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For the complete documentation index, see llms.txt. This page is also available as Markdown.

Geometry

Geometry Module

Provides utility functions for performing geometric and spatial calculations in 2D and 3D environments.

Accessing the Module

local GEOMETRY <const> = exports.boii_utils:get("modules.geometry")

Shared

distance_2d(p1, p2)

Calculates the distance between two 2D points.

Parameters

Name
Type
Description

p1

table

First point {x, y}

p2

table

Second point {x, y}

Example

local d = GEOMETRY.distance_2d({x = 0, y = 0}, {x = 3, y = 4})
-- d = 5

distance_3d(p1, p2)

Calculates the distance between two 3D points.

Parameters

Name
Type
Description

p1

table

First point {x, y, z}

p2

table

Second point {x, y, z}

Example

midpoint(p1, p2)

Returns the midpoint between two 3D points.

Parameters

Name
Type
Description

p1

table

First point {x, y, z}

p2

table

Second point {x, y, z}

Example

is_point_in_rect(point, rect)

Checks if a point is within a 2D rectangle.

Parameters

Name
Type
Description

point

table

The point {x, y}

rect

table

The rectangle {x, y, width, height}

Example

is_point_in_box(point, box)

Checks if a 3D point is within a box.

Parameters

Name
Type
Description

point

table

The point {x, y, z}

box

table

The box {x, y, z, width, height, depth}

Example

is_point_on_line_segment(point, line_start, line_end)

Checks if a 2D point lies on a line segment.

Parameters

Name
Type
Description

point

table

The point {x, y}

line_start

table

Line segment start {x, y}

line_end

table

Line segment end {x, y}

Example

project_point_on_line(p, p1, p2)

Projects a point onto a 2D line segment.

Parameters

Name
Type
Description

p

table

Point {x, y}

p1

table

Line start {x, y}

p2

table

Line end {x, y}

Example

calculate_slope(p1, p2)

Calculates the slope of a line between two 2D points.

Parameters

Name
Type
Description

p1

table

First point {x,y}

p2

table

Second point {x,y}

Example

angle_between_points(p1, p2)

Returns the angle between two 2D points in degrees.

Parameters

Name
Type
Description

p1

table

The first point {x, y}

p2

table

The second point {x, y}

Example

angle_between_3_points(p1, p2, p3)

Calculates the angle between three 3D points (with p2 as the vertex).

Parameters

Name
Type
Description

p1

table

First point {x, y, z}

p2

table

Center/vertex point {x, y, z}

p3

table

Third point {x, y, z}

Example

do_circles_intersect(c1_center, c1_radius, c2_center, c2_radius)

Checks if two 2D circles intersect.

Parameters

Name
Type
Description

c1_center

table

Center of first circle {x, y}

c1_radius

number

Radius of first circle

c2_center

table

Center of second circle {x, y}

c2_radius

number

Radius of second circle

Example

is_point_in_circle(point, circle_center, circle_radius)

Checks if a 2D point is inside a circle.

Parameters

Name
Type
Description

point

table

The point to check {x, y}

circle_center

table

Circle center {x, y}

circle_radius

number

Radius of the circle

Example

do_lines_intersect(l1_start, l1_end, l2_start, l2_end)

Determines whether two 2D line segments intersect.

Parameters

Name
Type
Description

l1_start

table

Start of line 1 {x, y}

l1_end

table

End of line 1 {x, y}

l2_start

table

Start of line 2 {x, y}

l2_end

table

End of line 2 {x, y}

Example

line_intersects_circle(line_start, line_end, circle_center, circle_radius)

Checks if a line segment intersects with a circle.

Parameters

Name
Type
Description

line_start

table

Line start {x, y}

line_end

table

Line end {x, y}

circle_center

table

Circle center {x, y}

circle_radius

number

Radius of circle

Example

does_rect_intersect_line(rect, line_start, line_end)

Checks if a 2D rectangle intersects with a line segment.

Parameters

Name
Type
Description

rect

table

Rectangle {x, y, width, height}

line_start

table

Line start {x, y}

line_end

table

Line end {x, y}

Example

closest_point_on_line_segment(point, line_start, line_end)

Returns the closest point on a line segment to a given point.

Parameters

Name
Type
Description

point

table

The point to check {x, y}

line_start

table

Line start {x, y}

line_end

table

Line end {x, y}

Example

triangle_area_3d(p1, p2, p3)

Returns the area of a 3D triangle given three vertices.

Parameters

Name
Type
Description

p1

table

Vertex 1 {x, y, z}

p2

table

Vertex 2 {x, y, z}

p3

table

Vertex 3 {x, y, z}

Example

is_point_in_sphere(point, sphere_center, sphere_radius)

Checks if a 3D point lies inside a sphere.

Parameters

Name
Type
Description

point

table

{x, y, z}

sphere_center

table

Sphere center {x, y, z}

sphere_radius

number

Radius of the sphere

Example

do_spheres_intersect(s1_center, s1_radius, s2_center, s2_radius)

Checks if two spheres intersect.

Parameters

Name
Type
Description

s1_center

table

Sphere 1 center {x,y,z}

s1_radius

number

Sphere 1 radius

s2_center

table

Sphere 2 center {x,y,z}

s2_radius

number

Sphere 2 radius

Example

is_point_in_convex_polygon(point, polygon)

Checks if a 2D point lies inside a convex polygon.

Parameters

Name
Type
Description

point

table

{x, y}

polygon

table

List of points { {x,y}, {x,y}, ... }

Example

rotate_point_around_point_2d(point, pivot, angle_degrees)

Rotates a point around another point by degrees.

Parameters

Name
Type
Description

point

table

{x, y}

pivot

table

Rotation center {x, y}

angle_degrees

number

Degrees to rotate

Example

distance_point_to_plane(point, plane_point, plane_normal)

Calculates the shortest distance from a point to a plane.

Parameters

Name
Type
Description

point

table

{x, y, z}

plane_point

table

Point on the plane

plane_normal

table

Normal of the plane

Example

rotation_to_direction(rotation)

Converts Euler angles into a directional vector.

Parameters

Name
Type
Description

rotation

table

Euler rotation {x, y, z} in °

Example

rotate_box(center, width, length, heading)

Returns the 4 rotated corners of a box in 3D.

Parameters

Name
Type
Description

center

table

Center of box {x, y, z}

width

number

Box width

length

number

Box length

heading

number

Heading in degrees

Example

calculate_rotation_matrix(heading, pitch, roll)

Returns a basic Z rotation matrix.

Parameters

Name
Type
Description

heading

number

Heading in degrees

pitch

number

Pitch in degrees

roll

number

Roll in degrees

Example

translate_point_to_local_space(point, box_origin, rot_matrix)

Converts world point into local box space.

Parameters

Name
Type
Description

point

table

Point {x, y, z}

box_origin

table

Origin {x, y, z}

rot_matrix

table

3x3 rotation matrix

Example

is_point_in_oriented_box(point, box)

Checks if a point is inside a rotated 3D box.

Parameters

Name
Type
Description

point

table

The point {x, y, z}

box

table

Box config with keys coords, width, height, depth, heading, pitch, roll

Example

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