The two-dimensional Euclidean vector space R^2. This type is intentionally abstract.

• To construct a vector, use r2, or ^& (from Diagrams.Coordinates):

 r2 (3,4) :: R2
 3 ^& 4    :: R2

Note that Diagrams.Coordinates is not re-exported by Diagrams.Prelude and must be explicitly imported.

• To construct the vector from the origin to a point p, use p .-. origin.
• To convert a vector v into the point obtained by following v from the origin, use origin .+^ v.
• To convert a vector back into a pair of components, use unv2 or coords (from Diagrams.Coordinates). These are typically used in conjunction with the ViewPatterns extension:

 foo (unr2 -> (x,y)) = ...
 foo (coords -> x :& y) = ...

Construct a 2D vector from a pair of components. See also &.

Convert a 2D vector back into a pair of components. See also coords.

Curried form of r2.

Points in R^2. This type is intentionally abstract.

• To construct a point, use p2, or ^& (see Diagrams.Coordinates):

 p2 (3,4)  :: P2
 3 ^& 4    :: P2

• To construct a point from a vector v, use origin .+^ v.
• To convert a point p into the vector from the origin to p, use p .-. origin.
• To convert a point back into a pair of coordinates, use unp2, or coords (from Diagrams.Coordinates). It's common to use these in conjunction with the ViewPatterns extension:

 foo (unp2 -> (x,y)) = ...
 foo (coords -> x :& y) = ...

Construct a 2D point from a pair of coordinates. See also ^&.

Convert a 2D point back into a pair of coordinates. See also coords.

Curried form of p2.

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.

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.

Compute the counterclockwise angle from the first vector to the second.

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

The circle constant, the ratio of a circle's circumference to its radius. Note that pi = tau/2.

For more information and a well-reasoned argument why we should all be using tau instead of pi, see The Tau Manifesto, http://tauday.com/.

To hear what it sounds like (and to easily memorize the first 30 digits or so), try http://youtu.be/3174T-3-59Q.

Angles can be expressed in a variety of units. Internally, they are represented in radians.

The radian measure of an Angle a can be accessed as a ^. rad. A new Angle can be defined in radians as pi @@ rad.

The measure of an Angle a in full circles can be accessed as a ^. turn. A new Angle of one-half circle can be defined in as 1/2 @@ turn.

The degree measure of an Angle a can be accessed as a ^. deg. A new Angle can be defined in degrees as 180 @@ deg.

An angle representing one full turn.

Deprecated synonym for fullTurn, retained for backwards compatibility.

Calculate ratio between two angles.

30 @@ deg is an Angle of the given measure and units.

More generally, @@ reverses the Iso' on its right, and applies the Iso' to the value on the left. Angles are the motivating example where this order improves readability.

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).

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.

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 strokeTrail as well. The solution is to give a type signature to expressions involving strokeTrail, or (recommended) upgrade GHC (the bug is fixed in 7.0.2 onwards).

Deprecated synonym for strokeTrail.

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

Deprecated synonym for strokeTrail'.

A composition of strokeT and wrapLine for conveniently converting a line directly into a diagram.

A composition of strokeT and wrapLoop for conveniently converting a loop directly into a diagram.

A convenience function for converting a Located Trail directly into a diagram; strokeLocTrail = stroke . trailLike.

Deprecated synonym for strokeLocTrail.

A convenience function for converting a Located line directly into a diagram; strokeLocLine = stroke . trailLike . mapLoc wrapLine.

A convenience function for converting a Located loop directly into a diagram; strokeLocLoop = stroke . trailLike . mapLoc wrapLoop.

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

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

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.

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.

The 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.

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 envelope of the diagram is unaffected.

Clip a diagram to the given path setting its envelope to the pointwise minimum of the envelopes of the diagram and path. The trace consists of those parts of the original diagram's trace which fall within the clipping path, or parts of the path's trace within the original diagram.

Clip a diagram to the clip path taking the envelope and trace of the clip path.

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

 hruleEx = vcat' (with & sep .~ 0.2) (map hrule [1..5])
         # centerXY # pad 1.1

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

 vruleEx = hcat' (with & sep .~ 0.2) (map vrule [1, 1.2 .. 2])
         # centerXY # pad 1.1

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

A circle of the given radius, centered at the origin. As a path, it begins at (r,0).

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 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.

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. The origin of the arc is its center.

Given a radus r, a start angle s and an end angle e, arc' r s e is the path of a radius (abs r) arc between the two angles. If a negative radius is given, the arc will be clockwise, otherwise it will be counterclockwise. The origin of the arc is its center.

 arc'Ex = mconcat [ arc' r 0 (1/4 \@\@ turn) | r <- [0.5,-1,1.5] ]
        # centerXY # pad 1.1

Like arc but clockwise.

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

 wedgeEx = hcat' (with & sep .~ 0.5)
   [ wedge 1 (0 \@\@ turn) (1/4)
   , wedge 1 (7/30 \@\@ turn) (11/30)
   , wedge 1 (1/8 \@\@ turn) (7/8)
   ]
   # fc blue
   # centerXY # pad 1.1

arcBetween p q height creates an arc beginning at p and ending at q, with its midpoint at a distance of abs height away from the straight line from p to q. A positive value of height results in an arc to the left of the line from p to q; a negative value yields one to the right.

 arcBetweenEx = mconcat
   [ arcBetween origin (p2 (2,1)) ht | ht <- [-0.2, -0.1 .. 0.2] ]
   # centerXY # pad 1.1

Create an annular wedge of the given radii, beginning at the first angle and extending counterclockwise to the second. The radius of the outer circle is given first.

 annularWedgeEx = hcat' (with & sep .~ 0.50)
   [ annularWedge 1 0.5 (0 \@\@ turn) (1/4)
   , annularWedge 1 0.3 (7/30 \@\@ turn) (11/30)
   , annularWedge 1 0.7 (1/8 \@\@ turn) (7/8)
   ]
   # fc blue
   # centerXY # pad 1.1

Generate the polygon described by the given options.

Generate a polygon. See PolygonOpts for more information.

Options for specifying a polygon.

Specification for the polygon's vertices.

Should a rotation be applied to the polygon in order to orient it in a particular way?

Should a translation be applied to the polygon in order to place the center at a particular location?

Method used to determine the vertices of a polygon.

Determine how a polygon should be oriented.

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

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 TrailLike. But of course the list can be generated any way you like. A Path R2 is returned (instead of any TrailLike) because the resulting path may have more than one component, for example if the vertices are to be connected in several disjoint cycles.

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.

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

A synonym for triangle, provided for backwards compatibility.

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

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

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

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

A synonym for heptagon. It is, however, completely inferior, being a base admixture of the Latin septum (seven) and the Greek γωνία (angl

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

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

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

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

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

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

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

roundedRect w h r generates a closed trail, or closed path centered at the origin, of an axis-aligned rectangle with width w, height h, and circular rounded corners of radius r. If r is negative the corner will be cut out in a reverse arc. If the size of r is larger than half the smaller dimension of w and h, then it will be reduced to fit in that range, to prevent the corners from overlapping. The trail or path begins with the right edge and proceeds counterclockwise. If you need to specify a different radius for each corner individually, use roundedRect' instead.

 roundedRectEx = pad 1.1 . centerXY $ hcat' (with & sep .~ 0.2)
   [ roundedRect  0.5 0.4 0.1
   , roundedRect  0.5 0.4 (-0.1)
   , roundedRect' 0.7 0.4 (with & radiusTL .~ 0.2
                                & radiusTR .~ -0.2
                                & radiusBR .~ 0.1)
   ]

roundedRect' works like roundedRect but allows you to set the radius of each corner indivually, using RoundedRectOpts. The default corner radius is 0. Each radius can also be negative, which results in the curves being reversed to be inward instead of outward.

arrowV v creates an arrow with the direction and magnitude of the vector v (with its tail at the origin), using default parameters.

arrowV' v creates an arrow with the direction and magnitude of the vector v (with its tail at the origin).

Create an arrow starting at s with length and direction determined by the vector v.

arrowBetween s e creates an arrow pointing from s to e with default parameters.

arrowBetween' opts s e creates an arrow pointing from s to e using the given options. In particular, it scales and rotates arrowShaft to go between s and e, taking head, tail, and gaps into account.

Connect two diagrams with a straight arrow.

Connect two diagrams with an arbitrary arrow.

Connect two diagrams at point on the perimeter of the diagrams, choosen by angle.

Draw an arrow from diagram named n1 to diagram named n2. The arrow lies on the line between the centres of the diagrams, but is drawn so that it stops at the boundaries of the diagrams, using traces to find the intersection points.

arrow len creates an arrow of length len with default parameters, starting at the origin and ending at the point (len,0).

arrow' opts len creates an arrow of length len using the given options, starting at the origin and ending at the point (len,0). In particular, it scales the given arrowShaft so that the entire arrow has length len.

Straight line arrow shaft.

A shape to place at the head of the arrow.

A shape to place at the tail of the arrow.

The trail to use for the arrow shaft.

Radius of a circumcircle around the head.

Radius of a circumcircle around the tail.

Distance to leave between the head and the target point.

Distance to leave between the starting point and the tail.

A lens for setting or modifying the color of an arrowhead. For example, one may write ... (with & headColor .~ blue) to get an arrow with a blue head, or ... (with & headColor %~ blend 0.5 white) to make an arrow's head a lighter color. For more general control over the style of arrowheads, see headStyle.

Note that the most general type of headColor would be

   (Color c, Color c') => Setter ArrowOpts ArrowOpts c c'

but that can cause problems for type inference when setting the color. However, using it at that more general type may occasionally be useful, for example, if you want to apply some opacity to a color, as in ... (with & headColor %~ (`withOpacity` 0.5)). If you want the more general type, you can use headStyle . styleFillColor in place of headColor.

Style to apply to the head. headStyle is modified by using the lens combinator %~ to change the current style. For example, to change an opaque black arrowhead to translucent orange: (with & headStyle %~ fc orange . opacity 0.75).

A lens for setting or modifying the color of an arrow tail. See headColor.

Style to apply to the tail. See headStyle.

A lens for setting or modifying the color of an arrow shaft. See headColor.

Style to apply to the shaft. See headStyle.

Create a primitive text diagram from the given string, with center alignment, equivalent to alignedText 0.5 0.5.

Note that it takes up no space, as text size information is not available.

Create a primitive text diagram from the given string, origin at the top left corner of the text's bounding box, equivalent to alignedText 0 1.

Note that it takes up no space.

Create a primitive text diagram from the given string, with the origin set to a point interpolated within the bounding box. The first parameter varies from 0 (left) to 1 (right), and the second parameter from 0 (bottom) to 1 (top).

The height of this box is determined by the font's potential ascent and descent, rather than the height of the particular string.

Note that it takes up no space.

Create a primitive text diagram from the given string, with the origin set to be on the baseline, at the beginning (although not bounding). This is the reference point of showText in the Cairo graphics library.

Note that it takes up no space.

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

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.

Set all text in italics.

Set all text using an oblique slant.

Set all text using a bold font weight.

An external image primitive, representing an image the backend should import from another file when rendering.

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.

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

Rotate about the local origin by the given angle. Positive angles correspond to counterclockwise rotation, negative to clockwise. The angle can be expressed using any of the Isos on Angle. For example, rotate (1/4 @@ turn), rotate (tau/4 @@ rad), and rotate (90 @@ deg) all represent the same transformation, namely, a counterclockwise rotation by a right angle. To rotate about some point other than the local origin, see rotateAbout.

Note that writing rotate (1/4), with no Angle constructor, 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 interprets its argument as a number of turns.

A synonym for rotate, interpreting its argument in units of turns; it can be more convenient to write rotateBy (1/4) than rotate (1/4 @@ turn).

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

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

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

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

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

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

Create a uniform scaling transformation.

Scale uniformly in every dimension by the given scalar.

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 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 height of 0, such as hrule.

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 h scales a diagram uniformly by whatever factor required to make its height h. scaleUToY should not be applied to diagrams with a height of 0, such as hrule.

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

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.

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

Create a translation.

Translate by a vector.

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

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).

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

shearingX d is the linear transformation which is the identity on y coordinates and sends (0,1) to (d,1).

shearX d performs a shear in the x-direction which sends (0,1) to (d,1).

shearingY d is the linear transformation which is the identity on x coordinates and sends (1,0) to (1,d).

shearY d performs a shear in the y-direction which sends (1,0) to (1,d).

The parallel projection onto the line x=0

The perspective division onto the line x=1 along lines going through the origin.

The parallel projection onto the line y=0

The perspective division onto the line y=1 along lines going through the origin.

The viewing transform for a viewer facing along the positive X axis. X coördinates stay fixed, while Y coördinates are compressed with increasing distance. asDeformation (translation unitX) parallelX0 frustrumX = perspectiveX1

Place two diagrams (or other 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. The local origin of the resulting combined diagram is the same as the local origin of the first. (===) is associative and has mempty as an identity. See the documentation of beside for more information.

Place two diagrams (or other juxtaposable objects) horizontally adjacent to one another, with the first diagram to the left of the second. The local origin of the resulting combined diagram is the same as the local origin of the first. (|||) is associative and has mempty as an identity. See the documentation of beside for more information.

Place two diagrams (or other juxtaposable objects) adjacent to one another, with the second diagram placed along a line at angle th from the first. The local origin of the resulting combined diagram is the same as the local origin of the first. See the documentation of beside for more information.

Lay out a list of juxtaposable objects in a row from left to right, so that their local origins lie along a single horizontal line, with successive envelopes 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.

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

Lay out a list of juxtaposable objects in a column from top to bottom, so that their local origins lie along a single vertical line, with successive envelopes 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.

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

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

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

padX s "pads" a diagram in the x-direction, expanding its envelope horizontally by a factor of s (factors between 0 and 1 can be used to shrink the envelope). Note that the envelope will expand with respect to the local origin, so if the origin is not centered horizontally the padding may appear "uneven". If this is not desired, the origin can be centered (using centerX) before applying padX.

padY s "pads" a diagram in the y-direction, expanding its envelope vertically by a factor of s (factors between 0 and 1 can be used to shrink the envelope). Note that the envelope will expand with respect to the local origin, so if the origin is not centered vertically the padding may appear "uneven". If this is not desired, the origin can be centered (using centerY) before applying padY.

extrudeLeft s "extrudes" a diagram in the negative x-direction, offsetting its envelope by the provided distance. When s < 0 , the envelope is inset instead.

See the documentation for extrudeEnvelope for more information.

extrudeRight s "extrudes" a diagram in the positive x-direction, offsetting its envelope by the provided distance. When s < 0 , the envelope is inset instead.

See the documentation for extrudeEnvelope for more information.

extrudeBottom s "extrudes" a diagram in the negative y-direction, offsetting its envelope by the provided distance. When s < 0 , the envelope is inset instead.

See the documentation for extrudeEnvelope for more information.

extrudeTop s "extrudes" a diagram in the positive y-direction, offsetting its envelope by the provided distance. When s < 0 , the envelope is inset instead.

See the documentation for extrudeEnvelope for more information.

view p v sets the envelope of a diagram to a rectangle whose lower-left corner is at p and whose upper-right corner is at p .+^ v. Useful for selecting the rectangular portion of a diagram which should actually be "viewed" in the final render, if you don't want to see the entire diagram.

Construct a bounding rectangle for an enveloped object, that is, the smallest axis-aligned rectangle which encloses the object.

"Set the background color" of a diagram. That is, place a diagram atop a bounding rectangle of the given color.

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 envelope.

Align along the right edge.

Align along the top edge.

Align along the bottom edge.

alignX and snugX move the local origin horizontally as follows:

• alignX (-1) moves the local origin to the left edge of the boundary;
• 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.
• snugX works the same way.

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.

Center the local origin along the X-axis.

Center the local origin along the Y-axis.

Center along both the X- and Y-axes.

See the documentation for alignX.

Compute the width of an enveloped object.

Compute the height of an enveloped object.

Compute the width and height of an enveloped object.

Compute the size of an enveloped object as a SizeSpec2D value.

Compute the absolute x-coordinate range of an enveloped object in R2, in the form (lo,hi). Return Nothing for objects with an empty envelope.

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

Compute the point at the center (in the x- and y-directions) of a enveloped object. Return the origin for objects with an empty envelope.

A specification of a (requested) rectangular size.

Create a size specification from a possibly-specified width and height.

Uniformly scale any enveloped object so that it fits within the given size.

Uniformly scale an enveloped object so that it "has the same size as" (fits within the width and height of) some other object.

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

Mark the origin of a diagram, with control over colour and scale of marker dot.