mirror of https://github.com/CGAL/cgal
Updated the documentation of Fuzzy Query Items
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Mael Rouxel-Labbé
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affece6748
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e64f271451
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@ -3,11 +3,15 @@ namespace CGAL {
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/*!
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\ingroup RangeQueryItemClasses
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The class `Fuzzy_iso_box` implements fuzzy `d`-dimensional iso boxes. A
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fuzzy iso box with fuzziness value \f$ \epsilon\f$ has as outer
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approximation a box dilated, and as inner approximation a box eroded
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by a `d`-dim square with side length \f$ \epsilon\f$.
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The class `Fuzzy_iso_box` implements fuzzy `d`-dimensional iso boxes. A fuzzy iso
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box with fuzziness value \f$ \epsilon\f$ has as inner and outer approximations
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a box respectively eroded and dilated by a `d`-dim square with side length \f$ \epsilon\f$.
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\attention Points in the interior of the inner approximation are always reported and points
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that are not in the closure of the outer approximation are never reported. Other
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points may or may not be reported. Subsequently, points on the boundary of the
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inner and outer approximations may or may not be reported. Specifically when \f$ \epsilon = 0\f$,
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points on the boundary of the box may or may not be reported.
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\tparam Traits must be a model of the concept
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`SearchTraits`, for example `CGAL::Search_traits_2<CGAL::Simple_cartesian<double> >`.
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@ -45,14 +49,15 @@ typedef Traits::FT FT;
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/// @{
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/*!
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Constructs a fuzzy iso box
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specified by the minimal iso box containing `p` and `q` and fuzziness value `epsilon`.
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\pre `p` must be lexicographically smaller than `q`.
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*/
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Fuzzy_iso_box(Point_d p, Point_d q, FT epsilon=FT(0),Traits t=Traits());
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Construct a fuzzy iso box
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specified by the minimal iso box containing `p` and `q` and fuzziness value `epsilon`.
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\pre `p` must be lexicographically smaller than `q`.
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*/
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Fuzzy_iso_box(Point_d p, Point_d q, FT epsilon=FT(0),Traits t=Traits());
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/*!
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Constructs a fuzzy iso box specified by the minimal iso box containing `p` and `q` and fuzziness value `epsilon`.
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Construct a fuzzy iso box specified by the minimal iso box containing `p` and `q` and fuzziness value `epsilon`.
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\attention Only available in case `Traits` is
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`Search_traits_adapter<Key,PointPropertyMap,BaseTraits>`.
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@ -67,20 +72,20 @@ Fuzzy_iso_box(Traits::Base::Point_d p, Traits::Base::Point_d q, FT epsilon=FT(0)
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/// @{
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/*!
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test whether the fuzzy iso box contains `p`.
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*/
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bool contains(Point_d p) const;
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Test whether the fuzzy iso box contains `p`.
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*/
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bool contains(Point_d p) const;
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/*!
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test whether the inner box intersects the rectangle
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associated with a node of a tree.
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*/
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bool inner_range_intersects(const Kd_tree_rectangle<FT,D>& rectangle) const;
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Test whether the inner box intersects the rectangle
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associated with a node of a tree.
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*/
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bool inner_range_intersects(const Kd_tree_rectangle<FT,D>& rectangle) const;
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/*!
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test whether the outer box encloses the rectangle associated with a node of a tree.
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*/
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bool outer_range_contains(const Kd_tree_rectangle<FT,D>& rectangle) const;
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Test whether the outer box encloses the rectangle associated with a node of a tree.
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*/
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bool outer_range_contains(const Kd_tree_rectangle<FT,D>& rectangle) const;
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/// @}
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@ -3,14 +3,22 @@ namespace CGAL {
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/*!
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\ingroup RangeQueryItemClasses
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The class `Fuzzy_sphere` implements fuzzy `d`-dimensional spheres.
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A fuzzy sphere with radius \f$ r\f$ and fuzziness value \f$ \epsilon\f$ has
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as outer approximation a sphere with radius \f$ r+\epsilon\f$ and
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as inner approximation a sphere with radius \f$ r-\epsilon\f$.
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The class `Fuzzy_sphere` implements fuzzy `d`-dimensional spheres.
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A fuzzy sphere with radius \f$ r\f$ and fuzziness value \f$ \epsilon\f$ has
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as inner approximation a sphere with radius \f$ r-\epsilon\f$ and
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as outer approximation a sphere with radius \f$ r+\epsilon\f$.
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\attention The fuzziness of a `Fuzzy_sphere` is specified by a parameter \f$ \epsilon\f$
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denoting a maximal allowed distance to the boundary of a sphere.
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If the distance to the boundary is at least \f$ \epsilon\f$, points inside the
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object are always reported and points outside the sphere are never reported.
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Points within distance \f$ \epsilon\f$ to the boundary may be or may be not reported.
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Subsequently, points on the inner and outer spheres may or may not be reported
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by a search query. Specifically when \f$ \epsilon = 0\f$, points on the sphere
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of radius \f$ r\f$ may or may not be reported.
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\tparam Traits must be a model of the concept
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`SearchTraits`, for example `CGAL::Cartesian_d<double>`.
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\tparam Traits must be a model of the concept
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`SearchTraits`, for example `CGAL::Cartesian_d<double>`.
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\cgalModels `FuzzyQueryItem`
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@ -46,13 +54,13 @@ typedef Traits::FT FT;
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/// @{
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/*!
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Constructs a fuzzy sphere
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centered at `center` with radius `radius` and fuzziness value `epsilon`.
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*/
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Fuzzy_sphere(Point_d center, FT radius, FT epsilon=FT(0),Traits t=Traits());
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Construct a fuzzy sphere
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centered at `center` with radius `radius` and fuzziness value `epsilon`.
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*/
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Fuzzy_sphere(Point_d center, FT radius, FT epsilon=FT(0),Traits t=Traits());
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/*!
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Constructs a fuzzy sphere centered at `center` with radius `radius` and fuzziness value `epsilon`.
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Construct a fuzzy sphere centered at `center` with radius `radius` and fuzziness value `epsilon`.
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\attention Only available in case `Traits` is `Search_traits_adapter<Key,PointPropertyMap,BaseTraits>`.
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*/
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Fuzzy_sphere(Traits::Base::Point_d center, FT radius, FT epsilon=FT(0), Traits t=Traits());
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@ -63,20 +71,29 @@ Fuzzy_sphere(Traits::Base::Point_d center, FT radius, FT epsilon=FT(0), Traits t
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/// @{
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/*!
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test whether the fuzzy sphere contains `p`.
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*/
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bool contains(const Point_d& p) const;
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Test whether the fuzzy sphere contains `p`.
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That is, whether the distance between the center of the fuzzy sphere and `p` is
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less than \f$ r\f$.
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*/
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bool contains(const Point_d& p) const;
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/*!
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test whether the inner sphere intersects the rectangle
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associated with a node of a tree.
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*/
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bool inner_range_intersects(const Kd_tree_rectangle<FT,D>& rectangle) const;
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Test whether the inner sphere intersects the rectangle
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associated with a node of a tree.
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That is, whether the minimal distance between the center of the fuzzy sphere and
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`rectangle` is less than \f$ r-\epsilon\f$.
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*/
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bool inner_range_intersects(const Kd_tree_rectangle<FT,D>& rectangle) const;
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/*!
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test whether the outer sphere encloses the rectangle associated with a node of a tree.
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*/
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bool outer_range_contains(const Kd_tree_rectangle<FT,D>& rectangle) const;
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Test whether the outer sphere encloses the rectangle associated with a node of a tree.
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That is, whether the minimal distance between the center of the fuzzy sphere and
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`rectangle` is less than \f$ r+\epsilon\f$.
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*/
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bool outer_range_contains(const Kd_tree_rectangle<FT,D>& rectangle) const;
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/// @}
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@ -148,23 +148,22 @@ GeneralDistance, Splitter, SpatialTree>`
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\subsection Spatial_searchingRangeSearching Range Searching
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<I>Exact range searching</I> and <I>approximate range searching</I> is
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<I>Exact range searching</I> and <I>approximate range searching</I> are
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supported using exact or fuzzy `d`-dimensional objects enclosing a
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region. The fuzziness of the query object is specified by a parameter
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\f$ \epsilon\f$ denoting a maximal allowed distance to the boundary of a
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query object. If the distance to the boundary is at least
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\f$ \epsilon\f$, points inside the object are always reported and points
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outside the object are never reported. Points within distance
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\f$ \epsilon\f$ to the boundary may be or may be not reported. For exact
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range searching the fuzziness parameter \f$ \epsilon\f$ is set to zero.
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\f$ \epsilon\f$ used to define inner and outer approximations of the query object.
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Points in the interior of the inner approximation are always reported and points
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that are not in the closure of the outer approximation are never reported. Other
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points may or may not be reported. For exact range searching,
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the fuzziness parameter \f$ \epsilon\f$ is set to zero.
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The class `Kd_tree` implements range searching in the method `search`,
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which is a template method with an output iterator and a model of the
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concept `FuzzyQueryItem` as `Fuzzy_iso_box`
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or `Fuzzy_sphere`.
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For range searching of large data sets the user may set the parameter `bucket_size`
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used in building the `kd` tree to a large value (e.g. 100),
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because in general the query time will be less then using the default value.
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concept `FuzzyQueryItem` as `Fuzzy_iso_box`
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or `Fuzzy_sphere`.
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For range searching of large data sets, the user may set the parameter `bucket_size`
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used in building the `kd` tree to a large value (e.g. 100),
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because in general the query time will be less than using the default value.
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\section Spatial_SearchingSplitting_rule_section Splitting Rules
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