Actualized traits concepts

Interpolation/doc/Interpolation/Concepts/GradientFittingTraits.h

@@ -15,9 +15,7 @@ concept `GradientFittingTraits` defines this common set of requirements.
 \sa `CGAL::sibson_c1_interpolation()`
 \sa `CGAL::farin_c1_interpolation()`
 \sa `CGAL::quadratic_interpolation()`
-
 */
-
 class GradientFittingTraits
 {
 public:
@@ -26,14 +24,12 @@ public:
 /// @{
 
 /*!
-The number type must follow the model
+The number type must follow the model `FieldNumberType`.
-`FieldNumberType`.
 */
 typedef unspecified_type FT;
 
 /*!
-The point type on
+The (weightless) point type.
-which the function is defined and interpolated.
 */
 typedef unspecified_type Point_d;
 
@@ -48,15 +44,11 @@ The corresponding vector type.
 typedef unspecified_type Vector_d;
 
 /*!
-defines a
+defines a matrix type. Must provide the following member functions :
-matrix type.
-Must provide the following member functions :
 
-`Aff_transformation tr.inverse ()` which gives the inverse
+`Aff_transformation tr.inverse ()`, which gives the inverse transformation, and
-transformation, and
 
-`Aff_transformation tr.transform( Vector v)` which returns the
+`Aff_transformation tr.transform(Vector v)`, which returns the multiplication of `tr` with `v`.
-multiplication of `tr` with `v`.
 
 */
 typedef unspecified_type Aff_transformation_d;
@@ -65,9 +57,9 @@ typedef unspecified_type Aff_transformation_d;
 A constructor object for `Point_d`.
 Provides :
 
-`Point_d operator() (Point_d p)` which simply returns `p`
+`Point_d operator() (Point_d p)`, which simply returns `p`
 
-`Point_d operator() (Weighted_point wp)` which returns the bare point contained in `wp`.
+`Point_d operator() (Weighted_point_d wp)`, which returns the bare point contained in `wp`.
 */
 typedef unspecified_type Construct_point_d;
 
@@ -76,11 +68,9 @@ A constructor object for
 `Vector_d`.
 Provides :
 
-`Vector_d operator() (Point_d a, Point_d b)` which produces the
+`Vector_d operator() (Point_d p, Point_d q)`, which produces the vector `q - p` and
-vector `b - a` and
 
-`Vector_d operator() (Null_vector NULL_VECTOR)` which introduces
+`Vector_d operator() (Null_vector NULL_VECTOR)`, which introduces the null vector.
-the null vector.
 */
 typedef unspecified_type Construct_vector_d;
 
@@ -89,44 +79,45 @@ Constructor object for
 `Vector_d`.
 Provides :
 
-`Vector_d operator() (Vector_d v,FT scale)` which produces the
+`Vector_d operator() (Vector_d v, FT scale)`, which produces the vector `v` scaled by a factor `scale`.
-vector `v` scaled by a factor `scale`.
 */
 typedef unspecified_type Construct_scaled_vector_d;
 
 /*!
-Constructor object for
+Constructor object for `FT`. Provides the operator:
-`Aff_transformation_d`. Provides :
 
-`Aff_transformation_d operator()()` which introduces an affine
+`FT operator() (Point_d p, Point_d q)`, which the squared distance between `p` and `q`.
-transformation whose matrix has only zero entries.
+*/
+typedef unspecified_type Compute_squared_distance_d;
+
+/*!
+Constructor object for `Aff_transformation_d`. Provides :
+
+`Aff_transformation_d operator()()`, which introduces an affine transformation
+whose matrix has only zero entries.
 */
 typedef unspecified_type Construct_null_matrix_d;
 
 /*!
-Constructor object for
+Constructor object for `Aff_transformation_d`. Provides :
-`Aff_transformation_d`. Provides :
 
-`Aff_transformation_d operator()(FT scale)` which introduces a
+`Aff_transformation_d operator()(FT scale)`, which introduces a scaling by a scale factor `scale`.
-scaling by a scale factor `scale`.
 */
 typedef unspecified_type Construct_scaling_matrix_d;
 
 /*!
-Constructor object for
+Constructor object for `Aff_transformation_d`. Provides :
-`Aff_transformation_d`. Provides :
 
-`Aff_transformation_d operator()(Aff_transformation_d tr1, Aff_transformation_d tr2)` which returns the sum of the two matrices
+`Aff_transformation_d operator()(Aff_transformation_d tr1, Aff_transformation_d tr2)`,
-representing `tr1` and `tr2`.
+ which returns the sum of the two matrices representing `tr1` and `tr2`.
 */
 typedef unspecified_type Construct_sum_matrix_d;
 
 /*!
-Constructor object for
+Constructor object for `Aff_transformation_d`. Provides :
-`Aff_transformation_d`. Provides :
 
-`Aff_transformation_d operator()(Vector v)` which returns the
+`Aff_transformation_d operator()(Vector v)`, which returns the outer product,
-outer product, i.e.\ the quadratic matrix `v`\f$ ^t\f$`v`.
+i.e.\ the quadratic matrix `v`\f$ ^t\f$`v`.
 */
 typedef unspecified_type Construct_outer_product_d;
 
@@ -149,6 +140,11 @@ GradientFittingTraits();
 
 /*!
 
+*/
+Construct_vector_d construct_point_d_object();
+
+/*!
+
 */
 Construct_vector_d construct_vector_d_object();
 
@@ -159,9 +155,20 @@ Construct_scaled_vector_d construct_scaled_vector_d_object();
 
 /*!
 
+*/
+Compute_squared_distance_d compute_squared_distance_d_object();
+
+/*!
+
 */
 Construct_null_matrix_d construct_null_matrix_d_object();
 
+/*!
+
+*/
+Construct_scaling_matrix_d construct_scaling_matrix_d_object();
+
+
 /*!
 
 */

Interpolation/doc/Interpolation/Concepts/InterpolationTraits.h

@@ -25,14 +25,17 @@ public:
 /// @{
 
 /*!
-The number type must follow the model
+The number type must follow the model `FieldNumberType`.
-`FieldNumberType`.
 */
 typedef unspecified_type FT;
 
 /*!
-The point type on
+The (weightless) point type.
-which the function is defined and interpolated.
+*/
+typedef unspecified_type Point_d;
+
+/*!
+The weighted point type.
 */
 typedef unspecified_type Point_d;
 
@@ -42,12 +45,19 @@ The corresponding vector type.
 typedef unspecified_type Vector_d;
 
 /*!
-A constructor object for
+A constructor object for `Point_d`. Provides :
-`Vector_d`.
-Provides :
 
-`Vector_d operator() (Point_d a, Point_d b)` which produces the
+`Point_d operator() (Point_d p)` which returns the point itself.
-vector `b - a` and
+
+`Point_d operator() (Weighted_point_d wp)` which extracts the bare point from the weighted point.
+*/
+typedef unspecified_type Construct_point_d;
+
+/*!
+A constructor object for `Vector_d`. Provides :
+
+`Vector_d operator() (Point_d p, Point_d q)` which produces the
+vector `q - p` and
 
 `Vector_d operator() (Null_vector NULL_VECTOR)` which introduces
 the null vector.
@@ -55,21 +65,18 @@ the null vector.
 typedef unspecified_type Construct_vector_d;
 
 /*!
-Constructor object for
+Constructor object for `Vector_d`. Provides :
-`Vector_d`.
-Provides :
 
-`Vector_d operator() (Vector_d v,FT scale)` which produces the
+`Vector_d operator() (Vector_d v, FT scale)` which produces the
 vector `v` scaled by a factor `scale`.
 */
 typedef unspecified_type Construct_scaled_vector_d;
 
 /*!
-Constructor
+Constructor object for `FT`. Provides the operator:
-object for `FT`. Provides the operator:
 
-`FT operator() (Point_d a, Point_d b)` returning the squared
+`FT operator() (Point_d p, Point_d q)` returning the squared
-distance between `a` and `b`.
+distance between `p` and `q`.
 */
 typedef unspecified_type Compute_squared_distance_d;
 
@@ -87,6 +94,11 @@ InterpolationTraits();
 
 /*!
 
+*/
+Construct_vector_d construct_point_d_object();
+
+/*!
+
 */
 Construct_vector_d construct_vector_d_object();