Physics.Transform

Types for keeping track of local spaces (transformed relative to global space). Also, tools for creating and composing 2D transformations.

Documentation

type WorldTransform = SP M3x3 M3x3

A pair of transformation matrices to and from world space, respectively. See transform and untransform.

The transformation matrices are multiplied with (2D affine) column vectors.

toTransform

Arguments

:: V2

Translation

-> Double#

Rotation

-> WorldTransform

Create a WorldTransform with a given translation and rotation.

Applying the resulting WorldTransform in the forward direction moves the origin to the first argument (:: V2), and rotates by the second argument (:: Double#).

Applying the result in the reverse direction will revert the transformation.

scaleTransform

Arguments

:: V2

Scale

-> WorldTransform

Create a WorldTransform with a given scale.

rotateTransform

Arguments

:: Double#

Rotation

-> WorldTransform

Create a WorldTransform with a given rotation.

translateTransform

Arguments

:: V2

Translation

-> WorldTransform

Create a WorldTransform with a given translation.

idTransform :: WorldTransform

Identity WorldTransform does not alter the space.

joinTransforms

Arguments

:: WorldTransform

The outer transform - applied last

-> WorldTransform

The inner transform - applied first

-> WorldTransform

The composite transform

Sequence two WorldTransforms to produce a third.

joinTransforms'

Arguments

:: [WorldTransform]

Transforms in order from outermost to innermost

-> WorldTransform

The composite transform

Sequence a list of WorldTransforms.

invertTransform :: WorldTransform -> WorldTransform

Reverse the direction of a WorldTransform. Simply swaps the two transformation matrices.

data LocalT b

Constructors

LocalT !WorldTransform !b

Instances

Functor LocalT

Methods

fmap :: (a -> b) -> LocalT a -> LocalT b

(<$) :: a -> LocalT b -> LocalT a

Show b => Show (LocalT b)

Methods

showsPrec :: Int -> LocalT b -> ShowS

show :: LocalT b -> String

showList :: [LocalT b] -> ShowS

WorldTransformable (LocalT b)

Methods

transform :: WorldTransform -> LocalT b -> LocalT b

untransform :: WorldTransform -> LocalT b -> LocalT b

wExtract :: LocalT (LocalT b) -> WorldT (LocalT b)

wExtract_ :: LocalT (LocalT b) -> LocalT b

wInject :: WorldTransform -> WorldT (LocalT b) -> LocalT (LocalT b)

wInject_ :: WorldTransform -> LocalT b -> LocalT b

type LV2 = LocalT V2

type LP2 = LocalT P2

data WorldT a

Constructors

WorldT !a

Instances

Functor WorldT

Methods

fmap :: (a -> b) -> WorldT a -> WorldT b

(<$) :: a -> WorldT b -> WorldT a

Eq a => Eq (WorldT a)

Methods

(==) :: WorldT a -> WorldT a -> Bool

(/=) :: WorldT a -> WorldT a -> Bool

Show a => Show (WorldT a)

Methods

showsPrec :: Int -> WorldT a -> ShowS

show :: WorldT a -> String

showList :: [WorldT a] -> ShowS

WorldTransformable t => WorldTransformable (WorldT t)

Methods

transform :: WorldTransform -> WorldT t -> WorldT t

untransform :: WorldTransform -> WorldT t -> WorldT t

wExtract :: LocalT (WorldT t) -> WorldT (WorldT t)

wExtract_ :: LocalT (WorldT t) -> WorldT t

wInject :: WorldTransform -> WorldT (WorldT t) -> LocalT (WorldT t)

wInject_ :: WorldTransform -> WorldT t -> WorldT t

type WV2 = WorldT V2

type WP2 = WorldT P2

iExtract :: WorldT a -> a

iInject :: a -> WorldT a

iInject_ :: b -> LocalT b

class WorldTransformable t where

Minimal complete definition

transform, untransform

Methods

transform :: WorldTransform -> t -> t

Apply WorldTransform in the forward direction (local space to world space).

untransform :: WorldTransform -> t -> t

Apply WorldTransform in the reverse direction (world space to local space).

wExtract :: LocalT t -> WorldT t

wExtract_ :: LocalT t -> t

wInject :: WorldTransform -> WorldT t -> LocalT t

wInject_ :: WorldTransform -> t -> t

Instances

WorldTransformable V2

Methods

transform :: WorldTransform -> V2 -> V2

untransform :: WorldTransform -> V2 -> V2

wExtract :: LocalT V2 -> WorldT V2

wExtract_ :: LocalT V2 -> V2

wInject :: WorldTransform -> WorldT V2 -> LocalT V2

wInject_ :: WorldTransform -> V2 -> V2

WorldTransformable P2

Methods

transform :: WorldTransform -> P2 -> P2

untransform :: WorldTransform -> P2 -> P2

wExtract :: LocalT P2 -> WorldT P2

wExtract_ :: LocalT P2 -> P2

wInject :: WorldTransform -> WorldT P2 -> LocalT P2

wInject_ :: WorldTransform -> P2 -> P2

WorldTransformable b => WorldTransformable [b]

Methods

transform :: WorldTransform -> [b] -> [b]

untransform :: WorldTransform -> [b] -> [b]

wExtract :: LocalT [b] -> WorldT [b]

wExtract_ :: LocalT [b] -> [b]

wInject :: WorldTransform -> WorldT [b] -> LocalT [b]

wInject_ :: WorldTransform -> [b] -> [b]

WorldTransformable b => WorldTransformable (Maybe b)

Methods

transform :: WorldTransform -> Maybe b -> Maybe b

untransform :: WorldTransform -> Maybe b -> Maybe b

wExtract :: LocalT (Maybe b) -> WorldT (Maybe b)

wExtract_ :: LocalT (Maybe b) -> Maybe b

wInject :: WorldTransform -> WorldT (Maybe b) -> LocalT (Maybe b)

wInject_ :: WorldTransform -> Maybe b -> Maybe b

WorldTransformable t => WorldTransformable (WorldT t)

Methods

transform :: WorldTransform -> WorldT t -> WorldT t

untransform :: WorldTransform -> WorldT t -> WorldT t

wExtract :: LocalT (WorldT t) -> WorldT (WorldT t)

wExtract_ :: LocalT (WorldT t) -> WorldT t

wInject :: WorldTransform -> WorldT (WorldT t) -> LocalT (WorldT t)

wInject_ :: WorldTransform -> WorldT t -> WorldT t

WorldTransformable (LocalT b)

Methods

transform :: WorldTransform -> LocalT b -> LocalT b

untransform :: WorldTransform -> LocalT b -> LocalT b

wExtract :: LocalT (LocalT b) -> WorldT (LocalT b)

wExtract_ :: LocalT (LocalT b) -> LocalT b

wInject :: WorldTransform -> WorldT (LocalT b) -> LocalT (LocalT b)

wInject_ :: WorldTransform -> LocalT b -> LocalT b

WorldTransformable b => WorldTransformable (b, b)

Methods

transform :: WorldTransform -> (b, b) -> (b, b)

untransform :: WorldTransform -> (b, b) -> (b, b)

wExtract :: LocalT (b, b) -> WorldT (b, b)

wExtract_ :: LocalT (b, b) -> (b, b)

wInject :: WorldTransform -> WorldT (b, b) -> LocalT (b, b)

wInject_ :: WorldTransform -> (b, b) -> (b, b)

WorldTransformable w => WorldTransformable (WaL w l)

Methods

transform :: WorldTransform -> WaL w l -> WaL w l

untransform :: WorldTransform -> WaL w l -> WaL w l

wExtract :: LocalT (WaL w l) -> WorldT (WaL w l)

wExtract_ :: LocalT (WaL w l) -> WaL w l

wInject :: WorldTransform -> WorldT (WaL w l) -> LocalT (WaL w l)

wInject_ :: WorldTransform -> WaL w l -> WaL w l

data WaL w l

Constructors

WaL

Fields

• _wlW :: !(WorldT w)
• _wlL :: !(LocalT l)

Instances

(Show l, Show w) => Show (WaL w l)

Methods

showsPrec :: Int -> WaL w l -> ShowS

show :: WaL w l -> String

showList :: [WaL w l] -> ShowS

WorldTransformable w => WorldTransformable (WaL w l)

Methods

transform :: WorldTransform -> WaL w l -> WaL w l

untransform :: WorldTransform -> WaL w l -> WaL w l

wExtract :: LocalT (WaL w l) -> WorldT (WaL w l)

wExtract_ :: LocalT (WaL w l) -> WaL w l

wInject :: WorldTransform -> WorldT (WaL w l) -> LocalT (WaL w l)

wInject_ :: WorldTransform -> WaL w l -> WaL w l

type WaL' t = WaL t t

wfmap :: Functor t => (a -> t b) -> WorldT a -> t (WorldT b)

wflip :: Functor t => WorldT (t a) -> t (WorldT a)

wmap :: (a -> b) -> WorldT a -> WorldT b

wlift2 :: (a -> b -> c) -> WorldT a -> WorldT b -> WorldT c

wlift2_ :: (a -> b -> c) -> WorldT a -> WorldT b -> c

wap :: WorldT (a -> b) -> WorldT a -> WorldT b

wlap :: WorldTransformable a => WorldT (a -> b) -> LocalT a -> WorldT b

lwap :: WorldTransformable a => LocalT (a -> b) -> WorldT a -> LocalT b

lap :: WorldTransformable a => LocalT (a -> b) -> LocalT a -> LocalT b

lmap :: (a -> b) -> LocalT a -> LocalT b

lfmap :: Functor t => (a -> t b) -> LocalT a -> t (LocalT b)

lunsafe_ :: (a -> b) -> LocalT a -> b

wlens :: Functor f => (a -> f a) -> WorldT a -> f (WorldT a)