Data.Geometry.Transformation

Matrices

newtype Matrix n m r

a matrix of n rows, each of m columns, storing values of type r

Constructors

Matrix (Vector n (Vector m r))

Instances

(Arity n, Arity m) => Functor (Matrix n m)

Defined in Data.Geometry.Transformation

Methods

fmap :: (a -> b) -> Matrix n m a -> Matrix n m b

(<$) :: a -> Matrix n m b -> Matrix n m a

(Eq r, Arity n, Arity m) => Eq (Matrix n m r)

Defined in Data.Geometry.Transformation

Methods

(==) :: Matrix n m r -> Matrix n m r -> Bool

(/=) :: Matrix n m r -> Matrix n m r -> Bool

(Ord r, Arity n, Arity m) => Ord (Matrix n m r)

Defined in Data.Geometry.Transformation

Methods

compare :: Matrix n m r -> Matrix n m r -> Ordering

(<) :: Matrix n m r -> Matrix n m r -> Bool

(<=) :: Matrix n m r -> Matrix n m r -> Bool

(>) :: Matrix n m r -> Matrix n m r -> Bool

(>=) :: Matrix n m r -> Matrix n m r -> Bool

max :: Matrix n m r -> Matrix n m r -> Matrix n m r

min :: Matrix n m r -> Matrix n m r -> Matrix n m r

(Show r, Arity n, Arity m) => Show (Matrix n m r)

Defined in Data.Geometry.Transformation

Methods

showsPrec :: Int -> Matrix n m r -> ShowS

show :: Matrix n m r -> String

showList :: [Matrix n m r] -> ShowS

multM :: (Arity r, Arity c, Arity c', Num a) => Matrix r c a -> Matrix c c' a -> Matrix r c' a

mult :: (Arity m, Arity n, Num r) => Matrix n m r -> Vector m r -> Vector n r

class Invertible n r where

Methods

inverse' :: Matrix n n r -> Matrix n n r

Instances

Fractional r => Invertible 2 r

Defined in Data.Geometry.Transformation

Methods

inverse' :: Matrix 2 2 r -> Matrix 2 2 r

Fractional r => Invertible 3 r

Defined in Data.Geometry.Transformation

Methods

inverse' :: Matrix 3 3 r -> Matrix 3 3 r

Fractional r => Invertible 4 r

Defined in Data.Geometry.Transformation

Methods

inverse' :: Matrix 4 4 r -> Matrix 4 4 r

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

(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 :: Lens' (Transformation d r) (Matrix (d + 1) (d + 1) r)

(|.|) :: (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

(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

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)) => 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

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

Common transformations

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

Functions that execute transformations

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

Helper functions to easily create matrices

mkRow :: forall d r. (Arity d, Num r) => Int -> r -> Vector d r

Creates a row with zeroes everywhere, except at position i, where the value is the supplied value.

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.