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)

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

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

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

IpeWriteText r => IpeWriteText (Matrix 3 3 r)

Coordinate r => IpeReadText (Matrix 3 3 r)

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)

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

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

(Show r, Arity ((+) 1 d)) => Show (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

Methods

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

Instances

IsTransformable g => IsTransformable (Boundary g)

Num r => IsTransformable (Image r)

Num r => IsTransformable (IpeSymbol r)

Num r => IsTransformable (MiniPage r)

Num r => IsTransformable (TextLabel r)

Num r => IsTransformable (PathSegment r)

Num r => IsTransformable (Path r)

Num r => IsTransformable (IpeObject r)

Num r => IsTransformable (Group r)

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

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

Num r => IsTransformable (Triangle d r)

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

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

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

Num r => IsTransformable (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