Spelling correction

After review: euclidean -> Euclidean

Bounding_volumes/doc/Bounding_volumes/CGAL/Min_ellipse_2.h

@@ -5,7 +5,7 @@ namespace CGAL {
 \ingroup PkgBoundingVolumesRef
 
 An object of the class `Min_ellipse_2` is the unique ellipse of smallest area
-enclosing a finite (multi)set of points in two-dimensional euclidean
+enclosing a finite (multi)set of points in two-dimensional Euclidean
 space \f$ \E^2\f$. For a point set \f$ P\f$ we denote by \f$ me(P)\f$ the smallest
 ellipse that contains all points of \f$ P\f$. Note that \f$ me(P)\f$ can be
 degenerate,

Documentation/doc/biblio/geom.bib

@@ -4493,7 +4493,7 @@ cell neighborhood in $O(m)$ time."
 , month =       nov
 , year =        1988
 , pages =       "75--80"
-, keywords =    "weighted euclidean metric, Voronoi partitions, Voronoi diagrams, geometrical problems, point set"
+, keywords =    "weighted Euclidean metric, Voronoi partitions, Voronoi diagrams, geometrical problems, point set"
 , update =      "93.05 schwarzkopf"
 , annote =      "Multiplicative weights in $n$ dimensions. Incremental
                  algorithm"
@@ -20463,7 +20463,7 @@ $O(n^2)$ in the plane."
 }
 
 @article{bg-sfche-89
-, title = "On the space-filling curve heuristic for the euclidean traveling salesman problem"
+, title = "On the space-filling curve heuristic for the Euclidean traveling salesman problem"
 , author = "D. Bertsimas and M. Grigni"
 , journal = "Operations Research Letters"
 , year = 1989
@@ -21005,7 +21005,7 @@ $O(n^2)$ in the plane."
 , update =      "98.11 bibrelex, 98.03 mitchell"
 , abstract =    "Let $\cal P$ be a finite arrangement of non-overlapping open
 cubes with side-lengths not exceeding 1 in the $3$-dimensional
-euclidean space. Let $S$ and $T$ be two points lying outside
+Euclidean space. Let $S$ and $T$ be two points lying outside
 the open cubes. Assume one needs to find a short path emanating
 from $S$ and terminating at $T$ avoiding the cubes of $\cal P$
 under the restriction that the cubes are not known prior to the search.
@@ -31216,7 +31216,7 @@ determinants."
 , volume =      5
 , year =        1995
 , pages =       "125--144"
-, keywords =    "spanners, geometric graphs, greedy algorithm, transformational method, sparse spanners, euclidean graphs"
+, keywords =    "spanners, geometric graphs, greedy algorithm, transformational method, sparse spanners, Euclidean graphs"
 , succeeds =    "cdns-nsrgs-92"
 , update =      "96.09 devillers"
 }
@@ -44361,7 +44361,7 @@ information is available.  In some cases, it is possible to improve the
 expected randomized complexity of algorithms from $O(n\log n)$ to
 $O(n\log^{\star} n)$.  This technique applies in the following
 applications~: triangulation of a simple polygon, skeleton of a simple
-polygon, Delaunay triangulation of points knowing the EMST (euclidean
+polygon, Delaunay triangulation of points knowing the EMST (Euclidean
 minimum spanning tree)."
 }
 
@@ -137480,7 +137480,7 @@ depth."
 , number =      3
 , year =        1991
 , pages =       "221--230"
-, keywords =    "constrained relative neighborhood graphs (crng), constrained gabriel graphs (cgg), euclidean plane, Delaunay triangulation"
+, keywords =    "constrained relative neighborhood graphs (crng), constrained gabriel graphs (cgg), Euclidean plane, Delaunay triangulation"
 , update =      "93.09 rote"
 , annote =      "CRNG and CGG are subgraphs of CDT."
 , abstract =    "The original relative neighborhood graph (RNG) and
@@ -149747,7 +149747,7 @@ code."
 
 @book{y-snegi-79
 , author =      "I. M. Yaglom"
-, title =       "A simple non-euclidean geometry and its physical basis"
+, title =       "A simple non-Euclidean geometry and its physical basis"
 , publisher =   "Springer-Verlag"
 , year =        1979
 , update =      "98.03 bibrelex"

GraphicsView/include/CGAL/Qt/manipulatedFrame_impl.h

@@ -475,7 +475,7 @@ void ManipulatedFrame::wheelEvent(QWheelEvent *const event,
 ////////////////////////////////////////////////////////////////////////////////
 
 /*! Returns "pseudo-distance" from (x,y) to ball of radius size.
-\arg for a point inside the ball, it is proportional to the euclidean distance
+\arg for a point inside the ball, it is proportional to the Euclidean distance
 to the ball \arg for a point outside the ball, it is proportional to the inverse
 of this distance (tends to zero) on the ball, the function is continuous. */
 static qreal projectOnBall(qreal x, qreal y) {

Hyperbolic_triangulation_2/TODO

@@ -19,7 +19,7 @@ remove variant for supporting circle or line of bisector
 call it only when we know that it is a circle
 it will simplify the code of Construct_hyperbolic_bisector_2 at least in some cases
 
-test bisectors dual functions in special cases of euclidean line segments
+test bisectors dual functions in special cases of Euclidean line segments
 
 ** Hyperbolic_random_points_in_disc
 

Lab/demo/Lab/Plugins/Point_set/Point_set_shape_detection_plugin.cpp

@@ -532,8 +532,8 @@ private:
     Ransac::Parameters op;
     op.probability = dialog.search_probability();       // probability to miss the largest primitive on each iteration.
     op.min_points = dialog.min_points();          // Only extract shapes with a minimum number of points.
-    op.epsilon = dialog.epsilon();          // maximum euclidean distance between point and shape.
+    op.epsilon = dialog.epsilon();          // maximum Euclidean distance between point and shape.
-    op.cluster_epsilon = dialog.cluster_epsilon();    // maximum euclidean distance between points to be clustered.
+    op.cluster_epsilon = dialog.cluster_epsilon();    // maximum Euclidean distance between points to be clustered.
     op.normal_threshold = std::cos(CGAL_PI * dialog.normal_tolerance() / 180.);   // normal_threshold < dot(surface_normal, point_normal);
 
     CGAL::Random rand(static_cast<unsigned int>(time(nullptr)));

Nef_2/include/CGAL/Nef_2/Polynomial.h

@@ -397,7 +397,7 @@ template <class pNT> class Polynomial :
   If |Number_type_traits<NT>::Has_gcd == Tag_true| then the division is
   done by \emph{pseudo division} based on a |gcd| operation of |NT|.  If
   |Number_type_traits<NT>::Has_gcd == Tag_false| then the division is done
-  by \emph{euclidean division} based on the division operation of the
+  by \emph{Euclidean division} based on the division operation of the
   field |NT|.
 
   \textbf{Note} that |NT=int| quickly leads to overflow
@@ -718,7 +718,7 @@ class Polynomial<int> :
   If |Number_type_traits<int>::Has_gcd == Tag_true| then the division is
   done by \emph{pseudo division} based on a |gcd| operation of |int|.  If
   |Number_type_traits<int>::Has_gcd == Tag_false| then the division is done
-  by \emph{euclidean division} based on the division operation of the
+  by \emph{Euclidean division} based on the division operation of the
   field |int|.
 
   \textbf{Note} that |int=int| quickly leads to overflow
@@ -1018,7 +1018,7 @@ determines the sign for the limit process $x \rightarrow \infty$.
   If |Number_type_traits<double>::Has_gcd == Tag_true| then the division is
   done by \emph{pseudo division} based on a |gcd| operation of |double|.  If
   |Number_type_traits<double>::Has_gcd == Tag_false| then the division is done
-  by \emph{euclidean division} based on the division operation of the
+  by \emph{Euclidean division} based on the division operation of the
   field |double|.
 
   \textbf{Note} that |double=int| quickly leads to overflow

Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/triangle_soup_snap_rounding.h

@@ -55,7 +55,7 @@ template <class NT>
 double double_ceil(const NT &x){
   using FT = Fraction_traits<NT>;
   if constexpr(FT::Is_fraction::value){
-    // If NT is a fraction, the ceil value is the result of the euclidean division of the numerator and the denominator.
+    // If NT is a fraction, the ceil value is the result of the Euclidean division of the numerator and the denominator.
     typename FT::Numerator_type num, r, e;
     typename FT::Denominator_type denom;
     typename FT::Decompose()(x,num,denom);

Polynomial/include/CGAL/Polynomial/polynomial_gcd.h

@@ -402,7 +402,7 @@ Polynomial<NT> gcdex_(
  *
  *  CGALially, computation is performed ``denominator-free'' if
  *  supported by the coefficient type via \c CGAL::Fraction_traits
- *  (using \c pseudo_gcdex() ), otherwise the euclidean remainder
+ *  (using \c pseudo_gcdex() ), otherwise the Euclidean remainder
  *  sequence is used.
  *
  *  \pre \c NT must be a \c Field.

QP_solver/doc/QP_solver/fig_src/documentation/QP_solver_talk.tex

@@ -81,7 +81,7 @@ Then
      &          & \sum_{i=r+1}^{n}x_{i} = 1 \\
      &          & x \geq 0,
 \end{eqnarray*}
-minimizes the square of the euclidean distance between $conv(P)$ and $conv(Q)$.
+minimizes the square of the Euclidean distance between $conv(P)$ and $conv(Q)$.
 \end{slide}
 
 \begin{note}
@@ -495,7 +495,7 @@ Then
      &          & \sum_{i=r+1}^{n}x_{i} = 1 \\
      &          & x \geq 0,
 \end{eqnarray*}
-minimizes the square of the euclidean distance between $conv(P)$ and $conv(Q)$.
+minimizes the square of the Euclidean distance between $conv(P)$ and $conv(Q)$.
 Here, $D=C^{T}C$ is an
 $n \times n$-matrix, but its rank is only $d$.
 \end{slide}

Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/Straight_skeleton_2.h

@@ -151,7 +151,7 @@ provided by the vertex class. The degree of a vertex is not cached and cannot be
 from the vertex, but you can calculate this number by manually counting the number of incident halfedges
 around the vertex.
 
-Each vertex stores a 2D point and a time, which is the euclidean distance from the vertex's point
+Each vertex stores a 2D point and a time, which is the Euclidean distance from the vertex's point
 to the lines supporting each of the defining contour edges of the vertex (the distance is
 the same to each line). Unless the polygon is convex, this distance is not equal to the edges,
 as in the case of a Medial Axis, therefore, the time of a skeleton vertex does not correspond

Straight_skeleton_2/doc/Straight_skeleton_2/CGAL/compute_outer_frame_margin.h

@@ -7,7 +7,7 @@ computes the separation required between a polygon and the outer frame used to o
 suitable for the computation of outer offset polygons at a given distance.
 
 Given a non-degenerate strictly-simple 2D polygon whose vertices are passed
-in the range [`first`,`beyond`), calculates the largest euclidean distance
+in the range [`first`,`beyond`), calculates the largest Euclidean distance
 `d` between each input vertex and its corresponding offset vertex at
 a distance `offset`.
 

Straight_skeleton_2/doc/Straight_skeleton_2/Straight_skeleton_2.txt

@@ -256,7 +256,7 @@ It is necessary to place the frame sufficiently far away from the contour. If it
 that the outward offset contour collides and merges with the inward offset frame, resulting in 1
 instead of 2 offset contours. However, the proper separation between the contour and the frame is
 not directly given by the offset distance at which you want the offset contour. That distance
-must be at least the desired offset plus the largest euclidean distance between an offset vertex
+must be at least the desired offset plus the largest Euclidean distance between an offset vertex
 and its original. This \cgal packages provides a helper function to compute the required separation:
 `compute_outer_frame_margin()`.
 \cgalAdvancedEnd

Triangulation/package_info/Triangulation/description.txt

@@ -1,4 +1,4 @@
 The package Triangulation provides classes for manipulating triangulations in
-euclidean spaces whose dimension can be specified at compile-time or at
+Euclidean spaces whose dimension can be specified at compile-time or at
 run-time. It also provides point location and a class for building Delaunay
 triangulation supporting both point insertion and removal.

Triangulation_on_hyperbolic_surface_2/demo/Triangulation_on_hyperbolic_surface_2/window.cpp

@@ -117,7 +117,7 @@ void DemoWindowItem::draw_edge(QPainter* painter, Point source, Point target)
 
   // 1. Compute the center of the circle supporting the geodesic between src and tar
 
-  // 1.a Inverse src and tar with respect to the unit circle and find the euclidean midpoints of the segments between respectively
+  // 1.a Inverse src and tar with respect to the unit circle and find the Euclidean midpoints of the segments between respectively
   //       src and its inversion, and tar and its inversion
 
   double src_norm_2 = src_x*src_x + src_y*src_y; // Can't be too close to zero because determinant was not
@@ -128,7 +128,7 @@ void DemoWindowItem::draw_edge(QPainter* painter, Point source, Point target)
   double tar_inv_x = tar_x / tar_norm_2;
   double tar_inv_y = tar_y / tar_norm_2;
 
-  // coordinates of the euclidean midpoints of the segments [src, src_inv] and [tar, tar_inv]
+  // coordinates of the Euclidean midpoints of the segments [src, src_inv] and [tar, tar_inv]
   double src_mid_x = (src_x + src_inv_x) / 2;
   double src_mid_y = (src_y + src_inv_y) / 2;
   double tar_mid_x = (tar_x + tar_inv_x) / 2;