--column major!
local love = assert( love )
local math = math
local t = {}

--scale
--rotate
--translate
function t.TRS( x, y, z, a, b, g, dx, dy, dz )
  local c, s = math.cos, math.sin
  local ca, sa, cb, sb, cg, sg = c(a), s(a), c(b), s(b), c(g), s(g)
  return {
    {x*ca*cb,              y*sa*cb,            z*(-sb),   0},
    {x*(ca*sb*sg - sa*cg), y*(sa*sb*sg+ca*cg), z*(cb*sg), 0},
    {x*(ca*sb*cg+sa*sg),   y*(sa*sb*cg-ca*sg), z*cb*cg,   0},
    {dx,                   dy,                 dz,        1}}
end

--position of camera x y z
--yaw a
--pitch b
function t.view( x, y, z, a, b )
  local c, s = math.cos, math.sin
  local ca, cb, sa, sb = c(a), c(b), s(a), s(b)
  return t.__mul(
      {
        {1,  0,  0, 0},
        {0, cb, sb, 0},
        {0,-sb, cb, 0},
        {0,  0, 0,  1},
      },
    t.__mul(
      {
        {ca, 0,-sa, 0},
        {0,  1, 0,  0},
        {sa, 0, ca, 0},
        {0,  0, 0,  1},
      },
      {
        {1, 0, 0, 0},
        {0, 1, 0, 0},
        {0, 0, 1, 0},
        {-x, -y, z, 1}
      }))
end

function t.projection(n, f, fov)
  local r = love.graphics.getWidth() / 2
  local t = love.graphics.getHeight() / 2
  local aspect = r/t
  local a = 1.0 / math.tan( fov / 2 )
  return 
  { {a, 0,  0,              0},
    {0,-a,  0,              0},
    {0, 0,  (f+n)/(n-f),   -1},
    {0, 0,  2*f*n/(n-f),    0},
  }
end

function t.transpose( A )
  for i = 1, 4 do
    for j = 1, 4 do
      A[i][j] = A[j][i]
    end
  end
end


function t.__mul( A, B )
  local C = {{},{},{},{}}
  for j = 1, 4 do
    for i = 1, 4 do
      C[j][i] =
      A[1][i] * B[j][1] +
      A[2][i] * B[j][2] +
      A[3][i] * B[j][3] +
      A[4][i] * B[j][4]
    end
  end
  return C
end

function t.__add( A, B )
  local C = {}
  for i = 1, 4 do
    for j = 1, 4 do
      C[i][j] = A[i][j] + B[i][j]
    end
  end
  return C
end


function t.id()
  return {{ 1, 0, 0, 0 },{ 0, 1, 0, 0 },{0, 0, 1, 0},{0, 0, 0, 1}}
end

return t