Data.Geometry.Transformation

Documentation

>>> import Data.Geometry.LineSegment
>>> import Data.Ext

Transformations

newtype Transformation d r

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)

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)

Defined in Data.Geometry.Transformation

Methods

fold :: Monoid m => Transformation d m -> m

foldMap :: Monoid m => (a -> m) -> Transformation d a -> 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)

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)

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)

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)

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)

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)

Transformations and Matrices are isomorphic.

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

Compose transformations (right to left)

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

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

A class representing types that can be transformed using a transformation

Methods

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

Instances

IsTransformable g => IsTransformable (Boundary g)

Defined in Data.Geometry.Boundary

Methods

transformBy :: Transformation (Dimension (Boundary g)) (NumType (Boundary g)) -> Boundary g -> Boundary g

Num r => IsTransformable (Ellipse r)

Defined in Data.Geometry.Ellipse

Methods

transformBy :: Transformation (Dimension (Ellipse r)) (NumType (Ellipse r)) -> Ellipse r -> Ellipse r

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Vector d r)

Defined in Data.Geometry.Transformation

Methods

transformBy :: Transformation (Dimension (Vector d r)) (NumType (Vector d r)) -> Vector d r -> Vector d r

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Point d r)

Defined in Data.Geometry.Transformation

Methods

transformBy :: Transformation (Dimension (Point d r)) (NumType (Point d r)) -> Point d r -> Point d r

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Line d r)

Lines are transformable, via line segments

Defined in Data.Geometry.Line

Methods

transformBy :: Transformation (Dimension (Line d r)) (NumType (Line d r)) -> Line d r -> Line d r

(Arity d, Arity (d + 1), Fractional r) => IsTransformable (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

Methods

transformBy :: Transformation (Dimension (HyperPlane d r)) (NumType (HyperPlane d r)) -> HyperPlane d r -> HyperPlane d r

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (HalfLine d r)

Defined in Data.Geometry.HalfLine

Methods

transformBy :: Transformation (Dimension (HalfLine d r)) (NumType (HalfLine d r)) -> HalfLine d r -> HalfLine d r

(Arity d, Arity (d + 1), Fractional r) => IsTransformable (HalfSpace d r)

Defined in Data.Geometry.HalfSpace

Methods

transformBy :: Transformation (Dimension (HalfSpace d r)) (NumType (HalfSpace d r)) -> HalfSpace d r -> HalfSpace d r

Fractional r => IsTransformable (ConvexPolygon p r)

Defined in Data.Geometry.Polygon.Convex

Methods

transformBy :: Transformation (Dimension (ConvexPolygon p r)) (NumType (ConvexPolygon p r)) -> ConvexPolygon p r -> ConvexPolygon p r

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Box d p r)

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

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (LineSegment d p r)

Defined in Data.Geometry.LineSegment.Internal

Methods

transformBy :: Transformation (Dimension (LineSegment d p r)) (NumType (LineSegment d p r)) -> LineSegment d p r -> LineSegment d p r

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (PolyLine d p r)

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

(Fractional r, Arity d, Arity (d + 1), Arity n) => IsTransformable (BezierSpline n d r)

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

(Fractional r, Arity d, Arity (d + 1)) => IsTransformable (Triangle d p r)

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

Fractional r => IsTransformable (Polygon t p r)

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

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

Apply a transformation to a collection of objects.

>>> transformAllBy (uniformScaling 2) [Point1 1, Point1 2, Point1 3]
[Point1 2.0,Point1 4.0,Point1 6.0]

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

Apply transformation to a PointFunctor, ie something that contains points. Polygons, triangles, line segments, etc, are all PointFunctors.

>>> transformPointFunctor (uniformScaling 2) $ OpenLineSegment (Point1 1 :+ ()) (Point1 2 :+ ())
OpenLineSegment (Point1 2.0 :+ ()) (Point1 4.0 :+ ())

Common transformations

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

Create translation transformation from a vector.

>>> transformBy (translation $ Vector2 1 2) $ Point2 2 3
Point2 3.0 5.0

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

Create scaling transformation from a vector.

>>> transformBy (scaling $ Vector2 2 (-1)) $ Point2 2 3
Point2 4.0 (-3.0)

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

Create scaling transformation from a scalar that is applied to all dimensions.

>>> transformBy (uniformScaling 5) $ Point2 2 3
Point2 10.0 15.0
>>> uniformScaling 5 == scaling (Vector2 5 5)
True
>>> uniformScaling 5 == scaling (Vector3 5 5 5)
True

Functions that execute transformations

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

Translate a given point.

>>> translateBy (Vector2 1 2) $ Point2 2 3
Point2 3.0 5.0

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

Scale a given point.

>>> scaleBy (Vector2 2 (-1)) $ Point2 2 3
Point2 4.0 (-3.0)

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

Scale a given point uniformly in all dimensions.

>>> scaleUniformlyBy 5 $ Point2 2 3
Point2 10.0 15.0

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

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

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

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