Quaternion.hs

-- This source file is part of HGamer3D
-- (A project to enable 3D game development in Haskell)
-- For the latest info, see http://www.althainz.de/HGamer3D.html
--
-- Copyright 2011 Dr. Peter Althainz
--
-- Licensed under the Apache License, Version 2.0 (the "License");
-- you may not use this file except in compliance with the License.
-- You may obtain a copy of the License at
--
--     http://www.apache.org/licenses/LICENSE-2.0
--
-- Unless required by applicable law or agreed to in writing, software
-- distributed under the License is distributed on an "AS IS" BASIS,
-- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-- See the License for the specific language governing permissions and
-- limitations under the License.

-- Quaternion.hs

module HGamer3D.Data.Quaternion 

(
	-- export Quaternion Type again
	Quaternion (Quaternion, qW, qV),
	quaternion,
	mulQ,
	conjQ,
	normQ,
	normalizeQ,
	dotQ,
	rotateVQ,
	fromRotationQ
	
	-- export all functions
)

where

import HGamer3D.Data.Vector3
import HGamer3D.Data.Vector4 (Vector4, vector4)

data Quaternion = Quaternion {
  qW :: Float,
  qV :: Vector3
} deriving (Eq, Show)

quaternion w x y z = Quaternion w (vector3 x y z)

mulQ :: Quaternion -> Quaternion -> Quaternion
mulQ q1 q2 = Quaternion ((w1 * w2) - (v1 `dotV3` v2)) ( (scaleV3 w1 v2) + (scaleV3 w2 v1) + (v1 `crossV3` v2) )  where
	w1 = qW q1
	w2 = qW q2
	v1 = qV q1
	v2 = qV q2 

conjQ :: Quaternion -> Quaternion
conjQ q = Quaternion (qW q) (scaleV3 (-1.0) (qV q)) 

normQ :: Quaternion -> Float 
normQ q = sqrt $ dotQ q (conjQ q)

normalizeQ :: Quaternion -> Quaternion
normalizeQ q = Quaternion ( (qW q) / n ) ( (scaleV3 (1/n)) (qV q) ) where
	n = normQ q

dotQ :: Quaternion -> Quaternion -> Float
dotQ q1 q2 = (w1 * w2) + (v1 `dotV3` v2) where
	w1 = qW q1
	w2 = qW q2
	v1 = qV q1
	v2 = qV q2 
 
fromRotationQ :: Float -> Vector3 -> Quaternion
fromRotationQ a v = Quaternion (cos h) (scaleV3 s v) where
					h = a/2.0
					s = sin h

rotateVQ :: Vector3 -> Quaternion -> Vector3
rotateVQ v q = qV (mulQ q (mulQ v' q')) where 
	v' = Quaternion 0.0 v
	q' = conjQ q

toVector4 :: Quaternion -> Vector4
toVector4 q = vector4 (v3X v) (v3Y v) (v3Z v) w where
	v = qV q
	w = qW q