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{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE TypeSynonymInstances #-}
module Spear.Math.Spatial3
where
import Spear.Math.Algebra
import qualified Spear.Math.Matrix4 as Matrix4
import Spear.Math.Matrix4 (Matrix4)
import Spear.Math.Spatial
import Spear.Math.Vector
import Spear.Prelude
data Rotation3
= Pitch Angle
| Yaw Angle
| Roll Angle
| AxisAngle Vector3 Angle
| RotationMatrix Matrix4
-- | A 3D transform.
newtype Transform3 = Transform3 { transform3Matrix :: Matrix4 } deriving Show
type Positional3 a = Positional a Vector3
type Rotational3 a = Rotational a Angle
type Spatial3 s = Spatial s Vector3 Rotation3 Transform3
instance Positional Transform3 Vector3 where
setPosition p (Transform3 matrix) =
Transform3 . Matrix4.setPosition p $ matrix
position = Matrix4.position . transform3Matrix
translate v t@(Transform3 matrix) = setPosition (Matrix4.position matrix + v) t
instance Rotational Transform3 Vector3 Rotation3 where
setRotation rotation _ = Transform3 $ case rotation of
Pitch angle -> Matrix4.rotateX angle
Yaw angle -> Matrix4.rotateY angle
Roll angle -> Matrix4.rotateZ angle
AxisAngle axis angle -> Matrix4.axisAngle axis angle
RotationMatrix matrix -> matrix
rotation (Transform3 matrix) = RotationMatrix $ Matrix4.rotation matrix
rotate rotation t@(Transform3 matrix) = case rotation of
Pitch angle -> pitch angle t
Yaw angle -> yaw angle t
Roll angle -> roll angle t
AxisAngle axis angle -> Transform3 $ Matrix4.axisAngle axis angle * matrix
RotationMatrix rot -> Transform3 $ rot * matrix
right (Transform3 matrix) = Matrix4.right matrix
up (Transform3 matrix) = Matrix4.up matrix
forward (Transform3 matrix )= Matrix4.forward matrix
setForward forward (Transform3 matrix) =
let right = forward `cross` unity3
up = right `cross` forward
in Transform3 $ Matrix4.transform right up (neg forward) (Matrix4.position matrix)
instance Spatial Transform3 Vector3 Rotation3 Matrix4 where
setTransform matrix _ = Transform3 $ Matrix4.transform
(Matrix4.right matrix)
(Matrix4.up matrix)
(neg $ Matrix4.forward matrix)
(Matrix4.position matrix)
transform (Transform3 matrix) = Matrix4.transform
(Matrix4.right matrix)
(Matrix4.up matrix)
(neg $ Matrix4.forward matrix)
(Matrix4.position matrix)
class Has3dTransform a where
-- | Set the object's 3d transform.
set3dTransform :: Transform3 -> a -> a
-- | Get the object's 3d transform.
transform3 :: a -> Transform3
with3dTransform :: Has3dTransform a => (Transform3 -> Transform3) -> a -> a
with3dTransform f obj = set3dTransform (f $ transform3 obj) obj
-- | Build a 3d transform from right, up, forward and position vectors.
newTransform3 :: Vector3 -> Vector3 -> Vector3 -> Vector3 -> Transform3
newTransform3 right up forward pos = Transform3 $
Matrix4.transform right up (neg forward) pos
-- | Rotate the object about the given axis.
rotate3 :: Vector3 -> Float -> Transform3 -> Transform3
rotate3 axis angle (Transform3 matrix) =
let axis' = Matrix4.inverseTransform matrix `Matrix4.muld` axis
in Transform3 $ matrix * Matrix4.axisAngle axis' angle
-- | Rotate the object about its local X axis.
pitch :: Float -> Transform3 -> Transform3
pitch angle (Transform3 matrix) =
let sa = sin angle
ca = cos angle
f' = normalise $ (ca * Matrix4.forward matrix) + (sa * Matrix4.up matrix)
u' = normalise $ Matrix4.right matrix `cross` f'
in Transform3 . Matrix4.setUp u' . Matrix4.setForward f' $ matrix
-- | Rotate the object about its local Y axis.
yaw :: Float -> Transform3 -> Transform3
yaw angle (Transform3 matrix) =
let sa = sin angle
ca = cos angle
r' = normalise $ (ca * Matrix4.right matrix) + (sa * Matrix4.forward matrix)
f' = normalise $ Matrix4.up matrix `cross` r'
in Transform3 . Matrix4.setRight r' . Matrix4.setForward f' $ matrix
-- | Rotate the object about its local Z axis.
roll :: Float -> Transform3 -> Transform3
roll angle (Transform3 matrix) =
let sa = sin angle
ca = cos angle
u' = normalise $ (ca * Matrix4.up matrix) - (sa * Matrix4.right matrix)
r' = normalise $ Matrix4.forward matrix `cross` u'
in Transform3 . Matrix4.setRight r' . Matrix4.setUp u' $ matrix
-- | Make the object orbit around the given point
orbit :: Positional a Vector3
=> Vector3 -- ^ Target point
-> Float -- ^ Horizontal angle
-> Float -- ^ Vertical angle
-> Float -- ^ Orbit radius.
-> a
-> a
orbit pt anglex angley radius =
let sx = sin anglex
sy = sin angley
cx = cos anglex
cy = cos angley
px = x pt + radius*cy*sx
py = y pt + radius*sy
pz = z pt + radius*cx*cy
in setPosition (vec3 px py pz)
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