K-dimensional tree, specialised for 2-dimensional space. More...

#include <kdtree.hpp>

Data Structures
struct	node
	Type of a node in the tree. More...

Public Member Functions
	Kdtree ()
	Construct a new Kdtree with the given xyfunc.
template<typename It>
void	Build (It begin, It end)
	Clear and rebuild the tree from a new sequence of elements,.
void	Clear ()
	Clear the tree.
void	Rebuild ()
	Reconstruct the tree with the same elements, letting it be fully balanced.
void	Insert (const T &element)
	Insert a single element in the tree.
void	Remove (const T &element)
	Remove a single element from the tree, if it exists.
size_t	Count () const
	Get number of elements stored in tree.
T	FindNearest (CoordT x, CoordT y) const
	Find the element closest to given coordinate, in Manhattan distance.
template<typename Outputter>
void	FindContained (CoordT x1, CoordT y1, CoordT x2, CoordT y2, const Outputter &outputter) const
	Find all items contained within the given rectangle.
std::vector< T >	FindContained (CoordT x1, CoordT y1, CoordT x2, CoordT y2) const
	Find all items contained within the given rectangle.

Private Types
using	node_distance = std::pair<T, DistT>
	A data element and its distance to a searched-for point.

Private Member Functions
size_t	AddNode (const T &element)
	Create one new node in the tree.
template<typename It>
CoordT	SelectSplitCoord (It begin, It end, int level)
	Find a coordinate value to split a range of elements at.
template<typename It>
size_t	BuildSubtree (It begin, It end, int level)
	Construct a subtree from elements between begin and end iterators.
bool	Rebuild (const T include_element, const T exclude_element)
	Rebuild the tree with all existing elements, optionally adding or removing one more.
void	InsertRecursive (const T &element, size_t node_idx, int level)
	Insert one element in the tree somewhere below node_idx.
std::vector< T >	FreeSubtree (size_t node_idx)
	Free all children of the given node.
size_t	RemoveRecursive (const T &element, size_t node_idx, int level)
	Find and remove one element from the tree.
DistT	ManhattanDistance (const T &element, CoordT x, CoordT y) const
node_distance	FindNearestRecursive (CoordT xy[2], size_t node_idx, int level, DistT limit=std::numeric_limits< DistT >::max()) const
	Search a sub-tree for the element nearest to a given point.
template<typename Outputter>
void	FindContainedRecursive (CoordT p1[2], CoordT p2[2], size_t node_idx, int level, const Outputter &outputter) const
size_t	CountValue (const T &element, size_t node_idx) const
	Debugging function, counts number of occurrences of an element regardless of its correct position in the tree.
void	IncrementUnbalanced (size_t amount=1)
bool	IsUnbalanced () const
	Check if the entire tree is in need of rebuilding.
void	CheckInvariant (size_t node_idx, int level, CoordT min_x, CoordT max_x, CoordT min_y, CoordT max_y) const
	Verify that the invariant is true for a sub-tree, assert if not.
void	CheckInvariant () const
	Verify the invariant for the entire tree, does nothing unless KDTREE_DEBUG is defined.

Static Private Member Functions
static node_distance	SelectNearestNodeDistance (const node_distance &a, const node_distance &b)
	Ordering function for node_distance objects, elements with equal distance are ordered by less-than comparison.

Private Attributes
std::vector< node >	nodes
	Pool of all nodes in the tree.
std::vector< size_t >	free_list
	List of dead indices in the nodes vector.
size_t	root
	Index of root node.
size_t	unbalanced
	Number approximating how unbalanced the tree might be.

Static Private Attributes
static const size_t	INVALID_NODE = SIZE_MAX
	Index value indicating no-such-node.
static const size_t	MIN_REBALANCE_THRESHOLD = 8
	Arbitrary value for "not worth rebalancing".

Detailed Description

template<typename T, typename TxyFunc, typename CoordT, typename DistT>
class Kdtree< T, TxyFunc, CoordT, DistT >

K-dimensional tree, specialised for 2-dimensional space.

This is not intended as a primary storage of data, but as an index into existing data. Usually the type stored by this tree should be an index into an existing array.

This implementation assumes Manhattan distances are used.

Be careful when using this in game code, depending on usage pattern, the tree shape may end up different for different clients in multiplayer, causing iteration order to differ and possibly having elements returned in different order. The using code should be designed to produce the same result regardless of iteration order.

The element type T must be less-than comparable for FindNearest to work.

Template Parameters

T	Type stored in the tree, should be cheap to copy.
TxyFunc	Functor type to extract coordinate from a T value and dimension index (0 or 1).
CoordT	Type of coordinate values extracted via TxyFunc.
DistT	Type to use for representing distance values.

Definition at line 33 of file kdtree.hpp.

Member Typedef Documentation

◆ node_distance

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

using Kdtree< T, TxyFunc, CoordT, DistT >::node_distance = std::pair<T, DistT>

private

A data element and its distance to a searched-for point.

Definition at line 254 of file kdtree.hpp.

Constructor & Destructor Documentation

◆ Kdtree()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

Kdtree< T, TxyFunc, CoordT, DistT >::Kdtree ( )

inline

Construct a new Kdtree with the given xyfunc.

Definition at line 406 of file kdtree.hpp.

Member Function Documentation

◆ AddNode()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

size_t Kdtree< T, TxyFunc, CoordT, DistT >::AddNode ( const T & element )

inlineprivate

Create one new node in the tree.

Parameters

element The element to add.

Returns: The element's index in the pool.

Definition at line 56 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::BuildSubtree(), Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Insert(), and Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::InsertRecursive().

◆ Build()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

template<typename It>

void Kdtree< T, TxyFunc, CoordT, DistT >::Build	(	It	begin,
		It	end )

inline

Clear and rebuild the tree from a new sequence of elements,.

Template Parameters

It	Iterator type for element sequence.

Parameters

begin	First element in sequence.
end	One past last element in sequence.

Definition at line 415 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Rebuild().

◆ BuildSubtree()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

template<typename It>

size_t Kdtree< T, TxyFunc, CoordT, DistT >::BuildSubtree	(	It	begin,
		It	end,
		int	level )

inlineprivate

Construct a subtree from elements between begin and end iterators.

Parameters

begin	The begin of the range to consider.
end	The end of the range to consider.
level	The depth into the tree.

Returns: The index of root.

Definition at line 92 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Build(), Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::BuildSubtree(), and Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::RemoveRecursive().

◆ CheckInvariant() [1/2]

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

void Kdtree< T, TxyFunc, CoordT, DistT >::CheckInvariant ( ) const

inlineprivate

Verify the invariant for the entire tree, does nothing unless KDTREE_DEBUG is defined.

Definition at line 397 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Build(), Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::CheckInvariant(), Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::CheckInvariant(), Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Insert(), and Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Remove().

◆ CheckInvariant() [2/2]

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

void Kdtree< T, TxyFunc, CoordT, DistT >::CheckInvariant	(	size_t	node_idx,
		int	level,
		CoordT	min_x,
		CoordT	max_x,
		CoordT	min_y,
		CoordT	max_y ) const

inlineprivate

Verify that the invariant is true for a sub-tree, assert if not.

Parameters

node_idx	The root of the sub-tree.
level	The current level in the tree.
min_x	The expected minimum X-coordinate.
max_x	The expected maximum X-coordinate.
min_y	The expected minimum Y-coordinate.
max_y	The expected maximum Y-coordinate.

Definition at line 372 of file kdtree.hpp.

◆ Clear()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

void Kdtree< T, TxyFunc, CoordT, DistT >::Clear ( )

inline

Clear the tree.

Definition at line 430 of file kdtree.hpp.

◆ Count()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

size_t Kdtree< T, TxyFunc, CoordT, DistT >::Count ( ) const

inline

Get number of elements stored in tree.

Returns: The element count.

Definition at line 488 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::FindContained(), Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::FindNearest(), Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Insert(), Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::IsUnbalanced(), Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Rebuild(), and Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Remove().

◆ CountValue()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

size_t Kdtree< T, TxyFunc, CoordT, DistT >::CountValue	(	const T &	element,
		size_t	node_idx ) const

inlineprivate

Debugging function, counts number of occurrences of an element regardless of its correct position in the tree.

Parameters

element	The element to look for.
node_idx	The root to start searching from.

Returns: The number of occurences.

Definition at line 340 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::CountValue().

◆ FindContained() [1/2]

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

std::vector< T > Kdtree< T, TxyFunc, CoordT, DistT >::FindContained	(	CoordT	x1,
		CoordT	y1,
		CoordT	x2,
		CoordT	y2 ) const

inline

Find all items contained within the given rectangle.

Note: End coordinates are exclusive, x1 < x2 && y1 < y2 is a precondition.

Parameters

x1	Start first coordinate, points found are greater or equals to this.
y1	Start second coordinate, points found are greater or equals to this.
x2	End first coordinate, points found are less than this.
y2	End second coordinate, points found are less than this.

Returns: The result of the search.

Definition at line 541 of file kdtree.hpp.

◆ FindContained() [2/2]

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

template<typename Outputter>

void Kdtree< T, TxyFunc, CoordT, DistT >::FindContained	(	CoordT	x1,
		CoordT	y1,
		CoordT	x2,
		CoordT	y2,
		const Outputter &	outputter ) const

inline

Find all items contained within the given rectangle.

Note: Start coordinates are inclusive, end coordinates are exclusive. x1 < x2 && y1 < y2 is a precondition.

Parameters

x1	Start first coordinate, points found are greater or equals to this.
y1	Start second coordinate, points found are greater or equals to this.
x2	End first coordinate, points found are less than this.
y2	End second coordinate, points found are less than this.
outputter	Callback used to return values from the search.

Definition at line 520 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::FindContained(), and ForAllStationsRadius().

◆ FindContainedRecursive()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

template<typename Outputter>

void Kdtree< T, TxyFunc, CoordT, DistT >::FindContainedRecursive	(	CoordT	p1[2],
		CoordT	p2[2],
		size_t	node_idx,
		int	level,
		const Outputter &	outputter ) const

inlineprivate

Definition at line 312 of file kdtree.hpp.

◆ FindNearest()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

T Kdtree< T, TxyFunc, CoordT, DistT >::FindNearest	(	CoordT	x,
		CoordT	y ) const

inline

Find the element closest to given coordinate, in Manhattan distance.

For multiple elements with the same distance, the one comparing smaller with a less-than comparison is chosen.

Parameters

x	The X-coordinate.
y	The Y-coordinate.

Returns: The nearest element.

Definition at line 502 of file kdtree.hpp.

◆ FindNearestRecursive()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

node_distance Kdtree< T, TxyFunc, CoordT, DistT >::FindNearestRecursive	(	CoordT	xy[2],
		size_t	node_idx,
		int	level,
		DistT	limit = std::numeric_limits<DistT>::max() ) const

inlineprivate

Search a sub-tree for the element nearest to a given point.

Parameters

xy	The coordinate to start from.
node_idx	The root node to start from.
level	The current search level.
limit	Distance to limit searching at.

Returns: The distance to the nearest element.

Definition at line 277 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::FindNearest(), and Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::FindNearestRecursive().

◆ FreeSubtree()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

std::vector< T > Kdtree< T, TxyFunc, CoordT, DistT >::FreeSubtree ( size_t node_idx )

inlineprivate

Free all children of the given node.

Parameters

node_idx The root node.

Returns: Collection of elements that were removed from tree.

Definition at line 178 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Rebuild(), and Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::RemoveRecursive().

◆ IncrementUnbalanced()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

void Kdtree< T, TxyFunc, CoordT, DistT >::IncrementUnbalanced ( size_t amount = 1 )

inlineprivate

Definition at line 347 of file kdtree.hpp.

◆ Insert()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

void Kdtree< T, TxyFunc, CoordT, DistT >::Insert ( const T & element )

inline

Insert a single element in the tree.

Repeatedly inserting single elements may cause the tree to become unbalanced. Undefined behaviour if the element already exists in the tree.

Parameters

element The elemnt to add.

Definition at line 452 of file kdtree.hpp.

◆ InsertRecursive()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

void Kdtree< T, TxyFunc, CoordT, DistT >::InsertRecursive	(	const T &	element,
		size_t	node_idx,
		int	level )

inlineprivate

Insert one element in the tree somewhere below node_idx.

Parameters

element	The element to insert.
node_idx	The root of the sub-tree to try to insert to.
level	The current depth in the tree.

Definition at line 148 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Insert(), and Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::InsertRecursive().

◆ IsUnbalanced()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

bool Kdtree< T, TxyFunc, CoordT, DistT >::IsUnbalanced ( ) const

inlineprivate

Check if the entire tree is in need of rebuilding.

Returns: true iff the tree should be rebalanced.

Definition at line 356 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Insert(), and Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Remove().

◆ ManhattanDistance()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

DistT Kdtree< T, TxyFunc, CoordT, DistT >::ManhattanDistance	(	const T &	element,
		CoordT	x,
		CoordT	y ) const

inlineprivate

Definition at line 248 of file kdtree.hpp.

◆ Rebuild() [1/2]

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

void Kdtree< T, TxyFunc, CoordT, DistT >::Rebuild ( )

inline

Reconstruct the tree with the same elements, letting it be fully balanced.

Definition at line 441 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Insert(), Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Rebuild(), and Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Remove().

◆ Rebuild() [2/2]

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

bool Kdtree< T, TxyFunc, CoordT, DistT >::Rebuild	(	const T *	include_element,
		const T *	exclude_element )

inlineprivate

Rebuild the tree with all existing elements, optionally adding or removing one more.

Parameters

include_element	Element to add to the tree, if not `nullptr`.
exclude_element	Element to remove from the tree, if not `nullptr`.

Returns: true iff the tree is still considered balanced.

Definition at line 118 of file kdtree.hpp.

◆ Remove()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

void Kdtree< T, TxyFunc, CoordT, DistT >::Remove ( const T & element )

inline

Remove a single element from the tree, if it exists.

Since elements are stored in interior nodes as well as leaf nodes, removing one may require a larger sub-tree to be re-built. Because of this, worst case run time is as bad as a full tree rebuild.

Parameters

element The element to remove.

Definition at line 472 of file kdtree.hpp.

◆ RemoveRecursive()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

size_t Kdtree< T, TxyFunc, CoordT, DistT >::RemoveRecursive	(	const T &	element,
		size_t	node_idx,
		int	level )

inlineprivate

Find and remove one element from the tree.

Parameters

element	The element to search for
node_idx	Sub-tree to search in
level	Current depth in the tree

Returns: New root node index of the sub-tree processed

Definition at line 209 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::Remove(), and Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::RemoveRecursive().

◆ SelectNearestNodeDistance()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

node_distance Kdtree< T, TxyFunc, CoordT, DistT >::SelectNearestNodeDistance	(	const node_distance &	a,
		const node_distance &	b )

inlinestaticprivate

Ordering function for node_distance objects, elements with equal distance are ordered by less-than comparison.

Parameters

a	The first distance to compare.
b	The second distance to compare.

Returns: The nearest distance.

Definition at line 261 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::FindNearestRecursive().

◆ SelectSplitCoord()

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

template<typename It>

CoordT Kdtree< T, TxyFunc, CoordT, DistT >::SelectSplitCoord	(	It	begin,
		It	end,
		int	level )

inlineprivate

Find a coordinate value to split a range of elements at.

Parameters

begin	The begin of the range to consider.
end	The end of the range to consider.
level	The depth into the tree.

Returns: The coordinate to split at.

Definition at line 77 of file kdtree.hpp.

Referenced by Kdtree< StationID, Kdtree_StationXYFunc, uint16_t, int >::BuildSubtree().

Field Documentation

◆ free_list

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

std::vector<size_t> Kdtree< T, TxyFunc, CoordT, DistT >::free_list

private

List of dead indices in the nodes vector.

Definition at line 47 of file kdtree.hpp.

◆ INVALID_NODE

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

const size_t Kdtree< T, TxyFunc, CoordT, DistT >::INVALID_NODE = SIZE_MAX

staticprivate

Index value indicating no-such-node.

Definition at line 43 of file kdtree.hpp.

◆ MIN_REBALANCE_THRESHOLD

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

const size_t Kdtree< T, TxyFunc, CoordT, DistT >::MIN_REBALANCE_THRESHOLD = 8

staticprivate

Arbitrary value for "not worth rebalancing".

Definition at line 44 of file kdtree.hpp.

◆ nodes

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

std::vector<node> Kdtree< T, TxyFunc, CoordT, DistT >::nodes

private

Pool of all nodes in the tree.

Definition at line 46 of file kdtree.hpp.

◆ root

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

size_t Kdtree< T, TxyFunc, CoordT, DistT >::root

private

Index of root node.

Definition at line 48 of file kdtree.hpp.

◆ unbalanced

template<typename T, typename TxyFunc, typename CoordT, typename DistT>

size_t Kdtree< T, TxyFunc, CoordT, DistT >::unbalanced

private

Number approximating how unbalanced the tree might be.

Definition at line 49 of file kdtree.hpp.

The documentation for this class was generated from the following file:

src/core/kdtree.hpp

Data Structures

Public Member Functions

Private Types

Private Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ node_distance

Constructor & Destructor Documentation

◆ Kdtree()

Member Function Documentation

◆ AddNode()

◆ Build()

◆ BuildSubtree()

◆ CheckInvariant() [1/2]

◆ CheckInvariant() [2/2]

◆ Clear()

◆ Count()

◆ CountValue()

◆ FindContained() [1/2]

◆ FindContained() [2/2]

◆ FindContainedRecursive()

◆ FindNearest()

◆ FindNearestRecursive()

◆ FreeSubtree()

◆ IncrementUnbalanced()

◆ Insert()

◆ InsertRecursive()

◆ IsUnbalanced()

◆ ManhattanDistance()

◆ Rebuild() [1/2]

◆ Rebuild() [2/2]

◆ Remove()

◆ RemoveRecursive()

◆ SelectNearestNodeDistance()

◆ SelectSplitCoord()

Field Documentation

◆ free_list

◆ INVALID_NODE

◆ MIN_REBALANCE_THRESHOLD

◆ nodes

◆ root

◆ unbalanced