Circular_arc_point_3<SphericalKernel>}{ca.is_x_monotone()}{}
 \ccThreeToTwo
 
-\ccMethod{SphericalKernel::Line_3 supporting_line();}{}
+\ccMethod{Line_3<SphericalKernel> supporting_line();}{}
 
-\ccMethod{SphericalKernel::Circular_arc_point_3 source();}{}
+\ccMethod{Circular_arc_point_3<SphericalKernel> source();}{}
 \ccGlue
-\ccMethod{SphericalKernel::Circular_arc_point_3 target();}{}
+\ccMethod{Circular_arc_point_3<SphericalKernel> target();}{}
 
-\ccMethod{SphericalKernel::Circular_arc_point_3 min();}
+\ccMethod{Circular_arc_point_3<SphericalKernel> min();}
 {Constructs the minimum vertex according to the lexicographic ordering 
 of coordinates.} 
 \ccGlue
-\ccMethod{SphericalKernel::Circular_arc_point_3 max();}
+\ccMethod{Circular_arc_point_3<SphericalKernel> max();}
 {Same for the maximum vertex.}
 
 \ccQueryFunctions