Maintainer  diagramsdiscuss@googlegroups.com 

This module defines the twodimensional vector space R^2, twodimensional transformations, and various predefined twodimensional shapes. This module reexports useful functionality from a group of more specific modules:
 Diagrams.TwoD.Types defines basic types for twodimensional 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^2specific transformations such as rotation by an angle, and scaling, translation, and reflection in the X and Y directions.
 Diagrams.TwoD.Ellipse defines ellipses.
 Diagrams.TwoD.Arc defines circular arcs.
 Diagrams.TwoD.Path exports various operations on twodimensional paths when viewed as regions of the plane.
 Diagrams.TwoD.Shapes defines other twodimensional shapes, e.g. various polygons.
 Diagrams.TwoD.Util defines some twodimensional 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.)
 type R2 = (Double, Double)
 type P2 = Point R2
 unitX :: R2
 unitY :: R2
 unit_X :: R2
 unit_Y :: R2
 direction :: R2 > CircleFrac
 tau :: Floating a => a
 class Num a => Angle a where
 toCircleFrac :: a > CircleFrac
 fromCircleFrac :: CircleFrac > a
 newtype CircleFrac = CircleFrac {}
 newtype Rad = Rad {}
 newtype Deg = Deg {}
 fullCircle :: Angle a => a
 convertAngle :: (Angle a, Angle b) => a > b
 stroke :: Renderable (Path R2) b => Path R2 > Diagram b R2
 strokeT :: Renderable (Path R2) b => Trail R2 > Diagram b R2
 newtype Clip = Clip [Path R2]
 clipBy :: (HasStyle a, V a ~ R2) => Path R2 > a > a
 hrule :: (Backend b R2, Renderable (Path R2) b) => Double > Diagram b R2
 vrule :: (Backend b R2, Renderable (Path R2) b) => Double > Diagram b R2
 circle :: (Backend b R2, Renderable Ellipse b) => Diagram b R2
 ellipse :: (Backend b R2, Renderable Ellipse b) => Double > Diagram b R2
 arc :: (Angle a, PathLike p, V p ~ R2) => a > a > p
 polygon :: (Backend b R2, Renderable (Path R2) b) => PolygonOpts > Diagram b R2
 polygonPath :: (PathLike p, V p ~ R2) => PolygonOpts > p
 polygonVertices :: PolygonOpts > [P2]
 data PolygonOpts = PolygonOpts {
 sides :: Int
 edgeSkip :: Int
 orientation :: PolygonOrientation
 data PolygonOrientation
 square :: (Backend b R2, Renderable (Path R2) b) => Diagram b R2
 rect :: (Backend b R2, Renderable (Path R2) b) => Double > Double > Diagram b R2
 starPolygon :: (Backend b R2, Renderable (Path R2) b) => Int > Int > Diagram b R2
 eqTriangle :: (Backend b R2, Renderable (Path R2) b) => Diagram b R2
 roundedRectPath :: (PathLike p, V p ~ R2) => R2 > Double > p
 roundedRect :: (Backend b R2, Renderable (Path R2) b) => R2 > Double > Diagram b R2
 rotation :: Angle a => a > T2
 rotate :: (Transformable t, V t ~ R2, Angle a) => a > t > t
 rotateBy :: (Transformable t, V t ~ R2) => CircleFrac > t > t
 rotationAbout :: Angle a => P2 > a > T2
 rotateAbout :: (Transformable t, V t ~ R2, Angle a) => P2 > a > t > t
 scalingX :: Double > T2
 scaleX :: (Transformable t, V t ~ R2) => Double > t > t
 scalingY :: Double > T2
 scaleY :: (Transformable t, V t ~ R2) => Double > t > t
 scaling :: (HasLinearMap v, Fractional (Scalar v)) => Scalar v > Transformation v
 scale :: (Transformable t, Fractional (Scalar (V t))) => Scalar (V t) > t > t
 scaleToX :: (Boundable t, Transformable t, V t ~ R2) => Double > t > t
 scaleToY :: (Boundable t, Transformable t, V t ~ R2) => Double > t > t
 translationX :: Double > T2
 translateX :: (Transformable t, V t ~ R2) => Double > t > t
 translationY :: Double > T2
 translateY :: (Transformable t, V t ~ R2) => Double > t > t
 translation :: HasLinearMap v => v > Transformation v
 translate :: (Transformable t, HasLinearMap (V t)) => V t > t > t
 reflectionX :: T2
 reflectX :: (Transformable t, V t ~ R2) => t > t
 reflectionY :: T2
 reflectY :: (Transformable t, V t ~ R2) => t > t
 reflectionAbout :: P2 > R2 > T2
 reflectAbout :: (Transformable t, V t ~ R2) => P2 > R2 > t > t
 strutX :: (Backend b R2, Monoid m) => Double > AnnDiagram b R2 m
 strutY :: (Backend b R2, Monoid m) => Double > AnnDiagram b R2 m
 (===) :: (HasOrigin a, Boundable a, V a ~ R2, Monoid a) => a > a > a
 () :: (HasOrigin a, Boundable a, V a ~ R2, Monoid a) => a > a > a
 hcat :: (HasOrigin a, Boundable a, Qualifiable a, V a ~ R2, Monoid a) => [a] > a
 hcat' :: (HasOrigin a, Boundable a, Qualifiable a, V a ~ R2, Monoid a) => CatOpts R2 > [a] > a
 vcat :: (HasOrigin a, Boundable a, Qualifiable a, V a ~ R2, Monoid a) => [a] > a
 vcat' :: (HasOrigin a, Boundable a, Qualifiable a, V a ~ R2, Monoid a) => CatOpts R2 > [a] > a
 alignL :: (HasOrigin a, Boundable a, V a ~ R2) => a > a
 alignR :: (HasOrigin a, Boundable a, V a ~ R2) => a > a
 alignT :: (HasOrigin a, Boundable a, V a ~ R2) => a > a
 alignB :: (HasOrigin a, Boundable a, V a ~ R2) => a > a
 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) => Rational > a > a
 alignY :: (HasOrigin a, Boundable a, V a ~ R2) => Rational > a > a
 centerX :: (HasOrigin a, Boundable a, V a ~ R2) => a > a
 centerY :: (HasOrigin a, Boundable a, V a ~ R2) => a > a
 centerXY :: (HasOrigin a, Boundable a, V a ~ R2) => a > a
 width :: (Boundable a, V a ~ R2) => a > Double
 height :: (Boundable a, V a ~ R2) => a > Double
 size2D :: (Boundable a, V a ~ R2) => a > (Double, Double)
 extentX :: (Boundable a, V a ~ R2) => a > (Double, Double)
 extentY :: (Boundable a, V a ~ R2) => a > (Double, Double)
 center2D :: (Boundable a, V a ~ R2) => a > P2
 showOrigin :: (Renderable Ellipse b, Backend b R2, Monoid m) => AnnDiagram b R2 m > AnnDiagram b R2 m
R^2
direction :: R2 > CircleFracSource
Compute the direction of a vector, measured counterclockwise from the positive xaxis as a fraction of a full turn. The zero vector is arbitrarily assigned the direction 0.
Angles
The circle constant, i.e. the ratio of a circle's circumference to its radius.
class Num a => Angle a whereSource
Type class for types that measure angles.
toCircleFrac :: a > CircleFracSource
Convert to a fraction of a circle.
fromCircleFrac :: CircleFrac > aSource
Convert from a fraction of a circle.
newtype CircleFrac Source
Newtype wrapper used to represent angles as fractions of a circle. For example, 13 = tau3 radians = 120 degrees.
Newtype wrapper for representing angles in radians.
Newtype wrapper for representing angles in degrees.
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.
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).
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).
Clipping
Clip
tracks the accumulated clipping paths applied to a
diagram. Note that the semigroup structure on Clip
is list
concatenation, so applying multiple clipping paths is sensible.
The clipping region is the intersection of all the applied
clipping paths.
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 :: (Backend b R2, Renderable (Path R2) b) => Double > Diagram b R2Source
Create a centered horizontal line of the given length.
vrule :: (Backend b R2, Renderable (Path R2) b) => Double > Diagram b R2Source
Create a centered vertical line of the given length.
Circleish things
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).
arc :: (Angle a, PathLike p, V p ~ R2) => a > a > pSource
Given a start angle s
and an end angle e
,
is the
path of a radius one arc counterclockwise between the two angles.
arc
s e
General polygons
polygon :: (Backend b R2, Renderable (Path R2) b) => PolygonOpts > Diagram b R2Source
Create a regular polygon from the given options.
polygonPath :: (PathLike p, V p ~ R2) => PolygonOpts > pSource
Create a closed regular polygonal path from the given options.
polygonVertices :: PolygonOpts > [P2]Source
Generate the vertices of a regular polygon from the given options.
data PolygonOpts Source
PolygonOpts  

data PolygonOrientation Source
Determine how a polygon should be oriented.
Special polygons
square :: (Backend b R2, Renderable (Path R2) b) => Diagram b R2Source
A sqaure with its center at the origin and sides of length 1, oriented parallel to the axes.
rect :: (Backend b R2, Renderable (Path R2) b) => Double > Double > Diagram b R2Source
rect w h
is an axisaligned rectangle of width w
and height
h
, centered at the origin.
starPolygon :: (Backend b R2, Renderable (Path R2) b) => Int > Int > Diagram b R2Source
starPolygon p q
creates a star polygon, where p
indicates the
number of vertices, and an edge connects every q
th vertex.
eqTriangle :: (Backend b R2, Renderable (Path R2) b) => Diagram b R2Source
An equilateral triangle, with radius 1 and base parallel to the xaxis.
Other shapes
roundedRectPath :: (PathLike p, V p ~ R2) => R2 > Double > pSource
roundedRectPath v r
generates a closed trail, or closed path
centered at the origin, of an axisaligned 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.
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 (14 :: 'CircleFrac')@, @rotate (pi2 ::
, and
Rad
)rotate (90 ::
all represent the same transformation, namely,
a counterclockwise rotation by a right angle.
Deg
)
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 (14)@ than @'rotate' (14 ::
.
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
scalingX :: Double > T2Source
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
.
scalingY :: Double > T2Source
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
.
Translation
translationX :: Double > T2Source
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.
translationY :: Double > T2Source
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 :: P2 > R2 > T2Source
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
and height 0.
strutY :: (Backend b R2, Monoid m) => Double > AnnDiagram b R2 mSource
strutY d
is an empty diagram with height d
and width 0.
(===) :: (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, Qualifiable 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
oralignB
) from Diagrams.TwoD.Align before applyinghcat
.  For nonaxisaligned layout, see
cat
.
hcat' :: (HasOrigin a, Boundable a, Qualifiable a, V a ~ R2, Monoid a) => CatOpts R2 > [a] > aSource
vcat :: (HasOrigin a, Boundable a, Qualifiable 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
oralignR
) from Diagrams.TwoD.Align before applyingvcat
.  For nonaxisaligned layout, see
cat
.
vcat' :: (HasOrigin a, Boundable a, Qualifiable a, V a ~ R2, Monoid a) => CatOpts R2 > [a] > aSource
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.
alignX :: (HasOrigin a, Boundable a, V a ~ R2) => Rational > 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) => Rational > 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 Xaxis.
centerY :: (HasOrigin a, Boundable a, V a ~ R2) => a > aSource
Center the local origin along the Yaxis.
centerXY :: (HasOrigin a, Boundable a, V a ~ R2) => a > aSource
Center along both the X and Yaxes.
Utilities
size2D :: (Boundable a, V a ~ R2) => a > (Double, Double)Source
Compute the width and height of a diagram.
extentX :: (Boundable a, V a ~ R2) => a > (Double, Double)Source
Compute the absolute xcoordinate range of a diagram in R2, in the form (lo,hi).
extentY :: (Boundable a, V a ~ R2) => a > (Double, Double)Source
Compute the absolute ycoordinate range of a diagram 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 ydirections) of a diagram.
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.