Wumpus.Core.AffineTrans

Affine transformations.

The common affine transformations represented as type classes - scaling, rotation, translation.

Unlike other functional graphics systems (e.g. Clastic), Wumpus performs the affine transformations as matrix operations. This simplifies the implementation of pictures (Wumpus.Core.PictureInternal). When a picture is composed and transformed, transformations will be performed only on the bounding box in Wumpus but the transformation of the picture content (paths or text labels) will be communicated to PostScript or SVG to render. This is because Wumpus has no access to the paths that make fonts so cannot transform them directly.

To generate efficient PostScript, Wumpus relies on the matrix representations of the affine transformations being invertible. Do not scale elements by zero!

Type classes

class Transform t where

Apply a matrix transformation directly.

Methods

transform :: u ~ DUnit t => Matrix3'3 u -> t -> t

Instances

Num u => Transform (Point2 u)

Num u => Transform (Vec2 u)

(Num u, Ord u) => Transform (BoundingBox u)

(Num u, Ord u) => Transform (Picture u)

class Rotate t where

Type class for rotation.

Methods

rotate :: Radian -> t -> t

Instances

(Floating u, Real u) => Rotate (Point2 u)

(Floating u, Real u) => Rotate (Vec2 u)

(Real u, Floating u) => Rotate (BoundingBox u)

(Real u, Floating u) => Rotate (Picture u)

class RotateAbout t where

Type class for rotation about a point.

Methods

rotateAbout :: u ~ DUnit t => Radian -> Point2 u -> t -> t

Instances

(Floating u, Real u) => RotateAbout (Point2 u)

(Floating u, Real u) => RotateAbout (Vec2 u)

(Real u, Floating u) => RotateAbout (BoundingBox u)

(Real u, Floating u) => RotateAbout (Picture u)

class Scale t where

Type class for scaling.

Methods

scale :: u ~ DUnit t => u -> u -> t -> t

Instances

Num u => Scale (Point2 u)

Num u => Scale (Vec2 u)

(Num u, Ord u) => Scale (BoundingBox u)

(Num u, Ord u) => Scale (Picture u)

class Translate t where

Type class for translation.

Methods

translate :: DUnit t -> DUnit t -> t -> t

Instances

Num u => Translate (Point2 u)

Num u => Translate (Vec2 u)

(Num u, Ord u) => Translate (BoundingBox u)

(Num u, Ord u) => Translate (Picture u)

Common rotations

rotate30 :: Rotate t => t -> t

Rotate by 30 degrees about the origin.

rotate30About :: (RotateAbout t, DUnit t ~ u) => Point2 u -> t -> t

Rotate by 30 degrees about the supplied point.

rotate45 :: Rotate t => t -> t

Rotate by 45 degrees about the origin.

rotate45About :: (RotateAbout t, DUnit t ~ u) => Point2 u -> t -> t

Rotate by 45 degrees about the supplied point.

rotate60 :: Rotate t => t -> t

Rotate by 60 degrees about the origin.

rotate60About :: (RotateAbout t, DUnit t ~ u) => Point2 u -> t -> t

Rotate by 60 degrees about the supplied point.

rotate90 :: Rotate t => t -> t

Rotate by 90 degrees about the origin.

rotate90About :: (RotateAbout t, DUnit t ~ u) => Point2 u -> t -> t

Rotate by 90 degrees about the supplied point.

rotate120 :: Rotate t => t -> t

Rotate by 120 degrees about the origin.

rotate120About :: (RotateAbout t, DUnit t ~ u) => Point2 u -> t -> t

Rotate by 120 degrees about the supplied point.

Common scalings

uniformScale :: (Scale t, DUnit t ~ u) => u -> t -> t

Scale both x and y dimensions by the same amount.

reflectX :: (Num u, Scale t, DUnit t ~ u) => t -> t

Reflect in the X-plane about the origin.

reflectY :: (Num u, Scale t, DUnit t ~ u) => t -> t

Reflect in the Y-plane about the origin.

Translate by a vector

translateBy :: (Translate t, DUnit t ~ u) => Vec2 u -> t -> t

Translate by the x and y components of a vector.

Reflections in supplied plane rather than about the origin

reflectXPlane :: (Num u, Scale t, Translate t, u ~ DUnit t) => Point2 u -> t -> t

Reflect in the X plane that intersects the supplied point.

reflectYPlane :: (Num u, Scale t, Translate t, u ~ DUnit t) => Point2 u -> t -> t

Reflect in the Y plane that intersects the supplied point.