Diagrams.TwoD

This module defines the two-dimensional vector space R^2, two-dimensional transformations, and various predefined two-dimensional shapes. This module re-exports useful functionality from a group of more specific modules:

• Diagrams.TwoD.Types defines basic types for two-dimensional diagrams, including types representing the 2D Euclidean vector space and various systems of angle measurement.
• Diagrams.TwoD.Align defines alignment combinators specialized to two dimensions (see Diagrams.Align for more general alignment).
• Diagrams.TwoD.Combinators defines ways of combining diagrams specialized to two dimensions (see also Diagrams.Combinators for more general combining).
• Diagrams.TwoD.Transform defines R^2-specific transformations such as rotation by an angle, and scaling, translation, and reflection in the X and Y directions.
• Diagrams.TwoD.Ellipse defines circles and ellipses.
• Diagrams.TwoD.Arc defines circular arcs.
• Diagrams.TwoD.Path exports various operations on two-dimensional paths when viewed as regions of the plane.
• Diagrams.TwoD.Shapes defines other two-dimensional shapes, e.g. various polygons.
• Diagrams.TwoD.Text defines primitive text diagrams.
• Diagrams.TwoD.Image allows importing external images into diagrams.
• Diagrams.TwoD.Util defines some two-dimensional utilities, such as unit vectors and functions for computing the size and extent of diagrams in R^2.
• Diagrams.TwoD.Model defines some aids for visualizing diagrams' internal model (local origins, bounding regions, etc.)

R^2

type R2 = (Double, Double)

The two-dimensional Euclidean vector space R^2.

type P2 = Point R2

Points in R^2.

type T2 = Transformation R2

Transformations in R^2.

unitX :: R2

The unit vector in the positive X direction.

unitY :: R2

The unit vector in the positive Y direction.

unit_X :: R2

The unit vector in the negative X direction.

unit_Y :: R2

The unit vector in the negative Y direction.

direction :: R2 -> CircleFrac

Compute the direction of a vector, measured counterclockwise from the positive x-axis as a fraction of a full turn. The zero vector is arbitrarily assigned the direction 0.

Angles

tau :: Floating a => a

The circle constant, i.e. the ratio of a circle's circumference to its radius. See http://tauday.com/.

class Num a => Angle a where

Type class for types that measure angles.

Methods

toCircleFrac :: a -> CircleFrac

Convert to a fraction of a circle.

fromCircleFrac :: CircleFrac -> a

Convert from a fraction of a circle.

Instances

Angle Deg

360 degrees = 1 full circle.

Angle Rad

tau radians = 1 full circle.

Angle CircleFrac

newtype CircleFrac

Newtype wrapper used to represent angles as fractions of a circle. For example, 13 = tau3 radians = 120 degrees.

Constructors

CircleFrac

Fields

getCircleFrac :: Double

Instances

Enum CircleFrac

Eq CircleFrac

Floating CircleFrac

Fractional CircleFrac

Num CircleFrac

Ord CircleFrac

Read CircleFrac

Real CircleFrac

RealFloat CircleFrac

RealFrac CircleFrac

Show CircleFrac

Angle CircleFrac

newtype Rad

Newtype wrapper for representing angles in radians.

Constructors

Rad

Fields

getRad :: Double

Instances

Enum Rad

Eq Rad

Floating Rad

Fractional Rad

Num Rad

Ord Rad

Read Rad

Real Rad

RealFloat Rad

RealFrac Rad

Show Rad

Angle Rad

tau radians = 1 full circle.

newtype Deg

Newtype wrapper for representing angles in degrees.

Constructors

Deg

Fields

getDeg :: Double

Instances

Enum Deg

Eq Deg

Floating Deg

Fractional Deg

Num Deg

Ord Deg

Read Deg

Real Deg

RealFloat Deg

RealFrac Deg

Show Deg

Angle Deg

360 degrees = 1 full circle.

fullCircle :: Angle a => a

An angle representing a full circle.

convertAngle :: (Angle a, Angle b) => a -> b

Convert between two angle representations.

Paths

Stroking

stroke :: Renderable (Path R2) b => Path R2 -> Diagram b R2

Convert a path into a diagram. The resulting diagram has the names 0, 1, ... assigned to each of the path's vertices.

See also stroke', which takes an extra options record allowing its behavior to be customized.

Note that a bug in GHC 7.0.1 causes a context stack overflow when inferring the type of stroke. The solution is to give a type signature to expressions involving stroke, or (recommended) upgrade GHC (the bug is fixed in 7.0.2 onwards).

stroke' :: (Renderable (Path R2) b, Atomic a) => StrokeOpts a -> Path R2 -> Diagram b R2

A variant of stroke that takes an extra record of options to customize its behavior. In particular:

• Names can be assigned to the path's vertices

StrokeOpts is an instance of Default, so stroke' with { ... } syntax may be used.

strokeT :: Renderable (Path R2) b => Trail R2 -> Diagram b R2

A composition of stroke and pathFromTrail for conveniently converting a trail directly into a diagram.

Note that a bug in GHC 7.0.1 causes a context stack overflow when inferring the type of stroke and hence of strokeT as well. The solution is to give a type signature to expressions involving strokeT, or (recommended) upgrade GHC (the bug is fixed in 7.0.2 onwards).

strokeT' :: (Renderable (Path R2) b, Atomic a) => StrokeOpts a -> Trail R2 -> Diagram b R2

A composition of stroke' and pathFromTrail for conveniently converting a trail directly into a diagram.

data StrokeOpts a

A record of options that control how a path is stroked. StrokeOpts is an instance of Default, so a StrokeOpts records can be created using with { ... } notation.

Constructors

StrokeOpts

Fields

vertexNames :: [[a]]

Atomic names that should be assigned to the vertices of the path so that they can be referenced later. If there are not enough names, the extra vertices are not assigned names; if there are too many, the extra names are ignored. Note that this is a list of lists of names, since paths can consist of multiple trails. The first list of names are assigned to the vertices of the first trail, the second list to the second trail, and so on.

The default value is the empty list.

Instances

Default (StrokeOpts a)

Clipping

clipBy :: (HasStyle a, V a ~ R2) => Path R2 -> a -> a

Clip a diagram by the given path:

• Only the parts of the diagram which lie in the interior of the path will be drawn.
• The bounding function of the diagram is unaffected.

Shapes

Rules

hrule :: (PathLike p, V p ~ R2) => Double -> p

Create a centered horizontal (L-R) line of the given length.

vrule :: (PathLike p, V p ~ R2) => Double -> p

Create a centered vertical (T-B) line of the given length.

Circle-ish things

unitCircle :: (Backend b R2, Renderable Ellipse b) => Diagram b R2

A circle of radius 1, with center at the origin.

circle :: (Backend b R2, Renderable Ellipse b) => Double -> Diagram b R2

A circle of the given radius, centered at the origin.

ellipse :: (Backend b R2, Renderable Ellipse b) => Double -> Diagram b R2

ellipse e constructs an ellipse with eccentricity e by scaling the unit circle in the X direction. The eccentricity must be within the interval [0,1).

ellipseXY :: (Backend b R2, Renderable Ellipse b) => Double -> Double -> Diagram b R2

ellipseXY x y creates an axis-aligned ellipse, centered at the origin, with radius x along the x-axis and radius y along the y-axis.

arc :: (Angle a, PathLike p, V p ~ R2) => a -> a -> p

Given a start angle s and an end angle e, arc s e is the path of a radius one arc counterclockwise between the two angles.

General polygons

polygon :: (PathLike p, V p ~ R2) => PolygonOpts -> p

Create a closed regular polygon from the given options.

polygonVertices :: PolygonOpts -> [P2]

Generate the vertices of a regular polygon from the given options.

data PolygonOpts

Constructors

PolygonOpts

Fields

sides :: Int

Number of sides; the default is 5.

edgeSkip :: Int

Create star polygons by setting the edge skip to some number other than 1 (the default). With an edge skip of n, edges will connect every nth vertex.

orientation :: PolygonOrientation

Determine how the polygon should be oriented.

Instances

Eq PolygonOpts

Ord PolygonOpts

Read PolygonOpts

Show PolygonOpts

Default PolygonOpts

data PolygonOrientation

Determine how a polygon should be oriented.

Constructors

NoOrient

No special orientation; one vertex will be at (1,0). This is the default.

OrientToX

Orient so the botommost edge is parallel to the x-axis.

OrientToY

Orient so the leftmost edge is parallel to the y-axis.

Instances

Eq PolygonOrientation

Ord PolygonOrientation

Read PolygonOrientation

Show PolygonOrientation

Special polygons

unitSquare :: (Transformable p, PathLike p, V p ~ R2) => p

A sqaure with its center at the origin and sides of length 1, oriented parallel to the axes.

square :: (PathLike p, Transformable p, V p ~ R2) => Double -> p

A sqaure with its center at the origin and sides of the given length, oriented parallel to the axes.

rect :: (PathLike p, Transformable p, V p ~ R2) => Double -> Double -> p

rect w h is an axis-aligned rectangle of width w and height h, centered at the origin.

starPolygon :: (PathLike p, Transformable p, V p ~ R2) => Int -> Int -> p

starPolygon p q creates a star polygon, where p indicates the number of vertices, and an edge connects every qth vertex.

eqTriangle :: (PathLike p, Transformable p, V p ~ R2) => p

An equilateral triangle, with radius 1 and base parallel to the x-axis.

Other shapes

roundedRect :: (PathLike p, V p ~ R2) => R2 -> Double -> p

roundedRect v r generates a closed trail, or closed path centered at the origin, of an axis-aligned rectangle with diagonal v and circular rounded corners of radius r. r must be between 0 and half the smaller dimension of v, inclusive; smaller or larger values of r will be treated as 0 or half the smaller dimension of v, respectively. The trail or path begins with the right edge and proceeds counterclockwise.

Text

text :: Renderable Text b => String -> Diagram b R2

Create a primitive text diagram from the given string, which takes up no space. By default, the text is centered with respect to its local origin (see alignText).

font :: HasStyle a => String -> a -> a

Specify a font family to be used for all text within a diagram.

fontSize :: HasStyle a => Double -> a -> a

Set the font size, that is, the size of the font's em-square as measured within the current local vector space. The default size is 1.

italic :: HasStyle a => a -> a

Set all text in italics.

oblique :: HasStyle a => a -> a

Set all text using an oblique slant.

bold :: HasStyle a => a -> a

Set all text using a bold font weight.

Images

image :: Renderable Image b => FilePath -> Double -> Double -> Diagram b R2

Take an external image from the specified file and turn it into a diagram with the specified width and height, centered at the origin. Note that the image's aspect ratio will be preserved; if the specified width and height have a different ratio than the image's aspect ratio, there will be extra space in one dimension.

Transformations

Rotation

rotation :: Angle a => a -> T2

Create a transformation which performs a rotation by the given angle. See also rotate.

rotate :: (Transformable t, V t ~ R2, Angle a) => a -> t -> t

Rotate by the given angle. Positive angles correspond to counterclockwise rotation, negative to clockwise. The angle can be expressed using any type which is an instance of Angle. For example, rotate (14 :: 'CircleFrac')@, @rotate (pi2 :: Rad), and rotate (90 :: Deg) all represent the same transformation, namely, a counterclockwise rotation by a right angle.

Note that writing rotate (1/4), with no type annotation, will yield an error since GHC cannot figure out which sort of angle you want to use. In this common situation you can use rotateBy, which is specialized to take a CircleFrac argument.

rotateBy :: (Transformable t, V t ~ R2) => CircleFrac -> t -> t

A synonym for rotate, specialized to only work with CircleFrac arguments; it can be more convenient to write rotateBy (14)@ than @'rotate' (14 :: CircleFrac).

rotationAbout :: Angle a => P2 -> a -> T2

rotationAbout p is a rotation about the point p (instead of around the local origin).

rotateAbout :: (Transformable t, V t ~ R2, Angle a) => P2 -> a -> t -> t

rotateAbout p is like rotate, except it rotates around the point p instead of around the local origin.

Scaling

scalingX :: Double -> T2

Construct a transformation which scales by the given factor in the x (horizontal) direction.

scaleX :: (Transformable t, V t ~ R2) => Double -> t -> t

Scale a diagram by the given factor in the x (horizontal) direction. To scale uniformly, use Graphics.Rendering.Diagrams.Transform.scale.

scalingY :: Double -> T2

Construct a transformation which scales by the given factor in the y (vertical) direction.

scaleY :: (Transformable t, V t ~ R2) => Double -> t -> t

Scale a diagram by the given factor in the y (vertical) direction. To scale uniformly, use Graphics.Rendering.Diagrams.Transform.scale.

scaling :: (HasLinearMap v, Fractional (Scalar v)) => Scalar v -> Transformation v

Create a uniform scaling transformation.

scale :: (Transformable t, Fractional (Scalar (V t))) => Scalar (V t) -> t -> t

Scale uniformly in every dimension by the given scalar.

scaleToX :: (Boundable t, Transformable t, V t ~ R2) => Double -> t -> t

scaleToX w scales a diagram in the x (horizontal) direction by whatever factor required to make its width w. scaleToX should not be applied to diagrams with a width of 0, such as vrule.

scaleToY :: (Boundable t, Transformable t, V t ~ R2) => Double -> t -> t

scaleToY h scales a diagram in the y (vertical) direction by whatever factor required to make its height h. scaleToY should not be applied to diagrams with a width of 0, such as hrule.

Translation

translationX :: Double -> T2

Construct a transformation which translates by the given distance in the x (horizontal) direction.

translateX :: (Transformable t, V t ~ R2) => Double -> t -> t

Translate a diagram by the given distance in the x (horizontal) direction.

translationY :: Double -> T2

Construct a transformation which translates by the given distance in the y (vertical) direction.

translateY :: (Transformable t, V t ~ R2) => Double -> t -> t

Translate a diagram by the given distance in the y (vertical) direction.

translation :: HasLinearMap v => v -> Transformation v

Create a translation.

translate :: (Transformable t, HasLinearMap (V t)) => V t -> t -> t

Translate by a vector.

Reflection

reflectionX :: T2

Construct a transformation which flips a diagram from left to right, i.e. sends the point (x,y) to (-x,y).

reflectX :: (Transformable t, V t ~ R2) => t -> t

Flip a diagram from left to right, i.e. send the point (x,y) to (-x,y).

reflectionY :: T2

Construct a transformation which flips a diagram from top to bottom, i.e. sends the point (x,y) to (x,-y).

reflectY :: (Transformable t, V t ~ R2) => t -> t

Flip a diagram from top to bottom, i.e. send the point (x,y) to (x,-y).

reflectionAbout :: P2 -> R2 -> T2

reflectionAbout p v is a reflection in the line determined by the point p and vector v.

reflectAbout :: (Transformable t, V t ~ R2) => P2 -> R2 -> t -> t

reflectAbout p v reflects a diagram in the line determined by the point p and the vector v.

Combinators

strutX :: (Backend b R2, Monoid m) => Double -> AnnDiagram b R2 m

strutX d is an empty diagram with width d and height 0. Note that strutX (-w) behaves the same as strutX w.

strutY :: (Backend b R2, Monoid m) => Double -> AnnDiagram b R2 m

strutY d is an empty diagram with height d and width 0. Note that strutX (-w) behaves the same as strutX w.

(===) :: (HasOrigin a, Boundable a, V a ~ R2, Monoid a) => a -> a -> a

Place two diagrams (or other boundable objects) vertically adjacent to one another, with the first diagram above the second. Since Haskell ignores whitespace in expressions, one can thus write

    c
   ===
    d

to place c above d.

(|||) :: (HasOrigin a, Boundable a, V a ~ R2, Monoid a) => a -> a -> a

Place two diagrams (or other boundable objects) horizontally adjacent to one another, with the first diagram to the left of the second.

hcat :: (HasOrigin a, Boundable a, Qualifiable a, V a ~ R2, Monoid a) => [a] -> a

Lay out a list of boundable objects in a row from left to right, so that their local origins lie along a single horizontal line, with successive bounding regions tangent to one another.

• For more control over the spacing, see hcat'.
• To align the diagrams vertically (or otherwise), use alignment combinators (such as alignT or alignB) from Diagrams.TwoD.Align before applying hcat.
• For non-axis-aligned layout, see cat.

hcat' :: (HasOrigin a, Boundable a, Qualifiable a, V a ~ R2, Monoid a) => CatOpts R2 -> [a] -> a

A variant of hcat taking an extra CatOpts record to control the spacing. See the cat' documentation for a description of the possibilities.

vcat :: (HasOrigin a, Boundable a, Qualifiable a, V a ~ R2, Monoid a) => [a] -> a

Lay out a list of boundable objects in a column from top to bottom, so that their local origins lie along a single vertical line, with successive bounding regions tangent to one another.

• For more control over the spacing, see vcat'.
• To align the diagrams horizontally (or otherwise), use alignment combinators (such as alignL or alignR) from Diagrams.TwoD.Align before applying vcat.
• For non-axis-aligned layout, see cat.

vcat' :: (HasOrigin a, Boundable a, Qualifiable a, V a ~ R2, Monoid a) => CatOpts R2 -> [a] -> a

A variant of vcat taking an extra CatOpts record to control the spacing. See the cat' documentation for a description of the possibilities.

Alignment

alignL :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

Align along the left edge, i.e. translate the diagram in a horizontal direction so that the local origin is on the left edge of the bounding region.

alignR :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

Align along the right edge.

alignT :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

Align along the top edge.

alignB :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

Align along the bottom edge.

alignTL :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

alignTR :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

alignBL :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

alignBR :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

alignX :: (HasOrigin a, Boundable a, V a ~ R2) => Double -> a -> a

alignX moves the local origin horizontally as follows:

• alignX (-1) moves the local origin to the left edge of the bounding region;
• align 1 moves the local origin to the right edge;
• any other argument interpolates linearly between these. For example, alignX 0 centers, alignX 2 moves the origin one "radius" to the right of the right edge, and so on.

alignY :: (HasOrigin a, Boundable a, V a ~ R2) => Double -> a -> a

Like alignX, but moving the local origin vertically, with an argument of 1 corresponding to the top edge and (-1) corresponding to the bottom edge.

centerX :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

Center the local origin along the X-axis.

centerY :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

Center the local origin along the Y-axis.

centerXY :: (HasOrigin a, Boundable a, V a ~ R2) => a -> a

Center along both the X- and Y-axes.

Size

Computing size

width :: (Boundable a, V a ~ R2) => a -> Double

Compute the width of a diagram.

height :: (Boundable a, V a ~ R2) => a -> Double

Compute the height of a diagram.

size2D :: (Boundable a, V a ~ R2) => a -> (Double, Double)

Compute the width and height of a diagram.

extentX :: (Boundable a, V a ~ R2) => a -> (Double, Double)

Compute the absolute x-coordinate range of a diagram in R2, in the form (lo,hi).

extentY :: (Boundable a, V a ~ R2) => a -> (Double, Double)

Compute the absolute y-coordinate range of a diagram in R2, in the form (lo,hi).

center2D :: (Boundable a, V a ~ R2) => a -> P2

Compute the point at the center (in the x- and y-directions) of a diagram.

Specifying size

data SizeSpec2D

A specification of a (requested) rectangular size.

Constructors

Width Double

Specify an explicit width. The height should be determined automatically (so as to preserve aspect ratio).

Height Double

Specify an explicit height. The width should be determined automatically (so as to preserve aspect ratio)

Dims Double Double

An explicit specification of both dimensions.

Absolute

Absolute size: use whatever size an object already has; do not rescale.

Visual aids for understanding the internal model

showOrigin :: (Renderable Ellipse b, Backend b R2, Monoid m) => AnnDiagram b R2 m -> AnnDiagram b R2 m

Mark the origin of a diagram by placing a red dot 1/50th its size.

showLabels :: (Renderable Text b, Backend b R2) => AnnDiagram b R2 m -> AnnDiagram b R2 Any