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AStar3D¶

An implementation of A* for finding the shortest path between two vertices on a connected graph in 3D space.

Description¶

A* (A star) is a computer algorithm used in pathfinding and graph traversal, the process of plotting short paths among vertices (points), passing through a given set of edges (segments). It enjoys widespread use due to its performance and accuracy. Redot's A* implementation uses points in 3D space and Euclidean distances by default.

You must add points manually with add_point and create segments manually with connect_points. Once done, you can test if there is a path between two points with the are_points_connected function, get a path containing indices by get_id_path, or one containing actual coordinates with get_point_path.

It is also possible to use non-Euclidean distances. To do so, create a class that extends AStar3D and override methods _compute_cost and _estimate_cost. Both take two indices and return a length, as is shown in the following example.

class MyAStar:
    extends AStar3D

    func _compute_cost(u, v):
        return abs(u - v)

    func _estimate_cost(u, v):
        return min(0, abs(u - v) - 1)

public partial class MyAStar : AStar3D
{
    public override float _ComputeCost(long fromId, long toId)
    {
        return Mathf.Abs((int)(fromId - toId));
    }

    public override float _EstimateCost(long fromId, long toId)
    {
        return Mathf.Min(0, Mathf.Abs((int)(fromId - toId)) - 1);
    }
}

_estimate_cost should return a lower bound of the distance, i.e. _estimate_cost(u, v) <= _compute_cost(u, v). This serves as a hint to the algorithm because the custom _compute_cost might be computation-heavy. If this is not the case, make _estimate_cost return the same value as _compute_cost to provide the algorithm with the most accurate information.

If the default _estimate_cost and _compute_cost methods are used, or if the supplied _estimate_cost method returns a lower bound of the cost, then the paths returned by A* will be the lowest-cost paths. Here, the cost of a path equals the sum of the _compute_cost results of all segments in the path multiplied by the weight_scales of the endpoints of the respective segments. If the default methods are used and the weight_scales of all points are set to 1.0, then this equals the sum of Euclidean distances of all segments in the path.

Methods¶

float	_compute_cost(from_id: int, to_id: int) virtual const
float	_estimate_cost(from_id: int, to_id: int) virtual const
void	add_point(id: int, position: Vector3, weight_scale: float = 1.0)
bool	are_points_connected(id: int, to_id: int, bidirectional: bool = true) const
void	clear()
void	connect_points(id: int, to_id: int, bidirectional: bool = true)
void	disconnect_points(id: int, to_id: int, bidirectional: bool = true)
int	get_available_point_id() const
int	get_closest_point(to_position: Vector3, include_disabled: bool = false) const
Vector3	get_closest_position_in_segment(to_position: Vector3) const
PackedInt64Array	get_id_path(from_id: int, to_id: int, allow_partial_path: bool = false)
int	get_point_capacity() const
PackedInt64Array	get_point_connections(id: int)
int	get_point_count() const
PackedInt64Array	get_point_ids()
PackedVector3Array	get_point_path(from_id: int, to_id: int, allow_partial_path: bool = false)
Vector3	get_point_position(id: int) const
float	get_point_weight_scale(id: int) const
bool	has_point(id: int) const
bool	is_point_disabled(id: int) const
void	remove_point(id: int)
void	reserve_space(num_nodes: int)
void	set_point_disabled(id: int, disabled: bool = true)
void	set_point_position(id: int, position: Vector3)
void	set_point_weight_scale(id: int, weight_scale: float)

Method Descriptions¶

float _compute_cost(from_id: int, to_id: int) virtual const 🔗

Called when computing the cost between two connected points.

Note that this function is hidden in the default AStar3D class.

float _estimate_cost(from_id: int, to_id: int) virtual const 🔗

Called when estimating the cost between a point and the path's ending point.

Note that this function is hidden in the default AStar3D class.

void add_point(id: int, position: Vector3, weight_scale: float = 1.0) 🔗

Adds a new point at the given position with the given identifier. The id must be 0 or larger, and the weight_scale must be 0.0 or greater.

The weight_scale is multiplied by the result of _compute_cost when determining the overall cost of traveling across a segment from a neighboring point to this point. Thus, all else being equal, the algorithm prefers points with lower weight_scales to form a path.

var astar = AStar3D.new()
astar.add_point(1, Vector3(1, 0, 0), 4) # Adds the point (1, 0, 0) with weight_scale 4 and id 1

var astar = new AStar3D();
astar.AddPoint(1, new Vector3(1, 0, 0), 4); // Adds the point (1, 0, 0) with weight_scale 4 and id 1

If there already exists a point for the given id, its position and weight scale are updated to the given values.

bool are_points_connected(id: int, to_id: int, bidirectional: bool = true) const 🔗

Returns whether the two given points are directly connected by a segment. If bidirectional is false, returns whether movement from id to to_id is possible through this segment.

void clear() 🔗

Clears all the points and segments.

void connect_points(id: int, to_id: int, bidirectional: bool = true) 🔗

Creates a segment between the given points. If bidirectional is false, only movement from id to to_id is allowed, not the reverse direction.

var astar = AStar3D.new()
astar.add_point(1, Vector3(1, 1, 0))
astar.add_point(2, Vector3(0, 5, 0))
astar.connect_points(1, 2, false)

var astar = new AStar3D();
astar.AddPoint(1, new Vector3(1, 1, 0));
astar.AddPoint(2, new Vector3(0, 5, 0));
astar.ConnectPoints(1, 2, false);

void disconnect_points(id: int, to_id: int, bidirectional: bool = true) 🔗

Deletes the segment between the given points. If bidirectional is false, only movement from id to to_id is prevented, and a unidirectional segment possibly remains.

int get_available_point_id() const 🔗

Returns the next available point ID with no point associated to it.

int get_closest_point(to_position: Vector3, include_disabled: bool = false) const 🔗

Returns the ID of the closest point to to_position, optionally taking disabled points into account. Returns -1 if there are no points in the points pool.

Note: If several points are the closest to to_position, the one with the smallest ID will be returned, ensuring a deterministic result.

Vector3 get_closest_position_in_segment(to_position: Vector3) const 🔗

Returns the closest position to to_position that resides inside a segment between two connected points.

var astar = AStar3D.new()
astar.add_point(1, Vector3(0, 0, 0))
astar.add_point(2, Vector3(0, 5, 0))
astar.connect_points(1, 2)
var res = astar.get_closest_position_in_segment(Vector3(3, 3, 0)) # Returns (0, 3, 0)

var astar = new AStar3D();
astar.AddPoint(1, new Vector3(0, 0, 0));
astar.AddPoint(2, new Vector3(0, 5, 0));
astar.ConnectPoints(1, 2);
Vector3 res = astar.GetClosestPositionInSegment(new Vector3(3, 3, 0)); // Returns (0, 3, 0)

The result is in the segment that goes from y = 0 to y = 5. It's the closest position in the segment to the given point.

PackedInt64Array get_id_path(from_id: int, to_id: int, allow_partial_path: bool = false) 🔗

Returns an array with the IDs of the points that form the path found by AStar3D between the given points. The array is ordered from the starting point to the ending point of the path.

If there is no valid path to the target, and allow_partial_path is true, returns a path to the point closest to the target that can be reached.

var astar = AStar3D.new()
astar.add_point(1, Vector3(0, 0, 0))
astar.add_point(2, Vector3(0, 1, 0), 1) # Default weight is 1
astar.add_point(3, Vector3(1, 1, 0))
astar.add_point(4, Vector3(2, 0, 0))

astar.connect_points(1, 2, false)
astar.connect_points(2, 3, false)
astar.connect_points(4, 3, false)
astar.connect_points(1, 4, false)

var res = astar.get_id_path(1, 3) # Returns [1, 2, 3]

var astar = new AStar3D();
astar.AddPoint(1, new Vector3(0, 0, 0));
astar.AddPoint(2, new Vector3(0, 1, 0), 1); // Default weight is 1
astar.AddPoint(3, new Vector3(1, 1, 0));
astar.AddPoint(4, new Vector3(2, 0, 0));
astar.ConnectPoints(1, 2, false);
astar.ConnectPoints(2, 3, false);
astar.ConnectPoints(4, 3, false);
astar.ConnectPoints(1, 4, false);
long[] res = astar.GetIdPath(1, 3); // Returns [1, 2, 3]

If you change the 2nd point's weight to 3, then the result will be [1, 4, 3] instead, because now even though the distance is longer, it's "easier" to get through point 4 than through point 2.

int get_point_capacity() const 🔗

Returns the capacity of the structure backing the points, useful in conjunction with reserve_space.

PackedInt64Array get_point_connections(id: int) 🔗

Returns an array with the IDs of the points that form the connection with the given point.

var astar = AStar3D.new()
astar.add_point(1, Vector3(0, 0, 0))
astar.add_point(2, Vector3(0, 1, 0))
astar.add_point(3, Vector3(1, 1, 0))
astar.add_point(4, Vector3(2, 0, 0))

astar.connect_points(1, 2, true)
astar.connect_points(1, 3, true)

var neighbors = astar.get_point_connections(1) # Returns [2, 3]

var astar = new AStar3D();
astar.AddPoint(1, new Vector3(0, 0, 0));
astar.AddPoint(2, new Vector3(0, 1, 0));
astar.AddPoint(3, new Vector3(1, 1, 0));
astar.AddPoint(4, new Vector3(2, 0, 0));
astar.ConnectPoints(1, 2, true);
astar.ConnectPoints(1, 3, true);

long[] neighbors = astar.GetPointConnections(1); // Returns [2, 3]

int get_point_count() const 🔗

Returns the number of points currently in the points pool.

PackedInt64Array get_point_ids() 🔗

Returns an array of all point IDs.

PackedVector3Array get_point_path(from_id: int, to_id: int, allow_partial_path: bool = false) 🔗

Returns an array with the points that are in the path found by AStar3D between the given points. The array is ordered from the starting point to the ending point of the path.

If there is no valid path to the target, and allow_partial_path is true, returns a path to the point closest to the target that can be reached.

Note: This method is not thread-safe. If called from a Thread, it will return an empty array and will print an error message.

Vector3 get_point_position(id: int) const 🔗

Returns the position of the point associated with the given id.

float get_point_weight_scale(id: int) const 🔗

Returns the weight scale of the point associated with the given id.

bool has_point(id: int) const 🔗

Returns whether a point associated with the given id exists.

bool is_point_disabled(id: int) const 🔗

Returns whether a point is disabled or not for pathfinding. By default, all points are enabled.

void remove_point(id: int) 🔗

Removes the point associated with the given id from the points pool.

void reserve_space(num_nodes: int) 🔗

Reserves space internally for num_nodes points. Useful if you're adding a known large number of points at once, such as points on a grid. New capacity must be greater or equals to old capacity.

void set_point_disabled(id: int, disabled: bool = true) 🔗

Disables or enables the specified point for pathfinding. Useful for making a temporary obstacle.

void set_point_position(id: int, position: Vector3) 🔗

Sets the position for the point with the given id.

void set_point_weight_scale(id: int, weight_scale: float) 🔗

Sets the weight_scale for the point with the given id. The weight_scale is multiplied by the result of _compute_cost when determining the overall cost of traveling across a segment from a neighboring point to this point.