**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

## 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

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).

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).

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 distiguished 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 distiguished by calling is_polygon_clockwise.

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.

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.

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.

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`

).

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.

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`

.

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.

- 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.

Returns if `point`

is inside the triangle specified by `a`

, `b`

and `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.

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.

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