R3.lua

local m = love.math
local g = love.graphics

local tmp = m.newTransform()
local bak = m.newTransform()
local R3 = {}

function R3.new_inverse(width, height)
	return m.newTransform():setMatrix(
		2 / width, 0, 0, -1,
		0, -2 / height, 0, 1,
		0, 0, -1 / 10, 0,
		0, 0, 0, 1
	):inverse()
end

function R3.new_perspective(width, height, near, hfov)
	local n = near or .1
	hfov = hfov or math.pi * .5
	local f = 1 / math.tan(hfov * .5)
	local ar = width / height
	return m.newTransform():setMatrix(
		f / ar, 0, 0, 0,
		0, f, 0, 0,
		0, 0, 1, -2 * n,
		0, 0, 1, 0
	)
end

function R3.new_ortho(width, height, near, far)
	return m.newTransform():setMatrix(
		2 / width, 0, 0, 0,
		0, 2 / height, 0, 0,
		0, 0, 2 / (far - near), -(far + near) / (far - near),
		0, 0, 0, 1
	)
end

function R3.new_origin(perspective, width, height, near, hfov)
	if perspective then
		return R3.new_inverse(width, height):apply(R3.new_perspective(width, height, near, hfov))
	else
		return R3.new_inverse(width, height):apply(R3.new_ortho(2, 2, near, hfov))
	end
end

function R3.translate(x, y, z)
	tmp:setMatrix(
		1, 0, 0, x,
		0, 1, 0, y,
		0, 0, 1, z,
		0, 0, 0, 1
	)
	tmp, bak = bak, tmp
	return bak
end

function R3.scale(x, y, z)
	tmp:setMatrix(
		x, 0, 0, 0,
		0, y, 0, 0,
		0, 0, z, 0,
		0, 0, 0, 1
	)
	tmp, bak = bak, tmp
	return bak
end

function R3.rotate(i, j, k, w)
	tmp:setMatrix(
		1 - 2 * j * j - 2 * k * k, 2 * i * j + 2 * w * k, 2 * i * k - 2 * w * j, 0,
		2 * i * j - 2 * w * k, 1 - 2 * i * i - 2 * k * k, 2 * j * k + 2 * w * i, 0,
		2 * i * k + 2 * w * j, 2 * j * k - 2 * w * i, 1 - 2 * i * i - 2 * j * j, 0,
		0, 0, 0, 1
	)
	tmp, bak = bak, tmp
	return bak
end

function R3.aa_to_quat(x, y, z, a)
	--let's turn axis angle into a quaternion
	local l = math.sqrt(x * x + y * y + z * z)
	x, y, z = x / l, y / l, z / l            --normalize imaginary part
	local w, s = math.cos(a / 2), math.sin(a / 2) --the real part is a COsine of half an angle
	--the imaginary part will get multiplied by sine of half an angle
	return x * s, y * s, z * s, w
end

return R3