Safe Haskell	Unsafe
Language	Haskell2010

Data.Geometry.Transformation

Contents

Transformations
Transformable geometry objects
Common transformations
Functions that execute transformations
3D Rotations
2D Transformations

Synopsis

newtype Transformation d r = Transformation {
- _transformationMatrix :: Matrix (d + 1) (d + 1) r
}
transformationMatrix :: Iso (Transformation d r) (Transformation d s) (Matrix (d + 1) (d + 1) r) (Matrix (d + 1) (d + 1) s)
(|.|) :: (Num r, Arity (d + 1)) => Transformation d r -> Transformation d r -> Transformation d r
inverseOf :: (Fractional r, Invertible (d + 1) r) => Transformation d r -> Transformation d r
class IsTransformable g where
- transformBy :: Transformation (Dimension g) (NumType g) -> g -> g
transformAllBy :: (Functor c, IsTransformable g) => Transformation (Dimension g) (NumType g) -> c g -> c g
transformPointFunctor :: (PointFunctor g, Fractional r, d ~ Dimension (g r), Arity d, Arity (d + 1)) => Transformation d r -> g r -> g r
translation :: (Num r, Arity d, Arity (d + 1)) => Vector d r -> Transformation d r
scaling :: (Num r, Arity d, Arity (d + 1)) => Vector d r -> Transformation d r
uniformScaling :: (Num r, Arity d, Arity (d + 1)) => r -> Transformation d r
translateBy :: (IsTransformable g, Num (NumType g), Arity (Dimension g), Arity (Dimension g + 1)) => Vector (Dimension g) (NumType g) -> g -> g
scaleBy :: (IsTransformable g, Num (NumType g), Arity (Dimension g), Arity (Dimension g + 1)) => Vector (Dimension g) (NumType g) -> g -> g
scaleUniformlyBy :: (IsTransformable g, Num (NumType g), Arity (Dimension g), Arity (Dimension g + 1)) => NumType g -> g -> g
transRow :: forall n r. (Arity n, Arity (n + 1), Num r) => Int -> r -> Vector (n + 1) r
rotateTo :: Num r => Vector 3 (Vector 3 r) -> Transformation 3 r
skewX :: Num r => r -> Transformation 2 r

Transformations

newtype Transformation d r Source #

A type representing a Transformation for d dimensional objects

Constructors

Transformation
Fields _transformationMatrix :: Matrix (d + 1) (d + 1) r

Instances

Arity (d + 1) => Functor (Transformation d) Source #
Instance details Defined in Data.Geometry.Transformation Methods fmap :: (a -> b) -> Transformation d a -> Transformation d b # (<$) :: a -> Transformation d b -> Transformation d a #
Arity (d + 1) => Foldable (Transformation d) Source #
Instance details Defined in Data.Geometry.Transformation Methods fold :: Monoid m => Transformation d m -> m # foldMap :: Monoid m => (a -> m) -> Transformation d a -> m # foldr :: (a -> b -> b) -> b -> Transformation d a -> b # foldr' :: (a -> b -> b) -> b -> Transformation d a -> b # foldl :: (b -> a -> b) -> b -> Transformation d a -> b # foldl' :: (b -> a -> b) -> b -> Transformation d a -> b # foldr1 :: (a -> a -> a) -> Transformation d a -> a # foldl1 :: (a -> a -> a) -> Transformation d a -> a # toList :: Transformation d a -> [a] # null :: Transformation d a -> Bool # length :: Transformation d a -> Int # elem :: Eq a => a -> Transformation d a -> Bool # maximum :: Ord a => Transformation d a -> a # minimum :: Ord a => Transformation d a -> a # sum :: Num a => Transformation d a -> a # product :: Num a => Transformation d a -> a #
Arity (d + 1) => Traversable (Transformation d) Source #
Instance details Defined in Data.Geometry.Transformation Methods traverse :: Applicative f => (a -> f b) -> Transformation d a -> f (Transformation d b) # sequenceA :: Applicative f => Transformation d (f a) -> f (Transformation d a) # mapM :: Monad m => (a -> m b) -> Transformation d a -> m (Transformation d b) # sequence :: Monad m => Transformation d (m a) -> m (Transformation d a) #
(Eq r, Arity (d + 1)) => Eq (Transformation d r) Source #
Instance details Defined in Data.Geometry.Transformation Methods (==) :: Transformation d r -> Transformation d r -> Bool # (/=) :: Transformation d r -> Transformation d r -> Bool #
(Ord r, Arity (d + 1)) => Ord (Transformation d r) Source #
Instance details Defined in Data.Geometry.Transformation Methods compare :: Transformation d r -> Transformation d r -> Ordering # (<) :: Transformation d r -> Transformation d r -> Bool # (<=) :: Transformation d r -> Transformation d r -> Bool # (>) :: Transformation d r -> Transformation d r -> Bool # (>=) :: Transformation d r -> Transformation d r -> Bool # max :: Transformation d r -> Transformation d r -> Transformation d r # min :: Transformation d r -> Transformation d r -> Transformation d r #
(Show r, Arity (d + 1)) => Show (Transformation d r) Source #
Instance details Defined in Data.Geometry.Transformation Methods showsPrec :: Int -> Transformation d r -> ShowS # show :: Transformation d r -> String # showList :: [Transformation d r] -> ShowS #
type NumType (Transformation d r) Source #
Instance details Defined in Data.Geometry.Transformation type NumType (Transformation d r) = r

transformationMatrix :: Iso (Transformation d r) (Transformation d s) (Matrix (d + 1) (d + 1) r) (Matrix (d + 1) (d + 1) s) Source #

(|.|) :: (Num r, Arity (d + 1)) => Transformation d r -> Transformation d r -> Transformation d r Source #

Compose transformations (right to left)

inverseOf :: (Fractional r, Invertible (d + 1) r) => Transformation d r -> Transformation d r Source #

Compute the inverse transformation

>>> inverseOf $ translation (Vector2 (10.0) (5.0))
Transformation {_transformationMatrix = Matrix Vector3 [Vector3 [1.0,0.0,-10.0],Vector3 [0.0,1.0,-5.0],Vector3 [0.0,0.0,1.0]]}

Transformable geometry objects

class IsTransformable g where Source #

A class representing types that can be transformed using a transformation

Methods

transformBy :: Transformation (Dimension g) (NumType g) -> g -> g Source #

Instances

IsTransformable g => IsTransformable (Boundary g) Source #
Instance details Defined in Data.Geometry.Boundary Methods transformBy :: Transformation (Dimension (Boundary g)) (NumType (Boundary g)) -> Boundary g -> Boundary g Source #
Num r => IsTransformable (Ellipse r) Source #
Instance details Defined in Data.Geometry.Ellipse Methods transformBy :: Transformation (Dimension (Ellipse r)) (NumType (Ellipse r)) -> Ellipse r -> Ellipse r Source #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Vector d r) Source #
Instance details Defined in Data.Geometry.Transformation Methods transformBy :: Transformation (Dimension (Vector d r)) (NumType (Vector d r)) -> Vector d r -> Vector d r Source #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Point d r) Source #
Instance details Defined in Data.Geometry.Transformation Methods transformBy :: Transformation (Dimension (Point d r)) (NumType (Point d r)) -> Point d r -> Point d r Source #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Line d r) Source #	Lines are transformable, via line segments
Instance details Defined in Data.Geometry.Line Methods transformBy :: Transformation (Dimension (Line d r)) (NumType (Line d r)) -> Line d r -> Line d r Source #
(Arity d, Arity (d + 1), Fractional r) => IsTransformable (HyperPlane d r) Source #
Instance details Defined in Data.Geometry.HyperPlane Methods transformBy :: Transformation (Dimension (HyperPlane d r)) (NumType (HyperPlane d r)) -> HyperPlane d r -> HyperPlane d r Source #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (HalfLine d r) Source #
Instance details Defined in Data.Geometry.HalfLine Methods transformBy :: Transformation (Dimension (HalfLine d r)) (NumType (HalfLine d r)) -> HalfLine d r -> HalfLine d r Source #
(Arity d, Arity (d + 1), Fractional r) => IsTransformable (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace Methods transformBy :: Transformation (Dimension (HalfSpace d r)) (NumType (HalfSpace d r)) -> HalfSpace d r -> HalfSpace d r Source #
Fractional r => IsTransformable (ConvexPolygon p r) Source #
Instance details Defined in Data.Geometry.Polygon.Convex Methods transformBy :: Transformation (Dimension (ConvexPolygon p r)) (NumType (ConvexPolygon p r)) -> ConvexPolygon p r -> ConvexPolygon p r Source #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Box d p r) Source #
Instance details Defined in Data.Geometry.Box.Internal Methods transformBy :: Transformation (Dimension (Box d p r)) (NumType (Box d p r)) -> Box d p r -> Box d p r Source #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (LineSegment d p r) Source #
Instance details Defined in Data.Geometry.LineSegment Methods transformBy :: Transformation (Dimension (LineSegment d p r)) (NumType (LineSegment d p r)) -> LineSegment d p r -> LineSegment d p r Source #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (PolyLine d p r) Source #
Instance details Defined in Data.Geometry.PolyLine Methods transformBy :: Transformation (Dimension (PolyLine d p r)) (NumType (PolyLine d p r)) -> PolyLine d p r -> PolyLine d p r Source #
(Fractional r, Arity d, Arity (d + 1), Arity n) => IsTransformable (BezierSpline n d r) Source #
Instance details Defined in Data.Geometry.BezierSpline Methods transformBy :: Transformation (Dimension (BezierSpline n d r)) (NumType (BezierSpline n d r)) -> BezierSpline n d r -> BezierSpline n d r Source #
(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Triangle d p r) Source #
Instance details Defined in Data.Geometry.Triangle Methods transformBy :: Transformation (Dimension (Triangle d p r)) (NumType (Triangle d p r)) -> Triangle d p r -> Triangle d p r Source #
Fractional r => IsTransformable (Polygon t p r) Source #
Instance details Defined in Data.Geometry.Polygon.Core Methods transformBy :: Transformation (Dimension (Polygon t p r)) (NumType (Polygon t p r)) -> Polygon t p r -> Polygon t p r Source #

transformAllBy :: (Functor c, IsTransformable g) => Transformation (Dimension g) (NumType g) -> c g -> c g Source #

transformPointFunctor :: (PointFunctor g, Fractional r, d ~ Dimension (g r), Arity d, Arity (d + 1)) => Transformation d r -> g r -> g r Source #

Common transformations

translation :: (Num r, Arity d, Arity (d + 1)) => Vector d r -> Transformation d r Source #

scaling :: (Num r, Arity d, Arity (d + 1)) => Vector d r -> Transformation d r Source #

uniformScaling :: (Num r, Arity d, Arity (d + 1)) => r -> Transformation d r Source #

Functions that execute transformations

translateBy :: (IsTransformable g, Num (NumType g), Arity (Dimension g), Arity (Dimension g + 1)) => Vector (Dimension g) (NumType g) -> g -> g Source #

scaleBy :: (IsTransformable g, Num (NumType g), Arity (Dimension g), Arity (Dimension g + 1)) => Vector (Dimension g) (NumType g) -> g -> g Source #

scaleUniformlyBy :: (IsTransformable g, Num (NumType g), Arity (Dimension g), Arity (Dimension g + 1)) => NumType g -> g -> g Source #

transRow :: forall n r. (Arity n, Arity (n + 1), Num r) => Int -> r -> Vector (n + 1) r Source #

Row in a translation matrix transRow :: forall n r. ( Arity n, Arity (n- 1), ((n - 1) + 1) ~ n , Num r) => Int -> r -> Vector n r transRow i x = set (V.element (Proxy :: Proxy (n-1))) x $ mkRow i 1

3D Rotations

rotateTo :: Num r => Vector 3 (Vector 3 r) -> Transformation 3 r Source #

Given three new unit-length basis vectors (u,v,w) that map to (x,y,z), construct the appropriate rotation that does this.

2D Transformations

skewX :: Num r => r -> Transformation 2 r Source #

Skew transformation that keeps the y-coordinates fixed and shifts the x coordinates.