leef-math-cd2025/modules/intersect.lua

local current_folder = (...):gsub('%.[^%.]+$', '') .. "."
local vec3 = require(current_folder .. "vec3")
local constants = require(current_folder .. "constants")

local intersect = {}

-- *COMPLETELY* untested!
function intersect.ray_aabb(ray, lb, rt)
	local min = math.min
	local max = math.max

	-- ray.direction is unit direction vector of ray
	local dir = ray.direction:normalize()
	local dirfrac = vec3(1/dir.x,1/dir.y,1/dir.z)

	-- lb is the corner of AABB with minimal coordinates - left bottom, rt is maximal corner
	-- ray.point is origin of ray
	local t1 = (lb.x - ray.point.x)*dirfrac.x
	local t2 = (rt.x - ray.point.x)*dirfrac.x
	local t3 = (lb.y - ray.point.y)*dirfrac.y
	local t4 = (rt.y - ray.point.y)*dirfrac.y
	local t5 = (lb.z - ray.point.z)*dirfrac.z
	local t6 = (rt.z - ray.point.z)*dirfrac.z

	local tmin = max(max(min(t1, t2), min(t3, t4)), min(t5, t6))
	local tmax = min(min(max(t1, t2), max(t3, t4)), max(t5, t6))

	-- if tmax < 0, ray (line) is intersecting AABB, but whole AABB is behing us
	if tmax < 0 then
		return false
	end

	-- if tmin > tmax, ray doesn't intersect AABB
	if tmin > tmax then
		return false
	end

	return true, tmin
end

-- ray = { point, direction }
-- plane = { point, normal }
-- https://www.cs.princeton.edu/courses/archive/fall00/cs426/lectures/raycast/sld017.htm
function intersect.ray_plane(ray, plane)
	-- t = distance of direction
	-- d = distance from ray point to plane point
	-- p = point of intersection

	local d = ray.point:dist(plane.point)
	local r = ray.direction:dot(plane.normal)

	if r <= 0 then
		return false
	end

	local t = -(ray.point:dot(plane.normal) + d) / r
	local p = ray.point + t * ray.direction

	if p:dot(plane.normal) + d < constants.FLT_EPSILON then
		return p
	end

	return false
end

-- http://www.lighthouse3d.com/tutorials/maths/ray-triangle-intersection/
function intersect.ray_triangle(ray, triangle)
	assert(ray.point ~= nil)
	assert(ray.direction ~= nil)
	assert(#triangle == 3)

	local p, d = ray.point, ray.direction

	local h, s, q = vec3(), vec3(), vec3()
	local a, f, u, v

	local e1 = triangle[2] - triangle[1]
	local e2 = triangle[3] - triangle[1]

	h = d:cross(e2)

	a = (e1:dot(h))

	if a > -0.00001 and a < 0.00001 then
		return false
	end

	f = 1/a
	s = p - triangle[1]
	u = f * (s:dot(h))

	if u < 0 or u > 1 then
		return false
	end

	q = s:cross(e1)
	v = f * (d:dot(q))

	if v < 0 or u + v > 1 then
		return false
	end

	-- at this stage we can compute t to find out where
	-- the intersection point is on the line
	t = f * (e2:dot(q))

	if t > constants.FLT_EPSILON then
		return p + t * d -- we've got a hit!
	else
		return false -- the line intersects, but it's behind the point
	end
end

-- Algorithm is ported from the C algorithm of
-- Paul Bourke at http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline3d/
-- Archive.org am hero \o/
function intersect.line_line(p1, p2, p3, p4)
	local epsilon = constants.FLT_EPSILON
	local resultSegmentPoint1 = vec3(0,0,0)
	local resultSegmentPoint2 = vec3(0,0,0)

	local p13 = p1 - p3
	local p43 = p4 - p3
	local p21 = p2 - p1

	if p43:len2() < epsilon then return false end
	if p21:len2() < epsilon then return false end

	local d1343 = p13.x * p43.x + p13.y * p43.y + p13.z * p43.z
	local d4321 = p43.x * p21.x + p43.y * p21.y + p43.z * p21.z
	local d1321 = p13.x * p21.x + p13.y * p21.y + p13.z * p21.z
	local d4343 = p43.x * p43.x + p43.y * p43.y + p43.z * p43.z
	local d2121 = p21.x * p21.x + p21.y * p21.y + p21.z * p21.z

	local denom = d2121 * d4343 - d4321 * d4321
	if math.abs(denom) < epsilon then return false end
	local numer = d1343 * d4321 - d1321 * d4343

	local mua = numer / denom
	local mub = (d1343 + d4321 * (mua)) / d4343

	resultSegmentPoint1.x = p1.x + mua * p21.x
	resultSegmentPoint1.y = p1.y + mua * p21.y
	resultSegmentPoint1.z = p1.z + mua * p21.z
	resultSegmentPoint2.x = p3.x + mub * p43.x
	resultSegmentPoint2.y = p3.y + mub * p43.y
	resultSegmentPoint2.z = p3.z + mub * p43.z

	return true, resultSegmentPoint1, resultSegmentPoint2
end

function intersect.segment_segment(p1, p2, p3, p4)
	local collision, c1, c2 = intersect.line_line(p1, p2, p3, p4)

	if collision then
		if  ((p1 <= c1 and c1 <= p2) or (p1 >= c1 and c1 >= p2))
		and ((p3 <= c2 and c2 <= p4) or (p3 >= c2 and c2 >= p4)) then
			return true, c1, c2
		end
	end
end

-- point is a vec3
-- box.position is a vec3
-- box.volume is a vec3
function intersect.point_AABB(point, box)
	if  box.position.x                <= point.x
	and box.position.x + box.volume.x >= point.x
	and box.position.y                <= point.y
	and box.position.y + box.volume.y >= point.y
	and box.position.z                <= point.z
	and box.position.z + box.volume.z >= point.z then
		return true
	end
end

function intersect.circle_circle(c1, c2)
	assert(type(c1.point)	== "table", "c1 point must be a table")
	assert(type(c1.radius)	== "number", "c1 radius must be a number")
	assert(type(c2.point)	== "table", "c2 point must be a table")
	assert(type(c2.radius)	== "number", "c2 radius must be a number")
	return c1.point:dist(c2.point) <= c1.radius + c2.radius
end

return intersect