line intersection triangle.lua

local maths = {}

function maths.cross(ux, uy, uz, vx, vy, vz)
	local nx = (uy*vz) - (uz*vy)
	local ny = (uz*vx) - (ux*vz)
	local nz = (ux*vy) - (uy*vx)
	return nx, ny, nz
end

function maths.dot(ux, uy, uz, vx, vy, vz)
	return ux*vx + uy*vy + uz*vz
end

-- line     = {{x,y,z},{x,y,z}}         -- Origin, Direction
-- triangle = {{x,y,z},{x,y,z},{x,y,z}} -- Point1, Point2, Point3

function maths.intersectTriangle(line, triangle)
	local l1 = line[1] -- Origin
	local l2 = line[2] -- Direction

	local p1 = triangle[1]
	local p2 = triangle[2]
	local p3 = triangle[3]
	
	local ux = p2[1] - p1[1]
	local uy = p2[2] - p1[2]
	local uz = p2[3] - p1[3]
	
	local vx = p3[1] - p1[1]
	local vy = p3[2] - p1[2]
	local vz = p3[3] - p1[3]
	
	local hx, hy, hz = maths.cross(l2[1], l2[2], l2[3], vx, vy, vz)
	local det = maths.dot(ux, uy, uz, hx, hy, hz)
	if det > -1e-6 and det < 1e-6 then
		return false
	end
	
	local invdet = 1.0/det
	
	local u = maths.dot(l2[1], l2[2], l2[3], hx, hy, hz) * invdet
	if u < 0.0 or u > 1.0 then
		return false
	end
	
	local sx = l1[1] - p1[1]
	local sy = l1[2] - p1[2]
	local sz = l1[3] - p1[3]
	
	local qx, qy, qz = maths.cross(sx, sy, sz, ux, uy, uz)
	
	local v = maths.dot(l2[1], l2[2], l2[3], qx, qy, qz) * invdet
	if v < 0.0 or u + v > 1.0 then
		return false
	end
	
	local t = maths.dot(vx, vy, vz, qx, qy, qz) * invdet
	if t > 1e-6 then
		-- intersection point
		local ix, iy, iz = l1[1] + l2[1] * t, l1[2] + l2[2] * t, l1[3] + l2[3] * t
		return true, ix, iy, iz
	end
	return false -- line, but not ray intersection
end

return maths