Projection.hs

---------------------------------------------------------------------------
-- |
-- Copyright   :  (C) 2014 Edward Kmett
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  experimental
-- Portability :  non-portable
--
-- Common projection matrices: e.g. perspective/orthographic transformation
-- matrices.
---------------------------------------------------------------------------
module Linear.Projection
  ( lookAt
  , perspective
  , infinitePerspective
  , ortho
  ) where

import Control.Lens hiding (index)
import Linear.V3
import Linear.V4
import Linear.Matrix
import Linear.Epsilon
import Linear.Metric

-- | Build a look at view matrix
lookAt
  :: (Epsilon a, Floating a)
  => V3 a -- ^ Eye
  -> V3 a -- ^ Center
  -> V3 a -- ^ Up
  -> M44 a
lookAt eye center up =
  V4 (V4 (xa^._x)  (xa^._y)  (xa^._z)  xd)
     (V4 (ya^._x)  (ya^._y)  (ya^._z)  yd)
     (V4 (-za^._x) (-za^._y) (-za^._z) zd)
     (V4 0         0         0          1)
  where za = normalize $ center - eye
        xa = normalize $ cross za up
        ya = cross xa za
        xd = -dot xa eye
        yd = -dot ya eye
        zd = dot za eye

-- | Build a matrix for a symmetric perspective-view frustum
perspective
  :: Floating a
  => a -- ^ FOV
  -> a -- ^ Aspect ratio
  -> a -- ^ Near plane
  -> a -- ^ Far plane
  -> M44 a
perspective fovy aspect near far =
  V4 (V4 x 0 0    0)
     (V4 0 y 0    0)
     (V4 0 0 z    w)
     (V4 0 0 (-1) 0)
  where tanHalfFovy = tan $ fovy / 2
        x = 1 / (aspect * tanHalfFovy)
        y = 1 / tanHalfFovy
        z = -(far + near) / (far - near)
        w = -(2 * far * near) / (far - near)

-- | Build a matrix for a symmetric perspective-view frustum with a far plane at infinite
infinitePerspective
  :: Floating a
  => a -- ^ FOV
  -> a -- ^ Aspect Ratio
  -> a -- ^ Near plane
  -> M44 a
infinitePerspective fovy aspect near =
  V4 (V4 x 0 0    0)
     (V4 0 y 0    0)
     (V4 0 0 (-1) w)
     (V4 0 0 (-1) 0)
  where range  = tan (fovy / 2) * near
        left   = -range * aspect
        right  = range * aspect
        bottom = -range
        top    = range
        x = (2 * near) / (right - left)
        y = (2 * near) / (top - bottom)
        w = -2 * near

-- | Build an orthographic perspective matrix from 6 clipping planes
ortho
  :: Floating a
  => a -- ^ Left
  -> a -- ^ Right
  -> a -- ^ Bottom
  -> a -- ^ Top
  -> a -- ^ Near
  -> a -- ^ Far
  -> M44 a
ortho left right bottom top near far =
  V4 (V4 (2 / a) 0       0        (negate (right + left) / a))
     (V4 0       (2 / b) 0        (negate (top + bottom) / b))
     (V4 0       0       (-2 / c) (negate (far + near) / c))
     (V4 0       0       0        1)
  where a = right - left
        b = top - bottom
        c = far - near