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module Spear.Math.Spatial3
(
Spatial3(..)
, Obj3
, fromVectors
, fromTransform
)
where
import Spear.Math.Vector
import Spear.Math.Matrix4 as M hiding (scale)
class Spatial3 s where
-- | Move the spatial.
move :: Vector3 -> s -> s
-- | Move the spatial forwards.
moveFwd :: Float -> s -> s
-- | Move the spatial backwards.
moveBack :: Float -> s -> s
-- | Make the spatial strafe left.
strafeLeft :: Float -> s -> s
-- | Make the spatial Strafe right.
strafeRight :: Float -> s -> s
-- | Rotate the spatial about its local X axis.
pitch :: Float -> s -> s
-- | Rotate the spatial about its local Y axis.
yaw :: Float -> s -> s
-- | Rotate the spatial about its local Z axis.
roll :: Float -> s -> s
-- | Get the spatial's position.
pos :: s -> Vector3
-- | Get the spatial's forward vector.
fwd :: s -> Vector3
-- | Get the spatial's up vector.
up :: s -> Vector3
-- | Get the spatial's right vector.
right :: s -> Vector3
-- | Get the spatial's transform.
transform :: s -> Matrix4
-- | Set the spatial's transform.
setTransform :: Matrix4 -> s -> s
-- | Set the spatial's position.
setPos :: Vector3 -> s -> s
-- | Make the spatial look at the given point.
lookAt :: Vector3 -> s -> s
lookAt pt s =
let position = pos s
fwd = normalise $ pt - position
r = fwd `cross` unity3
u = r `cross` fwd
in
setTransform (M.transform r u (-fwd) position) s
-- | Make the spatial orbit around the given point
orbit :: Vector3 -- ^ Target point
-> Float -- ^ Horizontal angle
-> Float -- ^ Vertical angle
-> Float -- ^ Orbit radius.
-> s
-> s
orbit pt anglex angley radius s =
let ax = anglex * pi / 180
ay = angley * pi / 180
sx = sin ax
sy = sin ay
cx = cos ax
cy = cos ay
px = (x pt) + radius*cy*sx
py = (y pt) + radius*sy
pz = (z pt) + radius*cx*cy
in
setPos (vec3 px py pz) s
-- | An object in 3D space.
data Obj3 = Obj3
{ r :: Vector3
, u :: Vector3
, f :: Vector3
, p :: Vector3
} deriving Show
instance Spatial3 Obj3 where
move d o = o { p = p o + d }
moveFwd s o = o { p = p o + scale (-s) (f o) }
moveBack s o = o { p = p o + scale s (f o) }
strafeLeft s o = o { p = p o + scale (-s) (r o) }
strafeRight s o = o { p = p o + scale s (r o) }
pitch a o =
let a' = toRAD a
sa = sin a'
ca = cos a'
r' = normalise $ scale ca (r o) + scale sa (f o)
f' = normalise $ r' `cross` u o
in o { r = r', f = f' }
yaw a o =
let a' = toRAD a
sa = sin a'
ca = cos a'
f' = normalise $ scale ca (f o) + scale sa (u o)
u' = normalise $ r o `cross` f'
in o { u = u', f = f' }
roll a o =
let a' = toRAD a
sa = sin a'
ca = cos a'
u' = normalise $ scale ca (u o) - scale sa (r o)
f' = normalise $ f o `cross` u'
in o { u = u', f = f' }
pos = p
fwd = f
up = u
right = r
transform o = M.transform (r o) (u o) (f o) (p o)
setTransform t o = Obj3
{ r = M.right t
, u = M.up t
, f = M.forward t
, p = M.position t
}
setPos pos o = o { p = pos }
fromVectors :: Right3 -> Up3 -> Forward3 -> Position3 -> Obj3
fromVectors = Obj3
fromTransform :: Matrix4 -> Obj3
fromTransform m = Obj3 (M.right m) (M.up m) (M.forward m) (M.position m)
toRAD = (*pi) . (/180)
|
