mirror of https://github.com/CGAL/cgal
Sebastien Loriot
GitHub
commit
e4860ccc92
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@ -5,7 +5,7 @@ namespace CGAL {
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\ingroup PkgBoundingVolumesRef
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An object of the class `Min_ellipse_2` is the unique ellipse of smallest area
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enclosing a finite (multi)set of points in two-dimensional euclidean
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enclosing a finite (multi)set of points in two-dimensional Euclidean
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space \f$ \E^2\f$. For a point set \f$ P\f$ we denote by \f$ me(P)\f$ the smallest
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ellipse that contains all points of \f$ P\f$. Note that \f$ me(P)\f$ can be
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degenerate,
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@ -4493,7 +4493,7 @@ cell neighborhood in $O(m)$ time."
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, month = nov
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, year = 1988
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, pages = "75--80"
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, keywords = "weighted euclidean metric, Voronoi partitions, Voronoi diagrams, geometrical problems, point set"
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, keywords = "weighted Euclidean metric, Voronoi partitions, Voronoi diagrams, geometrical problems, point set"
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, update = "93.05 schwarzkopf"
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, annote = "Multiplicative weights in $n$ dimensions. Incremental
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algorithm"
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@ -20463,7 +20463,7 @@ $O(n^2)$ in the plane."
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}
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@article{bg-sfche-89
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, title = "On the space-filling curve heuristic for the euclidean traveling salesman problem"
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, title = "On the space-filling curve heuristic for the Euclidean traveling salesman problem"
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, author = "D. Bertsimas and M. Grigni"
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, journal = "Operations Research Letters"
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, year = 1989
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@ -21005,7 +21005,7 @@ $O(n^2)$ in the plane."
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, update = "98.11 bibrelex, 98.03 mitchell"
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, abstract = "Let $\cal P$ be a finite arrangement of non-overlapping open
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cubes with side-lengths not exceeding 1 in the $3$-dimensional
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euclidean space. Let $S$ and $T$ be two points lying outside
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Euclidean space. Let $S$ and $T$ be two points lying outside
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the open cubes. Assume one needs to find a short path emanating
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from $S$ and terminating at $T$ avoiding the cubes of $\cal P$
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under the restriction that the cubes are not known prior to the search.
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@ -31216,7 +31216,7 @@ determinants."
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, volume = 5
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, year = 1995
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, pages = "125--144"
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, keywords = "spanners, geometric graphs, greedy algorithm, transformational method, sparse spanners, euclidean graphs"
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, keywords = "spanners, geometric graphs, greedy algorithm, transformational method, sparse spanners, Euclidean graphs"
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, succeeds = "cdns-nsrgs-92"
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, update = "96.09 devillers"
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}
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@ -44361,7 +44361,7 @@ information is available. In some cases, it is possible to improve the
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expected randomized complexity of algorithms from $O(n\log n)$ to
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$O(n\log^{\star} n)$. This technique applies in the following
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applications~: triangulation of a simple polygon, skeleton of a simple
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polygon, Delaunay triangulation of points knowing the EMST (euclidean
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polygon, Delaunay triangulation of points knowing the EMST (Euclidean
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minimum spanning tree)."
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}
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@ -137480,7 +137480,7 @@ depth."
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, number = 3
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, year = 1991
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, pages = "221--230"
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, keywords = "constrained relative neighborhood graphs (crng), constrained gabriel graphs (cgg), euclidean plane, Delaunay triangulation"
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, keywords = "constrained relative neighborhood graphs (crng), constrained gabriel graphs (cgg), Euclidean plane, Delaunay triangulation"
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, update = "93.09 rote"
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, annote = "CRNG and CGG are subgraphs of CDT."
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, abstract = "The original relative neighborhood graph (RNG) and
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@ -149747,7 +149747,7 @@ code."
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@book{y-snegi-79
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, author = "I. M. Yaglom"
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, title = "A simple non-euclidean geometry and its physical basis"
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, title = "A simple non-Euclidean geometry and its physical basis"
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, publisher = "Springer-Verlag"
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, year = 1979
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, update = "98.03 bibrelex"
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@ -475,7 +475,7 @@ void ManipulatedFrame::wheelEvent(QWheelEvent *const event,
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////////////////////////////////////////////////////////////////////////////////
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/*! Returns "pseudo-distance" from (x,y) to ball of radius size.
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\arg for a point inside the ball, it is proportional to the euclidean distance
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\arg for a point inside the ball, it is proportional to the Euclidean distance
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to the ball \arg for a point outside the ball, it is proportional to the inverse
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of this distance (tends to zero) on the ball, the function is continuous. */
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static qreal projectOnBall(qreal x, qreal y) {
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@ -19,7 +19,7 @@ remove variant for supporting circle or line of bisector
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call it only when we know that it is a circle
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it will simplify the code of Construct_hyperbolic_bisector_2 at least in some cases
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test bisectors dual functions in special cases of euclidean line segments
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test bisectors dual functions in special cases of Euclidean line segments
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** Hyperbolic_random_points_in_disc
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@ -532,8 +532,8 @@ private:
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Ransac::Parameters op;
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op.probability = dialog.search_probability(); // probability to miss the largest primitive on each iteration.
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op.min_points = dialog.min_points(); // Only extract shapes with a minimum number of points.
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op.epsilon = dialog.epsilon(); // maximum euclidean distance between point and shape.
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op.cluster_epsilon = dialog.cluster_epsilon(); // maximum euclidean distance between points to be clustered.
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op.epsilon = dialog.epsilon(); // maximum Euclidean distance between point and shape.
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op.cluster_epsilon = dialog.cluster_epsilon(); // maximum Euclidean distance between points to be clustered.
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op.normal_threshold = std::cos(CGAL_PI * dialog.normal_tolerance() / 180.); // normal_threshold < dot(surface_normal, point_normal);
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CGAL::Random rand(static_cast<unsigned int>(time(nullptr)));
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@ -397,7 +397,7 @@ template <class pNT> class Polynomial :
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If |Number_type_traits<NT>::Has_gcd == Tag_true| then the division is
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done by \emph{pseudo division} based on a |gcd| operation of |NT|. If
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|Number_type_traits<NT>::Has_gcd == Tag_false| then the division is done
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by \emph{euclidean division} based on the division operation of the
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by \emph{Euclidean division} based on the division operation of the
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field |NT|.
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\textbf{Note} that |NT=int| quickly leads to overflow
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@ -718,7 +718,7 @@ class Polynomial<int> :
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If |Number_type_traits<int>::Has_gcd == Tag_true| then the division is
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done by \emph{pseudo division} based on a |gcd| operation of |int|. If
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|Number_type_traits<int>::Has_gcd == Tag_false| then the division is done
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by \emph{euclidean division} based on the division operation of the
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by \emph{Euclidean division} based on the division operation of the
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field |int|.
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\textbf{Note} that |int=int| quickly leads to overflow
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@ -1018,7 +1018,7 @@ determines the sign for the limit process $x \rightarrow \infty$.
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If |Number_type_traits<double>::Has_gcd == Tag_true| then the division is
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done by \emph{pseudo division} based on a |gcd| operation of |double|. If
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|Number_type_traits<double>::Has_gcd == Tag_false| then the division is done
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by \emph{euclidean division} based on the division operation of the
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by \emph{Euclidean division} based on the division operation of the
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field |double|.
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\textbf{Note} that |double=int| quickly leads to overflow
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@ -1656,7 +1656,7 @@ bool autorefine_triangle_soup(PointRange& soup_points,
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* will be used in `soup_triangles`. if `apply_iterative_snap_rounding` is set to `true`, all duplicates points are removed.
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* `soup_triangles` will be updated to contain both the input triangles and the new subdivided triangles. Degenerate triangles will be removed.
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* Also if `apply_iterative_snap_rounding` option is set to `false`, triangles in `soup_triangles` will be triangles without intersection first, followed by triangles coming from a subdivision induced
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* by an intersection. The named parameter `visitor()` can be used to track the creation and removal of triangles independantly of
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* by an intersection. The named parameter `visitor()` can be used to track the creation and removal of triangles independently of
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* the `apply_iterative_snap_rounding` option.
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* If the `apply_iterative_snap_rounding` parameter is set to `true`, the coordinates of the vertices are rounded to fit within the precision of a double-precision floating point,
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* while trying to make the triangle soup free of intersections. The `snap_grid_size()` parameter limits the drift of the snapped vertices.
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@ -55,7 +55,7 @@ template <class NT>
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double double_ceil(const NT &x){
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using FT = Fraction_traits<NT>;
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if constexpr(FT::Is_fraction::value){
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// If NT is a fraction, the ceil value is the result of the euclidian division of the numerator and the denominator.
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// If NT is a fraction, the ceil value is the result of the Euclidean division of the numerator and the denominator.
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typename FT::Numerator_type num, r, e;
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typename FT::Denominator_type denom;
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typename FT::Decompose()(x,num,denom);
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@ -160,7 +160,7 @@ void repair_triangle_soup(PointRange& points,
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fixer(points, polygons, np);
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}
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// A visitor of Autorefinement to track the correspondance between input and output triangles
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// A visitor of Autorefinement to track the correspondence between input and output triangles
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struct Wrap_snap_visitor : public Autorefinement::Default_visitor
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{
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template< typename Triangle>
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@ -402,7 +402,7 @@ Polynomial<NT> gcdex_(
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*
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* CGALially, computation is performed ``denominator-free'' if
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* supported by the coefficient type via \c CGAL::Fraction_traits
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* (using \c pseudo_gcdex() ), otherwise the euclidean remainder
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* (using \c pseudo_gcdex() ), otherwise the Euclidean remainder
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* sequence is used.
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*
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* \pre \c NT must be a \c Field.
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@ -81,7 +81,7 @@ Then
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& & \sum_{i=r+1}^{n}x_{i} = 1 \\
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& & x \geq 0,
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\end{eqnarray*}
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minimizes the square of the euclidean distance between $conv(P)$ and $conv(Q)$.
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minimizes the square of the Euclidean distance between $conv(P)$ and $conv(Q)$.
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\end{slide}
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\begin{note}
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@ -495,7 +495,7 @@ Then
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& & \sum_{i=r+1}^{n}x_{i} = 1 \\
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& & x \geq 0,
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\end{eqnarray*}
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minimizes the square of the euclidean distance between $conv(P)$ and $conv(Q)$.
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minimizes the square of the Euclidean distance between $conv(P)$ and $conv(Q)$.
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Here, $D=C^{T}C$ is an
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$n \times n$-matrix, but its rank is only $d$.
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\end{slide}
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@ -151,7 +151,7 @@ provided by the vertex class. The degree of a vertex is not cached and cannot be
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from the vertex, but you can calculate this number by manually counting the number of incident halfedges
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around the vertex.
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Each vertex stores a 2D point and a time, which is the euclidean distance from the vertex's point
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Each vertex stores a 2D point and a time, which is the Euclidean distance from the vertex's point
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to the lines supporting each of the defining contour edges of the vertex (the distance is
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the same to each line). Unless the polygon is convex, this distance is not equal to the edges,
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as in the case of a Medial Axis, therefore, the time of a skeleton vertex does not correspond
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@ -7,7 +7,7 @@ computes the separation required between a polygon and the outer frame used to o
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suitable for the computation of outer offset polygons at a given distance.
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Given a non-degenerate strictly-simple 2D polygon whose vertices are passed
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in the range [`first`,`beyond`), calculates the largest euclidean distance
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in the range [`first`,`beyond`), calculates the largest Euclidean distance
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`d` between each input vertex and its corresponding offset vertex at
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a distance `offset`.
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@ -256,7 +256,7 @@ It is necessary to place the frame sufficiently far away from the contour. If it
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that the outward offset contour collides and merges with the inward offset frame, resulting in 1
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instead of 2 offset contours. However, the proper separation between the contour and the frame is
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not directly given by the offset distance at which you want the offset contour. That distance
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must be at least the desired offset plus the largest euclidean distance between an offset vertex
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must be at least the desired offset plus the largest Euclidean distance between an offset vertex
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and its original. This \cgal packages provides a helper function to compute the required separation:
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`compute_outer_frame_margin()`.
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\cgalAdvancedEnd
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@ -1,4 +1,4 @@
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The package Triangulation provides classes for manipulating triangulations in
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euclidean spaces whose dimension can be specified at compile-time or at
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Euclidean spaces whose dimension can be specified at compile-time or at
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run-time. It also provides point location and a class for building Delaunay
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triangulation supporting both point insertion and removal.
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@ -117,7 +117,7 @@ void DemoWindowItem::draw_edge(QPainter* painter, Point source, Point target)
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// 1. Compute the center of the circle supporting the geodesic between src and tar
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// 1.a Inverse src and tar with respect to the unit circle and find the euclidean midpoints of the segments between respectively
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// 1.a Inverse src and tar with respect to the unit circle and find the Euclidean midpoints of the segments between respectively
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// src and its inversion, and tar and its inversion
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double src_norm_2 = src_x*src_x + src_y*src_y; // Can't be too close to zero because determinant was not
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@ -128,7 +128,7 @@ void DemoWindowItem::draw_edge(QPainter* painter, Point source, Point target)
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double tar_inv_x = tar_x / tar_norm_2;
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double tar_inv_y = tar_y / tar_norm_2;
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// coordinates of the euclidean midpoints of the segments [src, src_inv] and [tar, tar_inv]
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// coordinates of the Euclidean midpoints of the segments [src, src_inv] and [tar, tar_inv]
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double src_mid_x = (src_x + src_inv_x) / 2;
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double src_mid_y = (src_y + src_inv_y) / 2;
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double tar_mid_x = (tar_x + tar_inv_x) / 2;
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