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)

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)

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)

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)

Methods

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

show :: Matrix n m r -> String

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

Coordinate r => IpeReadText (Matrix 3 3 r)

Methods

ipeReadText :: Text -> Either ConversionError (Matrix 3 3 r)

IpeWriteText r => IpeWriteText (Matrix 3 3 r)

Methods

ipeWriteText :: Matrix 3 3 r -> Maybe Text

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

Transformations

newtype Transformation d r

A type representing a Transformation for d dimensional objects

Constructors

Transformation

Fields

• _transformationMatrix :: Matrix (1 + d) (1 + d) r

Instances

Arity ((+) 1 d) => Functor (Transformation d)

Methods

fmap :: (a -> b) -> Transformation d a -> Transformation d b

(<$) :: a -> Transformation d b -> Transformation d a

(Eq r, Arity ((+) 1 d)) => Eq (Transformation d r)

Methods

(==) :: Transformation d r -> Transformation d r -> Bool

(/=) :: Transformation d r -> Transformation d r -> Bool

(Ord r, Arity ((+) 1 d)) => Ord (Transformation d r)

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 ((+) 1 d)) => Show (Transformation d r)

Methods

showsPrec :: Int -> Transformation d r -> ShowS

show :: Transformation d r -> String

showList :: [Transformation d r] -> ShowS

type NumType (Transformation d r)

type NumType (Transformation d r) = r

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

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

Compose transformations (right to left)

Transformable geometry objects

class IsTransformable g where

A class representing types that can be transformed using a transformation

Minimal complete definition

transformBy

Methods

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

Instances

IsTransformable g => IsTransformable (Boundary g)

Methods

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

Num r => IsTransformable (Image r)

Methods

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

Num r => IsTransformable (IpeSymbol r)

Methods

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

Num r => IsTransformable (MiniPage r)

Methods

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

Num r => IsTransformable (TextLabel r)

Methods

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

Num r => IsTransformable (PathSegment r)

Methods

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

Num r => IsTransformable (Path r)

Methods

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

Num r => IsTransformable (IpeObject r)

Methods

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

Num r => IsTransformable (Group r)

Methods

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

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

Methods

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

(Num r, AlwaysTruePFT d) => IsTransformable (HalfLine d r)

Methods

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

Num r => IsTransformable (ConvexPolygon p r)

Methods

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

Num r => IsTransformable (Triangle d r)

Methods

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

(Num r, AlwaysTruePFT d) => IsTransformable (Box d p r)

Methods

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

(Num r, AlwaysTruePFT d) => IsTransformable (LineSegment d p r)

Methods

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

(Num r, AlwaysTruePFT d) => IsTransformable (PolyLine d p r)

Methods

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

Num r => IsTransformable (Polygon t p r)

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

type AlwaysTruePFT d = AlwaysTrueDestruct d (1 + d)

transformPointFunctor :: (PointFunctor g, Num r, d ~ Dimension (g r), AlwaysTruePFT d) => Transformation d r -> g r -> g r

Common transformations

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

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

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

Functions that execute transformations

type AlwaysTrueTransformation d = (Arity (1 + d), AlwaysTrueSnoc d, Arity d, Index' ((1 + d) - 1) (1 + d))

translateBy :: (IsTransformable g, Num (NumType g), AlwaysTrueTransformation (Dimension g)) => Vector (Dimension g) (NumType g) -> g -> g

scaleBy :: (IsTransformable g, Num (NumType g), AlwaysTrueTransformation (Dimension g)) => Vector (Dimension g) (NumType g) -> g -> g

scaleUniformlyBy :: (IsTransformable g, Num (NumType g), AlwaysTrueTransformation (Dimension g)) => 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, Index' (n - 1) n, Num r) => Int -> r -> Vector n r

Row in a translation matrix