LEEF

• Index

Contents

• Functions
• Tables

Modules

• b3d_reader
• b3d_writer
• b3d_nodes
• proxy_table
• binary
• utils
• paths
• math.bound2
• math.bound3
• math.bvh
• math.color
• math.constants
• math.intersect
• math.mat4
• math.mesh
• math.octree
• math.quat
• math.simplex
• math.utils
• math.vec2
• math.vec3

Classes

• new_class

Module math.intersect

Various geometric intersections.

this is apart of the LEEF-math module. note that everything within this module uses CPML types. Since this had no documentation initially, documentation is a WIP.

Functions

point_aabb (point, aabb)	check if a point is inside an Axis Aligned Bounding Box
point_frustum (point, frustum)	check if a point intersects with a frustum
ray_triangle (ray, triangle, backface_cull)	check wether an infinite ray intersects with a triangle
ray_sphere (ray, sphere)	check if a ray and a sphere intersect
ray_aabb (ray, aabb)	check if a ray and an aabb
ray_plane (ray, plane)	check if a ray and a plane intersect
ray_capsule (ray, capsule)	check if a ray intersects a capsule
line_line (a, b, e)	compute the shortest line segment between two lines
segment_segment (a, b, e)	the same as line_line but the lines represent segments (which are not infinite)
aabb_aabb (a, b)	check if two aabbs intersect
aabb_obb (aabb, obb)	check if an aabb and a obb (oriented bounding box) intersect WARNING: this does not use the previously established system for aabbs
aabb_sphere (aabb, sphere)	check wheter an aabb and sphere intersection
aabb_frustum (aabb, frustum)	check if an aabb and frustum intersect
encapsulate_aabb (outer, inner)	check if an aabb encapsulates (contains fully) another aabb
sphere_sphere (a, b)	check if two spheres intersect
sphere_triangle (sphere, triangle)	check if a sphere and a triangle intersect
sphere_frustum (sphere, frustum)	check if a sphere intersects with a frustum
capsule_capsule (c1, c2)	check if two capsules intersect

Tables

frustum	A frustum where a, b, c and d are vec3s
ray	An infinite ray
sphere	A sphere
triangle	A 3d triangle
aabb	An axis aligned bounding box
plane	An infinite plane
capsule	a segment with a radius

Functions

point_aabb (point, aabb)

check if a point is inside an Axis Aligned Bounding Box

Parameters:

• point vec3
• aabb table aabb

Returns:

bool

point_frustum (point, frustum)

check if a point intersects with a frustum

Parameters:

• point vec3
• frustum table a frustum

Returns:

bool

ray_triangle (ray, triangle, backface_cull)

check wether an infinite ray intersects with a triangle

Parameters:

• ray table ray
• triangle table triangle
• backface_cull bool (optional) wether backface culling is enabled

Returns:

1. (false | Vec3) false if does not intersect, intersection point if true
2. (nil | float) distance from ray origin

ray_sphere (ray, sphere)

check if a ray and a sphere intersect

Parameters:

• ray table a ray
• sphere table a sphere

Returns:

1. (false | Vec3) false if does not intersect, intersection point if true
2. (nil | float) distance from ray origin

ray_aabb (ray, aabb)

check if a ray and an aabb

Parameters:

• ray table ray
• aabb table aabb

Returns:

1. (false | Vec3) false if does not intersect, intersection point if true
2. (nil | float) distance from ray origin

ray_plane (ray, plane)

check if a ray and a plane intersect

Parameters:

• ray table ray
• plane table plane

Returns:

1. (false | Vec3) false if does not intersect, intersection point if true
2. (nil | float) distance from ray origin

ray_capsule (ray, capsule)

check if a ray intersects a capsule

Parameters:

• ray table ray
• capsule table capsule

Returns:

(false | Vec3) closest point on line to ray

line_line (a, b, e)

compute the shortest line segment between two lines

Parameters:

• a table line {vec3, vec3}
• b table line {vec3, vec3}
• e float (optional) the minimum distance between the two lines

Returns:

1. (false | table). Closest points on both lines: {vec3, vec3}, where the first vector is a, and second b.
2. (nil | vec3). Distance between the lines

segment_segment (a, b, e)

the same as line_line but the lines represent segments (which are not infinite)

Parameters:

• a table segment {vec3, vec3}
• b table segment {vec3, vec3}
• e float (optional) the minimum distance between the two lines

Returns:

1. (false | table). Closest points on both segments: {vec3, vec3}, where the first vector is a, and second b.
2. (nil | float). Distance between the segments

aabb_aabb (a, b)

check if two aabbs intersect

Parameters:

• a table aabb
• b table aabb

Returns:

bool

aabb_obb (aabb, obb)

check if an aabb and a obb (oriented bounding box) intersect WARNING: this does not use the previously established system for aabbs

Parameters:

• aabb table {position=vec3, extent=vec3} where position is the center of the object, and extent is the width on each axis.
• obb table {position=vec3, extent=vec3, rotation=mat4}

Returns:

(false | vec3). Side of the obb that intersects

aabb_sphere (aabb, sphere)

check wheter an aabb and sphere intersection

Parameters:

• aabb table aabb
• sphere sphere }

Returns:

bool

aabb_frustum (aabb, frustum)

check if an aabb and frustum intersect

Parameters:

• aabb table aabb
• frustum table frustum

Returns:

bool

encapsulate_aabb (outer, inner)

check if an aabb encapsulates (contains fully) another aabb

Parameters:

• outer table an aabb, the outside aabb
• inner table an aabb, the inner contained aabb

Returns:

bool

sphere_sphere (a, b)

check if two spheres intersect

Parameters:

• a table sphere
• b table sphere

Returns:

bool

sphere_triangle (sphere, triangle)

check if a sphere and a triangle intersect

Parameters:

• sphere table sphere
• triangle table triangle

Returns:

bool

sphere_frustum (sphere, frustum)

check if a sphere intersects with a frustum

Parameters:

• sphere table frustum
• frustum table frustum

Returns:

(false | float) distance from the nearplane

capsule_capsule (c1, c2)

check if two capsules intersect

Parameters:

• c1 table capsule
• c2 table capsule

Returns:

1. (false | Vec3) false if no intersections, vec3 on the first capsule's line if intersection occours
2. (nil | Vec3) second line intersect

Tables

frustum

A frustum where a, b, c and d are vec3s

Fields:

• left plane {a, b, c, d}
• right plane {a, b, c, d}
• bottom plane {a, b, c, d}
• top plane {a, b, c, d}
• near plane {a, b, c, d}
• far plane {a, b, c, d} (optional)

ray

An infinite ray

Fields:

• direction (vec3)
• position (vec3)

sphere

A sphere

Fields:

• position (vec3)
• radius (float)

triangle

A 3d triangle

Fields:

• 1 (vec3)
• 2 (vec3)
• 3 (vec3)

aabb

An axis aligned bounding box

Fields:

• min (vec3)
• max (vec3)

plane

An infinite plane

Fields:

• position (vec3)
• normal (vec3) "upward" direction of the plane

capsule

a segment with a radius

Fields:

• a (vec3) first position of the "segment"
• b (vec3) second position of the "segment"
• radius (float)