Wumpus.Core.AffineTrans

Affine transformations.

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

Internally, when a picture is composed and transformed, Wumpus only transforms the bounding box - transformations of the picture content (paths or text labels) are communicated to PostScript or SVG for final rendering. This is because Wumpus has no access to the paths that make fonts so cannot transform them directly.

As well as Pictures, some elements - e.g. Vectors, Points and BoundingBoxes - are also instances of the affine classes. The implementation of the instances considers that under transformation these objects are implicitly within the standard affine frame (origin at point zero and unit basis vectors for the horizontal and vertical).

This assumption cannot hold for primitives because text is special in PostScript and SVG, so there are no instances of the affine classes for Primitive or PrimElement.

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.