Safe Haskell	None
Language	Haskell2010

Data.Geometry.Transformation

Contents

Matrices
Transformations
Transformable geometry objects
Common transformations
Functions that execute transformations
Helper functions to easily create matrices

Synopsis

newtype Matrix n m r = Matrix (Vector n (Vector m 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
newtype Transformation d r = Transformation {
- _transformationMatrix :: Matrix (d + 1) (d + 1) 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
class IsTransformable g where
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
mkRow :: forall d r. (Arity d, Num r) => Int -> r -> Vector d r
transRow :: forall n r. (Arity n, Arity (n + 1), Num r) => Int -> r -> Vector (n + 1) r

Matrices

newtype Matrix n m r Source #

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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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 #
IpeWriteText r => IpeWriteText (Matrix 3 3 r) Source #
Instance details Defined in Data.Geometry.Ipe.Writer Methods ipeWriteText :: Matrix 3 3 r -> Maybe Text Source #
Coordinate r => IpeReadText (Matrix 3 3 r) Source #
Instance details Defined in Data.Geometry.Ipe.Reader Methods ipeReadText :: Text -> Either ConversionError (Matrix 3 3 r) Source #

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

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

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

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

Compose transformations (right to left)

Transformable geometry objects

class IsTransformable g where Source #

A class representing types that can be transformed using a transformation

Minimal complete definition

transformBy

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 #
Fractional r => IsTransformable (Image r) Source #
Instance details Defined in Data.Geometry.Ipe.Types Methods transformBy :: Transformation (Dimension (Image r)) (NumType (Image r)) -> Image r -> Image r Source #
Fractional r => IsTransformable (IpeSymbol r) Source #
Instance details Defined in Data.Geometry.Ipe.Types Methods transformBy :: Transformation (Dimension (IpeSymbol r)) (NumType (IpeSymbol r)) -> IpeSymbol r -> IpeSymbol r Source #
Fractional r => IsTransformable (MiniPage r) Source #
Instance details Defined in Data.Geometry.Ipe.Types Methods transformBy :: Transformation (Dimension (MiniPage r)) (NumType (MiniPage r)) -> MiniPage r -> MiniPage r Source #
Fractional r => IsTransformable (TextLabel r) Source #
Instance details Defined in Data.Geometry.Ipe.Types Methods transformBy :: Transformation (Dimension (TextLabel r)) (NumType (TextLabel r)) -> TextLabel r -> TextLabel r Source #
Fractional r => IsTransformable (PathSegment r) Source #
Instance details Defined in Data.Geometry.Ipe.Types Methods transformBy :: Transformation (Dimension (PathSegment r)) (NumType (PathSegment r)) -> PathSegment r -> PathSegment r Source #
Fractional r => IsTransformable (Path r) Source #
Instance details Defined in Data.Geometry.Ipe.Types Methods transformBy :: Transformation (Dimension (Path r)) (NumType (Path r)) -> Path r -> Path r Source #
Fractional r => IsTransformable (IpeObject r) Source #
Instance details Defined in Data.Geometry.Ipe.Types Methods transformBy :: Transformation (Dimension (IpeObject r)) (NumType (IpeObject r)) -> IpeObject r -> IpeObject r Source #
Fractional r => IsTransformable (Group r) Source #
Instance details Defined in Data.Geometry.Ipe.Types Methods transformBy :: Transformation (Dimension (Group r)) (NumType (Group r)) -> Group r -> Group 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 #
(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 #
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)) => 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 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 #

Helper functions to easily create matrices

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

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 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