mirror of https://github.com/CGAL/cgal
123 lines
7.4 KiB
TeX
123 lines
7.4 KiB
TeX
% +------------------------------------------------------------------------+
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% | Reference manual page: AABBTraits.tex
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% +------------------------------------------------------------------------+
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% | 21.02.2009 Author
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% | Package: Package
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\RCSdef{\RCSAABBTraitsRev}{$Id: header.tex 40270 2007-09-07 15:29:10Z lsaboret $}
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\RCSdefDate{\RCSAABBTraitsDate}{$Date: 2007-09-07 17:29:10 +0200 (Ven, 07 sep 2007) $}
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% |
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\ccRefPageBegin
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%%RefPage: end of header, begin of main body
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% +------------------------------------------------------------------------+
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\begin{ccRefConcept}{AABBTraits}
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%% \ccHtmlCrossLink{} %% add further rules for cross referencing links
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%% \ccHtmlIndexC[concept]{} %% add further index entries
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\ccDefinition
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The concept \ccRefName\ provides the geometric primitive types and methods for the class \ccc{AABB_tree<AT>}.
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\ccTypes
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\ccNestedType{FT}{Value type of the \ccc{Squared_distance} functor.}
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\ccNestedType{Point_3}{Type of a 3D point.}
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\ccNestedType{Primitive}{Type of primitive.
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Must be a model of the concept \ccc{AABBPrimitive}.}
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\ccNestedType{Bounding_box}{Bounding box type.}
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\ccNestedType{enum Axis \{ X_AXIS, Y_AXIS, Z_AXIS \}}{}
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\ccTypedef{typedef std::pair<Point_3, Primitive::Id> Point_and_primitive_id;}{}
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\begin{ccDeprecated}
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\ccTypedef{typedef std::pair<Object, Primitive::Id> Object_and_primitive_id;}{}
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\end{ccDeprecated}
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\ccNestedType{Intersection_and_primitive_id<Query>}{An unary metafunction to aquire the
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return type of intersections with an object of type \ccStyle{Query} through the member typedef \ccStyle{Type}.}
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During the construction of the \ccc{AABB_tree}, the primitives are sorted according to some comparison functions related to the $x$, $y$ or $z$ coordinate axis:
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\ccNestedType{Split_primitives_along_x_axis}{A functor object to split a range of primitives into two sub-ranges along the X-axis. Provides the operator:
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\ccc{void operator()(InputIterator first, InputIterator beyond);} Iterator \ccc{InputIterator} must be a model of RandomAccessIterator and have \ccc{Primitive} as value type. The operator is used for determining the primitives assigned to the two children nodes of a given node, assuming that the goal is to split the X-dimension of the bounding box of the node. The primitives assigned to this node are passed as argument to the operator. It should modify the iterator range in such a way that its first half and its second half correspond to the two children nodes.}
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\ccNestedType{Split_primitives_along_y_axis}{A functor object to split a range of primitives into two sub-ranges along the Y-axis. See \ccc{Split_primitives_along_x_axis} for the detailed description.}
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\ccNestedType{Split_primitives_along_z_axis}{A functor object to split a range of primitives into two sub-ranges along the Z-axis. See \ccc{Split_primitives_along_x_axis} for the detailed description.}
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\ccNestedType{Compute_bbox}{A functor object to compute the bounding box of a set of primitives. Provides the operator:
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\ccc{Bounding_box operator()(Input_iterator begin, Input_iterator beyond);} Iterator \ccc{InputIterator} must have \ccc{Primitive} as value type. }
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\ccNestedType{Splitting_direction}{A functor object to specify the direction along which the bounding box should be split:
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\ccc{Axis operator()(const Bounding_box& bbox);} which returns the direction used for splitting \ccc{bbox}. It is usually the axis aligned with the longest edge of \ccc{bbox}.}
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The following predicates are required for each type \ccc{Query}
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for which the class \ccc{AABB_tree<AT>} may receive an intersection detection or computation query.
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\ccNestedType{Do_intersect}{A functor object to compute intersection predicates between the query and the nodes of the tree. Provides the operators:
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\ccc{bool operator()(const Query & q, const Bounding_box & box);} which returns \ccc{true} iff the query intersects the bounding box, and \ccc{bool operator()(const Query & q, const Primitive & primitive);} which returns \ccc{true} iff the query intersects the primitive.}
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\begin{ccDeprecated}
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\ccNestedType{Intersect}{A functor object to compute the intersection of a query and a primitive. Provides the operator:
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\ccc{boost::optional<Object_and_primitive_id> operator()(const Query & q, const Primitive& primitive);} which returns the intersection as a pair composed of an object and a primitive id, iff the query intersects the primitive.}
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\end{ccDeprecated}
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\ccNestedType{Intersect}{A functor object to compute the intersection of a query and a primitive. Provides the operator:
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\ccc{Intersection_and_primitive_id<Query>::type operator()(const Query & q, const Primitive& primitive);} which returns the intersection as a pair composed of an intersection object and the id of the primitive.}
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The following predicates are required for each type \ccc{Query}
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for which the class \ccc{AABB_tree<AT>} may receive a distance query.
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\ccNestedType{Compare_distance}{A functor object to compute distance comparisons between the query and the nodes of the tree. Provides the operators:
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\ccc{bool operator()(const Query & query, const Bounding_box& box, const Point & closest);} which returns \ccc{true} iff the bounding box is closer to \ccc{query} than \ccc{closest} is, and \ccc{bool operator()(const Query & query, const Primitive & primitive, const Point & closest);} which returns \ccc{true} iff \ccc{primitive} is closer to the \ccc{query} than \ccc{closest} is.}
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\ccNestedType{Closest_point}{A functor object to compute closest point from the query on a primitive. Provides the operator:
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\ccc{Point_3 operator()(const Query& query, const Primitive& primitive, const Point_3 & closest);} which returns the closest point to \ccc{query}, among \ccc{closest} and all points of the primitive.}
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\ccNestedType{Squared_distance}{A functor object to compute the squared distance between the query and a point. Provides the operator:
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\ccc{FT operator()(const Query& query, const Point_3 & p);} which returns the squared distance between \ccc{query} and \ccc{p}.}
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\ccCreationVariable{traits} %% choose variable name
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\ccOperations
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\ccMethod{Split_primitives_along_x_axis split_primitives_along_x_axis_object();}{Returns the primitive splitting functor for the X axis.}
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\ccMethod{Split_primitives_along_y_axis split_primitives_along_y_axis_object();}{Returns the primitive splitting functor for the Y axis.}
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\ccMethod{Split_primitives_along_z_axis split_primitives_along_z_axis_object();}{Returns the primitive splitting functor for the Z axis.}
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\ccMethod{Compute_bbox compute_bbox_object();}{Returns the bounding box constructor.}
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\ccMethod{Do_intersect do_intersect_object();}{Returns the intersection detection functor.}
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\ccMethod{Intersect intersect_object();}{Returns the intersection constructor.}
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\ccMethod{Compare_distance compare_distance_object();}{Returns the distance comparison functor.}
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\ccMethod{Closest_point closest_point_object();}{Returns the closest point constructor.}
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\ccHasModels
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\ccc{AABB_traits<GeomTraits,TrianglePrimitive>}.
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\ccSeeAlso
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\ccc{AABB_traits<GeomTraits,TrianglePrimitive>}\\
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\ccc{AABB_tree<AT>}
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\ccc{AABBPrimitive}
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\end{ccRefConcept}
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% +------------------------------------------------------------------------+
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%%RefPage: end of main body, begin of footer
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\ccRefPageEnd
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% EOF
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% +------------------------------------------------------------------------+
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