diagrams-lib-0.4.0.1: Embedded domain-specific language for declarative graphics

Diagrams.TwoD

Description

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:

Synopsis

# R^2

type R2 = (Double, Double)Source

The two-dimensional Euclidean vector space R^2.

type P2 = Point R2Source

Points in R^2.

Transformations in R^2.

The unit vector in the positive X direction.

The unit vector in the positive Y direction.

The unit vector in the negative X direction.

The unit vector in the negative Y direction.

direction :: Angle a => R2 -> aSource

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.

fromDirection :: Angle a => a -> R2Source

Convert an angle into a unit vector pointing in that direction.

e :: Angle a => a -> R2Source

A convenient synonym for `fromDirection`.

# Angles

tau :: Floating a => a

A convenient synonym for those wishing to avoid Unicode identifiers.

class Num a => Angle a whereSource

Type class for types that measure angles.

Methods

toCircleFrac :: a -> CircleFracSource

Convert to a fraction of a circle.

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 Source

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

Constructors

 CircleFrac FieldsgetCircleFrac :: Double

Newtype wrapper for representing angles in radians.

Constructors

Instances

newtype Deg Source

Newtype wrapper for representing angles in degrees.

Constructors

 Deg FieldsgetDeg :: 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 => aSource

An angle representing a full circle.

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

Convert between two angle representations.

# Paths

## Stroking

stroke :: Renderable (Path R2) b => Path R2 -> Diagram b R2Source

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, IsName a) => StrokeOpts a -> Path R2 -> Diagram b R2Source

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 R2Source

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, IsName a) => StrokeOpts a -> Trail R2 -> Diagram b R2Source

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

data FillRule Source

Enumeration of algorithms or "rules" for determining which points lie in the interior of a (possibly self-intersecting) closed path.

Constructors

 Winding Interior points are those with a nonzero winding number. See http://en.wikipedia.org/wiki/Nonzero-rule. EvenOdd Interior points are those where a ray extended infinitely in a particular direction crosses the path an odd number of times. See http://en.wikipedia.org/wiki/Even-odd_rule.

fillRule :: HasStyle a => FillRule -> a -> aSource

Specify the fill rule that should be used for determining which points are inside a path.

data StrokeOpts a Source

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 FieldsvertexNames :: [[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. queryFillRule :: FillRuleThe fill rule used for determining which points are inside the path. The default is `Winding`. NOTE: for now, this only affects the resulting diagram's `Query`, not how it will be drawn! To set the fill rule determining how it is to be drawn, use the `fillRule` function.

Instances

 Default (StrokeOpts a)

## Clipping

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

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 -> pSource

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

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

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

## Circle-ish things

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

circle :: (Backend b R2, Renderable Ellipse b) => Double -> Diagram b R2Source

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

circlePath :: (PathLike p, Closeable p, V p ~ R2, Transformable p) => Double -> pSource

Create a closed circular path of the given radius, centered at the origin, beginning at (r,0).

ellipse :: (Backend b R2, Renderable Ellipse b) => Double -> Diagram b R2Source

`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 R2Source

`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 -> pSource

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.

wedge :: (Angle a, PathLike p, V p ~ R2) => Double -> a -> a -> pSource

Create a circular wedge of the given radius, beginning at the first angle and extending counterclockwise to the second.

## General polygons

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

Generate the vertices of a polygon. See `PolygonOpts` for more information.

Options for specifying a polygon.

Constructors

 PolygonOpts FieldspolyType :: PolyTypeSpecification for the polygon's vertices. polyOrient :: PolyOrientationShould a rotation be applied to the polygon in order to orient it in a particular way? polyCenter :: P2Should a translation be applied to the polygon in order to place the center at a particular location?

Instances

 Default PolygonOpts The default polygon is a regular pentagon of radius 1, centered at the origin, aligned to the x-axis.

data PolyType Source

Method used to determine the vertices of a polygon.

Constructors

 forall a . Angle a => PolyPolar [a] [Double] A "polar" polygon. The first argument is a list of central angles from each vertex to the next. The second argument is a list of radii from the origin to each successive vertex. To construct an n-gon, use a list of n-1 angles and n radii. Extra angles or radii are ignored. Cyclic polygons (with all vertices lying on a circle) can be constructed using a second argument of `(repeat r)`. forall a . Angle a => PolySides [a] [Double] A polygon determined by the distance between successive vertices and the angles formed by each three successive vertices. In other words, a polygon specified by "turtle graphics": go straight ahead x1 units; turn by angle a1; go straght ahead x2 units; turn by angle a2; etc. The polygon will be centered at the centroid of its vertices. The first argument is a list of vertex angles, giving the angle at each vertex from the previous vertex to the next. The first angle in the list is the angle at the second vertex; the first edge always starts out heading in the positive y direction from the first vertex. The second argument is a list of distances between successive vertices. To construct an n-gon, use a list of n-2 angles and n-1 edge lengths. Extra angles or lengths are ignored. PolyRegular Int Double A regular polygon with the given number of sides (first argument) and the given radius (second argument).

Determine how a polygon should be oriented.

Constructors

 NoOrient No special orientation; the first vertex will be at (1,0). This is the default. OrientH Orient horizontally, so the bottommost edge is parallel to the x-axis. OrientV Orient vertically, so the leftmost edge is parallel to the y-axis. OrientTo R2 Orient so some edge is facing in the direction of, that is, perpendicular to, the given vector.

## Star polygons

data StarOpts Source

Options for creating "star" polygons, where the edges connect possibly non-adjacent vertices.

Constructors

 StarFun (Int -> Int) Specify the order in which the vertices should be connected by a function that maps each vertex index to the index of the vertex that should come next. Indexing of vertices begins at 0. StarSkip Int Specify a star polygon by a "skip". A skip of 1 indicates a normal polygon, where edges go between successive vertices. A skip of 2 means that edges will connect every second vertex, skipping one in between. Generally, a skip of n means that edges will connect every nth vertex.

star :: StarOpts -> [P2] -> Path R2Source

Create a generalized star polygon. The `StarOpts` are used to determine in which order the given vertices should be connected. The intention is that the second argument of type `[P2]` could be generated by a call to `polygon`, `regPoly`, or the like, since a list of vertices is `PathLike`. But of course the list can be generated any way you like. A `Path R2` is returned (instead of any `PathLike`) because the resulting path may have more than one component, for example if the vertices are to be connected in several disjoint cycles.

## Regular polygons

regPoly :: (PathLike p, V p ~ R2) => Int -> Double -> pSource

Create a regular polygon. The first argument is the number of sides, and the second is the length of the sides. (Compare to the `polygon` function with a `PolyRegular` option, which produces polygons of a given radius).

The polygon will be oriented with one edge parallel to the x-axis.

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

An equilateral triangle, with sides of the given length and base parallel to the x-axis.

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

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

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

A regular pentagon, with sides of the given length and base parallel to the x-axis.

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

A regular hexagon, with sides of the given length and base parallel to the x-axis.

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

A regular septagon, with sides of the given length and base parallel to the x-axis.

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

A regular octagon, with sides of the given length and base parallel to the x-axis.

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

A regular nonagon, with sides of the given length and base parallel to the x-axis.

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

A regular decagon, with sides of the given length and base parallel to the x-axis.

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

A regular hendecagon, with sides of the given length and base parallel to the x-axis.

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

A regular dodecagon, with sides of the given length and base parallel to the x-axis.

## Other special polygons

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

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

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

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

## Other shapes

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

`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

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 -> aSource

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

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

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 -> aSource

Set all text in italics.

oblique :: HasStyle a => a -> aSource

Set all text using an oblique slant.

bold :: HasStyle a => a -> aSource

Set all text using a bold font weight.

# Images

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 -> T2Source

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

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

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 (1/4 :: CircleFrac)`, `rotate (tau/4 :: 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 -> tSource

A synonym for `rotate`, specialized to only work with `CircleFrac` arguments; it can be more convenient to write `rotateBy (1/4)` than `rotate (1/4 :: CircleFrac)`.

rotationAbout :: Angle a => P2 -> a -> T2Source

`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 -> tSource

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

## Scaling

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

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

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

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

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

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 -> tSource

`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 -> tSource

`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`.

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

`scaleUToX w` scales a diagram uniformly by whatever factor required to make its width `w`. `scaleUToX` should not be applied to diagrams with a width of 0, such as `vrule`.

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

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

## Translation

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

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

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

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

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

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

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 -> tSource

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

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 -> tSource

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

`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 -> tSource

`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 mSource

`strutX d` is an empty diagram with width `d`, height 0, and a centered local origin. Note that `strutX (-w)` behaves the same as `strutX w`.

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

`strutY d` is an empty diagram with height `d`, width 0, and a centered local origin. Note that `strutX (-w)` behaves the same as `strutX w`.

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

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 -> aSource

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, V a ~ R2, Monoid a) => [a] -> aSource

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, V a ~ R2, Monoid a) => CatOpts R2 -> [a] -> aSource

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, V a ~ R2, Monoid a) => [a] -> aSource

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, V a ~ R2, Monoid a) => CatOpts R2 -> [a] -> aSource

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 -> aSource

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 -> aSource

Align along the right edge.

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

Align along the top edge.

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

Align along the bottom edge.

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

`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 -> aSource

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 -> aSource

Center the local origin along the X-axis.

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

Center the local origin along the Y-axis.

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

Center along both the X- and Y-axes.

# Size

## Computing size

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

Compute the width of a boundable object.

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

Compute the height of a boundable object.

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

Compute the width and height of a boundable object.

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

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

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

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

center2D :: (Boundable a, V a ~ R2) => a -> P2Source

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

## Specifying size

data SizeSpec2D Source

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 mSource

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