Geometry

Inherits: Object

Helper node to calculate generic geometry operations.

Description

Geometry provides users with a set of helper functions to create geometric shapes, compute intersections between shapes, and process various other geometric operations.

Methods

Array	build_box_planes ( Vector3 extents )
Array	build_capsule_planes ( float radius, float height, int sides, int lats, Vector3.Axis axis=2 )
Array	build_cylinder_planes ( float radius, float height, int sides, Vector3.Axis axis=2 )
PoolVector3Array	clip_polygon ( PoolVector3Array points, Plane plane )
Array	clip_polygons_2d ( PoolVector2Array polygon_a, PoolVector2Array polygon_b )
Array	clip_polyline_with_polygon_2d ( PoolVector2Array polyline, PoolVector2Array polygon )
PoolVector2Array	convex_hull_2d ( PoolVector2Array points )
Array	exclude_polygons_2d ( PoolVector2Array polygon_a, PoolVector2Array polygon_b )
Vector3	get_closest_point_to_segment ( Vector3 point, Vector3 s1, Vector3 s2 )
Vector2	get_closest_point_to_segment_2d ( Vector2 point, Vector2 s1, Vector2 s2 )
Vector3	get_closest_point_to_segment_uncapped ( Vector3 point, Vector3 s1, Vector3 s2 )
Vector2	get_closest_point_to_segment_uncapped_2d ( Vector2 point, Vector2 s1, Vector2 s2 )
PoolVector3Array	get_closest_points_between_segments ( Vector3 p1, Vector3 p2, Vector3 q1, Vector3 q2 )
PoolVector2Array	get_closest_points_between_segments_2d ( Vector2 p1, Vector2 q1, Vector2 p2, Vector2 q2 )
int	get_uv84_normal_bit ( Vector3 normal )
Array	intersect_polygons_2d ( PoolVector2Array polygon_a, PoolVector2Array polygon_b )
Array	intersect_polyline_with_polygon_2d ( PoolVector2Array polyline, PoolVector2Array polygon )
bool	is_point_in_circle ( Vector2 point, Vector2 circle_position, float circle_radius )
bool	is_point_in_polygon ( Vector2 point, PoolVector2Array polygon )
bool	is_polygon_clockwise ( PoolVector2Array polygon )
Variant	line_intersects_line_2d ( Vector2 from_a, Vector2 dir_a, Vector2 from_b, Vector2 dir_b )
Dictionary	make_atlas ( PoolVector2Array sizes )
Array	merge_polygons_2d ( PoolVector2Array polygon_a, PoolVector2Array polygon_b )
Array	offset_polygon_2d ( PoolVector2Array polygon, float delta, PolyJoinType join_type=0 )
Array	offset_polyline_2d ( PoolVector2Array polyline, float delta, PolyJoinType join_type=0, PolyEndType end_type=3 )
bool	point_is_inside_triangle ( Vector2 point, Vector2 a, Vector2 b, Vector2 c ) const
Variant	ray_intersects_triangle ( Vector3 from, Vector3 dir, Vector3 a, Vector3 b, Vector3 c )
float	segment_intersects_circle ( Vector2 segment_from, Vector2 segment_to, Vector2 circle_position, float circle_radius )
PoolVector3Array	segment_intersects_convex ( Vector3 from, Vector3 to, Array planes )
PoolVector3Array	segment_intersects_cylinder ( Vector3 from, Vector3 to, float height, float radius )
Variant	segment_intersects_segment_2d ( Vector2 from_a, Vector2 to_a, Vector2 from_b, Vector2 to_b )
PoolVector3Array	segment_intersects_sphere ( Vector3 from, Vector3 to, Vector3 sphere_position, float sphere_radius )
Variant	segment_intersects_triangle ( Vector3 from, Vector3 to, Vector3 a, Vector3 b, Vector3 c )
PoolIntArray	triangulate_delaunay_2d ( PoolVector2Array points )
PoolIntArray	triangulate_polygon ( PoolVector2Array polygon )

Enumerations

enum PolyBooleanOperation:

• OPERATION_UNION = 0 --- Create regions where either subject or clip polygons (or both) are filled.
• OPERATION_DIFFERENCE = 1 --- Create regions where subject polygons are filled except where clip polygons are filled.
• OPERATION_INTERSECTION = 2 --- Create regions where both subject and clip polygons are filled.
• OPERATION_XOR = 3 --- Create regions where either subject or clip polygons are filled but not where both are filled.

enum PolyJoinType:

• JOIN_SQUARE = 0 --- Squaring is applied uniformally at all convex edge joins at 1 * delta.
• JOIN_ROUND = 1 --- While flattened paths can never perfectly trace an arc, they are approximated by a series of arc chords.
• JOIN_MITER = 2 --- There's a necessary limit to mitered joins since offsetting edges that join at very acute angles will produce excessively long and narrow "spikes". For any given edge join, when miter offsetting would exceed that maximum distance, "square" joining is applied.

enum PolyEndType:

• END_POLYGON = 0 --- Endpoints are joined using the PolyJoinType value and the path filled as a polygon.
• END_JOINED = 1 --- Endpoints are joined using the PolyJoinType value and the path filled as a polyline.
• END_BUTT = 2 --- Endpoints are squared off with no extension.
• END_SQUARE = 3 --- Endpoints are squared off and extended by delta units.
• END_ROUND = 4 --- Endpoints are rounded off and extended by delta units.

Method Descriptions

Array build_box_planes ( Vector3 extents )

Returns an array with 6 Planes that describe the sides of a box centered at the origin. The box size is defined by extents, which represents one (positive) corner of the box (i.e. half its actual size).

Array build_capsule_planes ( float radius, float height, int sides, int lats, Vector3.Axis axis=2 )

Returns an array of Planes closely bounding a faceted capsule centered at the origin with radius radius and height height. The parameter sides defines how many planes will be generated for the side part of the capsule, whereas lats gives the number of latitudinal steps at the bottom and top of the capsule. The parameter axis describes the axis along which the capsule is oriented (0 for X, 1 for Y, 2 for Z).

Array build_cylinder_planes ( float radius, float height, int sides, Vector3.Axis axis=2 )

Returns an array of Planes closely bounding a faceted cylinder centered at the origin with radius radius and height height. The parameter sides defines how many planes will be generated for the round part of the cylinder. The parameter axis describes the axis along which the cylinder is oriented (0 for X, 1 for Y, 2 for Z).

PoolVector3Array clip_polygon ( PoolVector3Array points, Plane plane )

Clips the polygon defined by the points in points against the plane and returns the points of the clipped polygon.

Array clip_polygons_2d ( PoolVector2Array polygon_a, PoolVector2Array polygon_b )

Clips polygon_a against polygon_b and returns an array of clipped polygons. This performs OPERATION_DIFFERENCE between polygons. Returns an empty array if polygon_b completely overlaps polygon_a.

If polygon_b is enclosed by polygon_a, returns an outer polygon (boundary) and inner polygon (hole) which could be distinguished by calling is_polygon_clockwise.

Array clip_polyline_with_polygon_2d ( PoolVector2Array polyline, PoolVector2Array polygon )

Clips polyline against polygon and returns an array of clipped polylines. This performs OPERATION_DIFFERENCE between the polyline and the polygon. This operation can be thought of as cutting a line with a closed shape.

PoolVector2Array convex_hull_2d ( PoolVector2Array points )

Given an array of Vector2s, returns the convex hull as a list of points in counterclockwise order. The last point is the same as the first one.

Array exclude_polygons_2d ( PoolVector2Array polygon_a, PoolVector2Array polygon_b )

Mutually excludes common area defined by intersection of polygon_a and polygon_b (see intersect_polygons_2d) and returns an array of excluded polygons. This performs OPERATION_XOR between polygons. In other words, returns all but common area between polygons.

The operation may result in an outer polygon (boundary) and inner polygon (hole) produced which could be distinguished by calling is_polygon_clockwise.

Vector3 get_closest_point_to_segment ( Vector3 point, Vector3 s1, Vector3 s2 )

Returns the 3D point on the 3D segment (s1, s2) that is closest to point. The returned point will always be inside the specified segment.

Vector2 get_closest_point_to_segment_2d ( Vector2 point, Vector2 s1, Vector2 s2 )

Returns the 2D point on the 2D segment (s1, s2) that is closest to point. The returned point will always be inside the specified segment.

Vector3 get_closest_point_to_segment_uncapped ( Vector3 point, Vector3 s1, Vector3 s2 )

Returns the 3D point on the 3D line defined by (s1, s2) that is closest to point. The returned point can be inside the segment (s1, s2) or outside of it, i.e. somewhere on the line extending from the segment.

Vector2 get_closest_point_to_segment_uncapped_2d ( Vector2 point, Vector2 s1, Vector2 s2 )

Returns the 2D point on the 2D line defined by (s1, s2) that is closest to point. The returned point can be inside the segment (s1, s2) or outside of it, i.e. somewhere on the line extending from the segment.

PoolVector3Array get_closest_points_between_segments ( Vector3 p1, Vector3 p2, Vector3 q1, Vector3 q2 )

Given the two 3D segments (p1, p2) and (q1, q2), finds those two points on the two segments that are closest to each other. Returns a PoolVector3Array that contains this point on (p1, p2) as well the accompanying point on (q1, q2).

PoolVector2Array get_closest_points_between_segments_2d ( Vector2 p1, Vector2 q1, Vector2 p2, Vector2 q2 )

Given the two 2D segments (p1, p2) and (q1, q2), finds those two points on the two segments that are closest to each other. Returns a PoolVector2Array that contains this point on (p1, p2) as well the accompanying point on (q1, q2).

int get_uv84_normal_bit ( Vector3 normal )

Used internally by the engine.

Array intersect_polygons_2d ( PoolVector2Array polygon_a, PoolVector2Array polygon_b )

Intersects polygon_a with polygon_b and returns an array of intersected polygons. This performs OPERATION_INTERSECTION between polygons. In other words, returns common area shared by polygons. Returns an empty array if no intersection occurs.

The operation may result in an outer polygon (boundary) and inner polygon (hole) produced which could be distinguished by calling is_polygon_clockwise.

Array intersect_polyline_with_polygon_2d ( PoolVector2Array polyline, PoolVector2Array polygon )

Intersects polyline with polygon and returns an array of intersected polylines. This performs OPERATION_INTERSECTION between the polyline and the polygon. This operation can be thought of as chopping a line with a closed shape.

bool is_point_in_circle ( Vector2 point, Vector2 circle_position, float circle_radius )

Returns true if point is inside the circle or if it's located exactly on the circle's boundary, otherwise returns false.

bool is_point_in_polygon ( Vector2 point, PoolVector2Array polygon )

Returns true if point is inside polygon or if it's located exactly on polygon's boundary, otherwise returns false.

bool is_polygon_clockwise ( PoolVector2Array polygon )

Returns true if polygon's vertices are ordered in clockwise order, otherwise returns false.

Variant line_intersects_line_2d ( Vector2 from_a, Vector2 dir_a, Vector2 from_b, Vector2 dir_b )

Checks if the two lines (from_a, dir_a) and (from_b, dir_b) intersect. If yes, return the point of intersection as Vector2. If no intersection takes place, returns an empty Variant.

Note: The lines are specified using direction vectors, not end points.

Dictionary make_atlas ( PoolVector2Array sizes )

Given an array of Vector2s representing tiles, builds an atlas. The returned dictionary has two keys: points is a vector of Vector2 that specifies the positions of each tile, size contains the overall size of the whole atlas as Vector2.

Array merge_polygons_2d ( PoolVector2Array polygon_a, PoolVector2Array polygon_b )

Merges (combines) polygon_a and polygon_b and returns an array of merged polygons. This performs OPERATION_UNION between polygons.

The operation may result in an outer polygon (boundary) and inner polygon (hole) produced which could be distinguished by calling is_polygon_clockwise.

Array offset_polygon_2d ( PoolVector2Array polygon, float delta, PolyJoinType join_type=0 )

Inflates or deflates polygon by delta units (pixels). If delta is positive, makes the polygon grow outward. If delta is negative, shrinks the polygon inward. Returns an array of polygons because inflating/deflating may result in multiple discrete polygons. Returns an empty array if delta is negative and the absolute value of it approximately exceeds the minimum bounding rectangle dimensions of the polygon.

Each polygon's vertices will be rounded as determined by join_type, see PolyJoinType.

The operation may result in an outer polygon (boundary) and inner polygon (hole) produced which could be distinguished by calling is_polygon_clockwise.

Note: To translate the polygon's vertices specifically, use the Transform2D.xform method:

var polygon = PoolVector2Array([Vector2(0, 0), Vector2(100, 0), Vector2(100, 100), Vector2(0, 100)])
var offset = Vector2(50, 50)
polygon = Transform2D(0, offset).xform(polygon)
print(polygon) # prints [Vector2(50, 50), Vector2(150, 50), Vector2(150, 150), Vector2(50, 150)]

Array offset_polyline_2d ( PoolVector2Array polyline, float delta, PolyJoinType join_type=0, PolyEndType end_type=3 )

Inflates or deflates polyline by delta units (pixels), producing polygons. If delta is positive, makes the polyline grow outward. Returns an array of polygons because inflating/deflating may result in multiple discrete polygons. If delta is negative, returns an empty array.

Each polygon's vertices will be rounded as determined by join_type, see PolyJoinType.

Each polygon's endpoints will be rounded as determined by end_type, see PolyEndType.

The operation may result in an outer polygon (boundary) and inner polygon (hole) produced which could be distinguished by calling is_polygon_clockwise.

bool point_is_inside_triangle ( Vector2 point, Vector2 a, Vector2 b, Vector2 c ) const

Returns if point is inside the triangle specified by a, b and c.

Variant ray_intersects_triangle ( Vector3 from, Vector3 dir, Vector3 a, Vector3 b, Vector3 c )

Tests if the 3D ray starting at from with the direction of dir intersects the triangle specified by a, b and c. If yes, returns the point of intersection as Vector3. If no intersection takes place, an empty Variant is returned.

float segment_intersects_circle ( Vector2 segment_from, Vector2 segment_to, Vector2 circle_position, float circle_radius )

Given the 2D segment (segment_from, segment_to), returns the position on the segment (as a number between 0 and 1) at which the segment hits the circle that is located at position circle_position and has radius circle_radius. If the segment does not intersect the circle, -1 is returned (this is also the case if the line extending the segment would intersect the circle, but the segment does not).

PoolVector3Array segment_intersects_convex ( Vector3 from, Vector3 to, Array planes )

Given a convex hull defined though the Planes in the array planes, tests if the segment (from, to) intersects with that hull. If an intersection is found, returns a PoolVector3Array containing the point the intersection and the hull's normal. If no intersecion is found, an the returned array is empty.

PoolVector3Array segment_intersects_cylinder ( Vector3 from, Vector3 to, float height, float radius )

Checks if the segment (from, to) intersects the cylinder with height height that is centered at the origin and has radius radius. If no, returns an empty PoolVector3Array. If an intersection takes place, the returned array contains the point of intersection and the cylinder's normal at the point of intersection.

Variant segment_intersects_segment_2d ( Vector2 from_a, Vector2 to_a, Vector2 from_b, Vector2 to_b )

Checks if the two segments (from_a, to_a) and (from_b, to_b) intersect. If yes, return the point of intersection as Vector2. If no intersection takes place, returns an empty Variant.

PoolVector3Array segment_intersects_sphere ( Vector3 from, Vector3 to, Vector3 sphere_position, float sphere_radius )

Checks if the segment (from, to) intersects the sphere that is located at sphere_position and has radius sphere_radius. If no, returns an empty PoolVector3Array. If yes, returns a PoolVector3Array containing the point of intersection and the sphere's normal at the point of intersection.

Variant segment_intersects_triangle ( Vector3 from, Vector3 to, Vector3 a, Vector3 b, Vector3 c )

Tests if the segment (from, to) intersects the triangle a, b, c. If yes, returns the point of intersection as Vector3. If no intersection takes place, an empty Variant is returned.

PoolIntArray triangulate_delaunay_2d ( PoolVector2Array points )

Triangulates the area specified by discrete set of points such that no point is inside the circumcircle of any resulting triangle. Returns a PoolIntArray where each triangle consists of three consecutive point indices into points (i.e. the returned array will have n * 3 elements, with n being the number of found triangles). If the triangulation did not succeed, an empty PoolIntArray is returned.

PoolIntArray triangulate_polygon ( PoolVector2Array polygon )

Triangulates the polygon specified by the points in polygon. Returns a PoolIntArray where each triangle consists of three consecutive point indices into polygon (i.e. the returned array will have n * 3 elements, with n being the number of found triangles). If the triangulation did not succeed, an empty PoolIntArray is returned.