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
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 = 5distance_3d(p1, p2)
Calculates the distance between two 3D points.
Parameters
p1
table
First point {x, y, z}
p2
table
Second point {x, y, z}
Example
local d = GEOMETRY.distance_3d({x = 0, y = 0, z = 0}, {x = 0, y = 0, z = 10})
-- d = 10midpoint(p1, p2)
Returns the midpoint between two 3D points.
Parameters
p1
table
First point {x, y, z}
p2
table
Second point {x, y, z}
Example
local mid = GEOMETRY.midpoint({x = 0, y = 0, z = 0}, {x = 4, y = 4, z = 4})
-- mid = {x = 2, y = 2, z = 2}is_point_in_rect(point, rect)
Checks if a point is within a 2D rectangle.
Parameters
point
table
The point {x, y}
rect
table
The rectangle {x, y, width, height}
Example
local inside = GEOMETRY.is_point_in_rect({x = 5, y = 5}, {x = 0, y = 0, width = 10, height = 10})
-- inside = trueis_point_in_box(point, box)
Checks if a 3D point is within a box.
Parameters
point
table
The point {x, y, z}
box
table
The box {x, y, z, width, height, depth}
Example
local inside = GEOMETRY.is_point_in_box({x = 2, y = 2, z = 2}, {x = 0, y = 0, z = 0, width = 5, height = 5, depth = 5})is_point_on_line_segment(point, line_start, line_end)
Checks if a 2D point lies on a line segment.
Parameters
point
table
The point {x, y}
line_start
table
Line segment start {x, y}
line_end
table
Line segment end {x, y}
Example
local result = GEOMETRY.is_point_on_line_segment({x = 2, y = 2}, {x = 0, y = 0}, {x = 4, y = 4})project_point_on_line(p, p1, p2)
Projects a point onto a 2D line segment.
Parameters
p
table
Point {x, y}
p1
table
Line start {x, y}
p2
table
Line end {x, y}
Example
local projected = GEOMETRY.project_point_on_line({x = 3, y = 4}, {x = 0, y = 0}, {x = 5, y = 0}) -- projected = {x = 3, y = 0}calculate_slope(p1, p2)
Calculates the slope of a line between two 2D points.
Parameters
p1
table
First point {x,y}
p2
table
Second point {x,y}
Example
local slope = GEOMETRY.calculate_slope({x = 1, y = 2}, {x = 4, y = 6}) -- slope = 1.333angle_between_points(p1, p2)
Returns the angle between two 2D points in degrees.
Parameters
p1
table
The first point {x, y}
p2
table
The second point {x, y}
Example
local angle = GEOMETRY.angle_between_points({ x = 0, y = 0 }, { x = 1, y = 1 })angle_between_3_points(p1, p2, p3)
Calculates the angle between three 3D points (with p2 as the vertex).
Parameters
p1
table
First point {x, y, z}
p2
table
Center/vertex point {x, y, z}
p3
table
Third point {x, y, z}
Example
local angle = GEOMETRY.angle_between_3_points(p1, p2, p3)do_circles_intersect(c1_center, c1_radius, c2_center, c2_radius)
Checks if two 2D circles intersect.
Parameters
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
local result = GEOMETRY.do_circles_intersect({ x = 0, y = 0 }, 5, { x = 3, y = 0 }, 5)is_point_in_circle(point, circle_center, circle_radius)
Checks if a 2D point is inside a circle.
Parameters
point
table
The point to check {x, y}
circle_center
table
Circle center {x, y}
circle_radius
number
Radius of the circle
Example
local inside = GEOMETRY.is_point_in_circle({ x = 2, y = 2 }, { x = 0, y = 0 }, 5)do_lines_intersect(l1_start, l1_end, l2_start, l2_end)
Determines whether two 2D line segments intersect.
Parameters
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
local intersects = GEOMETRY.do_lines_intersect(p1, p2, p3, p4)line_intersects_circle(line_start, line_end, circle_center, circle_radius)
Checks if a line segment intersects with a circle.
Parameters
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
local hit = GEOMETRY.line_intersects_circle(p1, p2, { x = 0, y = 0 }, 10)does_rect_intersect_line(rect, line_start, line_end)
Checks if a 2D rectangle intersects with a line segment.
Parameters
rect
table
Rectangle {x, y, width, height}
line_start
table
Line start {x, y}
line_end
table
Line end {x, y}
Example
local crosses = GEOMETRY.does_rect_intersect_line(rect, p1, p2)closest_point_on_line_segment(point, line_start, line_end)
Returns the closest point on a line segment to a given point.
Parameters
point
table
The point to check {x, y}
line_start
table
Line start {x, y}
line_end
table
Line end {x, y}
Example
local closest = GEOMETRY.closest_point_on_line_segment({ x = 2, y = 2 }, p1, p2)triangle_area_3d(p1, p2, p3)
Returns the area of a 3D triangle given three vertices.
Parameters
p1
table
Vertex 1 {x, y, z}
p2
table
Vertex 2 {x, y, z}
p3
table
Vertex 3 {x, y, z}
Example
local area = GEOMETRY.triangle_area_3d(p1, p2, p3)is_point_in_sphere(point, sphere_center, sphere_radius)
Checks if a 3D point lies inside a sphere.
Parameters
point
table
{x, y, z}
sphere_center
table
Sphere center {x, y, z}
sphere_radius
number
Radius of the sphere
Example
local inside = GEOMETRY.is_point_in_sphere(pos, center, 10)do_spheres_intersect(s1_center, s1_radius, s2_center, s2_radius)
Checks if two spheres intersect.
Parameters
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
local hit = GEOMETRY.do_spheres_intersect(c1, 5, c2, 6)is_point_in_convex_polygon(point, polygon)
Checks if a 2D point lies inside a convex polygon.
Parameters
point
table
{x, y}
polygon
table
List of points { {x,y}, {x,y}, ... }
Example
local inside = GEOMETRY.is_point_in_convex_polygon({ x = 2, y = 3 }, polygon)rotate_point_around_point_2d(point, pivot, angle_degrees)
Rotates a point around another point by degrees.
Parameters
point
table
{x, y}
pivot
table
Rotation center {x, y}
angle_degrees
number
Degrees to rotate
Example
local result = GEOMETRY.rotate_point_around_point_2d({x = 3, y = 3}, {x = 0, y = 0}, 90)distance_point_to_plane(point, plane_point, plane_normal)
Calculates the shortest distance from a point to a plane.
Parameters
point
table
{x, y, z}
plane_point
table
Point on the plane
plane_normal
table
Normal of the plane
Example
local dist = GEOMETRY.distance_point_to_plane(p, plane_p, normal)rotation_to_direction(rotation)
Converts Euler angles into a directional vector.
Parameters
rotation
table
Euler rotation {x, y, z} in °
Example
local dir = GEOMETRY.rotation_to_direction({x = 0, y = 0, z = 90})rotate_box(center, width, length, heading)
Returns the 4 rotated corners of a box in 3D.
Parameters
center
table
Center of box {x, y, z}
width
number
Box width
length
number
Box length
heading
number
Heading in degrees
Example
local corners = GEOMETRY.rotate_box({x=0,y=0,z=0}, 4, 2, 45)calculate_rotation_matrix(heading, pitch, roll)
Returns a basic Z rotation matrix.
Parameters
heading
number
Heading in degrees
pitch
number
Pitch in degrees
roll
number
Roll in degrees
Example
local matrix = GEOMETRY.calculate_rotation_matrix(90, 0, 0)translate_point_to_local_space(point, box_origin, rot_matrix)
Converts world point into local box space.
Parameters
point
table
Point {x, y, z}
box_origin
table
Origin {x, y, z}
rot_matrix
table
3x3 rotation matrix
Example
local local_point = GEOMETRY.translate_point_to_local_space(p, origin, matrix)is_point_in_oriented_box(point, box)
Checks if a point is inside a rotated 3D box.
Parameters
point
table
The point {x, y, z}
box
table
Box config with keys coords, width, height, depth, heading, pitch, roll
Example
local inside = GEOMETRY.is_point_in_oriented_box(pos, box)Last updated