# Introduction

This tutorial will walk you through the basics of using the diagrams DSL to create graphics in a powerful, modular, and declarative way. There’s enough here to get you started quickly; for more in-depth information, see the user manual.

This is not a Haskell tutorial (although a Haskell-tutorial-via-diagrams is a fun idea and may happen in the future). For now, we recommend Learn You a Haskell for a nice introduction to Haskell; Chapters 1-6 should give you pretty much all you need for working with diagrams.

This tutorial is available in several formats:

Whatever you do, don’t just read it: download the .lhs version so you can play around with the content of the tutorial interactively!

# Resources

Some resources that may be helpful to you as you learn about diagrams:

# Getting started

Before getting on with generating beautiful diagrams, you’ll need a few things:

You’ll need a recent version of the Glasgow Haskell Compiler (7.0.2 or later), as well as some standard libraries and tools. There are several methods for obtaining these:

• The Haskell Platform has everything you need in one convenient package. If you are unsure, you should use this.

• If you already have GHC and/or know what you are doing and want to install things yourself, just make sure you have GHC and a recent version of the cabal-install tool.

## Installation

Once you have the prerequisites, installing the diagrams libraries themselves should be a snap:

cabal install diagrams

diagrams is just a wrapper package which pulls in the following four packages:

• diagrams-core contains the core data structures and definitions that form the abstract heart of the library.

• diagrams-lib is a standard library of drawing primitives, attributes, and combinators built on top of the core library.

• diagrams-contrib is a library of user-contributed extensions.

• diagrams-svg is a backend which renders diagrams as SVG files.

There are other backends as well; see the diagrams package documentation and the diagrams wiki for more information.

# Philosophy

Before diving in to create some diagrams, it’s worth taking a minute to explain some of the philosophy that drove many of the design decisions. (If you’re particularly impatient, feel free to skip this section for now—but you might want to come back and read it later!)

• Positioning and scaling are always relative. There is never any global coordinate system to think about; everything is done relative to diagrams’ local vector spaces. This is not only easier to think about, it also increases modularity and compositionality, since diagrams can always be designed without thought for the context in which they will eventually be used. Doing things this way is more work for the library and less work for the user, which is the way it should be.

• Almost everything is based around the concept of monoids (more on this later).

• The core library is as simple and elegant as possible – almost everything is built up from a very small set of primitive types and operations. One consequence is that diagrams is optimized for simplicity and flexibility rather than for speed; if you are looking to do real-time graphics generation you will probably be best served by looking elsewhere! (With that said, however, we certainly are interested in making diagrams as fast as possible without sacrificing other features.)

Create a file called DiagramsTutorial.lhs with the following contents (or you can simply edit this file itself):

> {-# LANGUAGE NoMonomorphismRestriction #-}
>
> import Diagrams.Prelude
> import Diagrams.Backend.SVG.CmdLine
>
> main = defaultMain (circle 1)

Turning off the Dreaded Monomorphism Restriction is quite important: if you don’t, you will almost certainly run into it (and be very confused by the resulting error messages).

The first import statement brings into scope the entire diagrams DSL and standard library. The second import is so that we can use the SVG backend for rendering diagrams. Among other things, it provides the function defaultMain, which takes a diagram as input (in this case, a circle of radius 1) and creates a command-line-driven application for rendering it.

Let’s compile and run it:

$ghc --make DiagramsTutorial.lhs [1 of 1] Compiling Main ( DiagramsTutorial.lhs, DiagramsTutorial.o ) Linking DiagramsTutorial ...$ ./DiagramsTutorial -o circle.svg -w 400

If you now view circle.svg in your favorite web browser, you should see an unfilled black circle on a white background (actually, it’s on a transparent background, but most browsers I know of use white).

Be careful not to omit the -w 400 argument! This specifies that the width of the output file should be 400 units, and the height should be determined automatically. You can also specify just a height (using -h), or both a width and a height if you know the exact dimensions of the output image you want (note that the diagram will not be stretched; extra padding will be added if the aspect ratios do not match). If you do not specify a width or a height, the absolute scale of the diagram itself will be used, which in this case would be rather tiny—only 2x2.

There are several more options besides -o, -w, and -h; you can see what they are by typing ./DiagramsTutorial --help.

# Attributes

Suppose we want our circle to be blue, with a thick dashed purple outline (there’s no accounting for taste). We can apply attributes to the circle diagram with the (#) operator:

> circle1 = circle 1 # fc blue
>                    # lw 0.05
>                    # lc purple
>                    # dashing [0.2,0.05] 0

(To render this new diagram, just replace defaultMain (circle 1) with defaultMain circle1.)

Note that the dashed purple border is cut off a bit at the edges of the image. This is by design: diagrams’ bounds are computed based on their “abstract shapes”, without taking into account how they are actually drawn. Future versions of diagrams may give you the option of taking things such as thick borders into account when computing boundaries. For now, we can simply add a bit of “padding” to make the whole drawing visible. 10% should do nicely:

> pCircle1 = circle1 # pad 1.1

There’s actually nothing special about the (#) operator: it’s just reverse function application, that is,

x # f = f x

Just to illustrate,

> pCircle1' = pad 1.1 . dashing [0.2,0.05] 0 . lc purple . lw 0.05 . fc blue $circle 1 produces exactly the same diagram as pCircle1. So why bother with (#)? First, it’s often more natural to write (and easier to read) what a diagram is first, and what it is like second. Second, (#) has a high precedence (8), making it more convenient to combine diagrams with specified attributes. For example, circle 1 # fc red # lw 0 ||| circle 1 # fc green # lw 0 places a red circle with no border next to a green circle with no border (we’ll see more about the (|||) operator shortly). Without (#) we would have to write something with more parentheses, like (fc red . lw 0$ circle 1) ||| (fc green . lw 0 circle 1) For information on other standard attributes, see Diagrams.Attributes. # Combining diagrams OK, so we can draw a single circle: boring! Much of the power of the diagrams framework, of course, comes from the ability to build up complex diagrams by combining simpler ones. Let’s start with the most basic way of combining two diagrams: superimposing one diagram on top of another. We can accomplish this with atop: > circleSq = square 1 # fc aqua atop pCircle1 (Incidentally, these colors are coming from Data.Colour.Names.) “Putting one thing on top of another” sounds rather vague: how do we know exactly where the circle and square will end up relative to one another? To answer this question, we must introduce the fundamental notion of a local origin. ## Local origins Every diagram has a distinguished point called its local origin. Many operations on diagrams – such as atop – work somehow with respect to the local origin. atop in particular works by superimposing two diagrams so that their local origins coincide (and this point becomes the local origin of the new, combined diagram). The showOrigin function is provided for conveniently visualizing the local origin of a diagram. > circleWithO = circle 1 # showOrigin Not surprisingly, the local origin of circle is at its center. So is the local origin of square. This is why square 1 atop circle 1 produces a square centered on a circle. > circleSqWithO = circleSq # showOrigin ## Side-by-side Another fundamental way to combine two diagrams is by placing them next to each other. The (|||) and (===) operators let us conveniently put two diagrams next to each other in the horizontal or vertical directions, respectively. For example: > circleSqH = circle 1 ||| square 2 > > circleSqV = circle 1 === square 2 The two diagrams are arranged next to each other so that their local origins are on the same horizontal or vertical line. As you can ascertain for yourself with showOrigin, the local origin of the new, combined diagram coincides with the local origin of the first diagram. (|||) and (===) are actually just convenient specializations of the more general beside combinator. beside takes as arguments a vector and two diagrams, and places them next to each other “along the vector” — that is, in such a way that the vector points from the local origin of the first diagram to the local origin of the second. > circleSqV1 = beside (r2 (1,1)) (circle 1) (square 2) > > circleSqV2 = beside (r2 (1,-2)) (circle 1) (square 2) Notice how we use the r2 function to create a 2D vector from a pair of coordinates. ## Envelopes How does the diagrams library figure out how to place two diagrams “next to” each other? And what exactly does “next to” mean? There are many possible definitions of “next to” that one could imagine choosing, with varying degrees of flexibility, simplicity, and tractability. The definition of “next to” adopted by diagrams is as follows: To place two diagrams next to each other in the direction of a vector v, place them as close as possible so that there is a separating line perpendicular to v; that is, a line perpendicular to v such that the first diagram lies completely on one side of the line and the other diagram lies completely on the other side. There are certainly some tradeoffs in this choice. The biggest downside is that adjacent diagrams sometimes end up with undesired space in between them. For example, the two rotated ellipses in the diagram below have some space between them. (Try adding a vertical line between them with vrule and you will see why.) > e2 = ell ||| ell > where ell = circle 1 # scaleX 0.5 # rotateBy (1/6) If we want to position these ellipses next to each other horizontally so that they are tangent, it is not clear how to accomplish this. (However, it should be possible to create higher-level modules for automatically accomplishing this in certain cases.) However: • This rule is very simple, in that it is easy to predict what will happen when placing two diagrams next to each other. • It is also tractable. Every diagram carries along with it an “envelope”—a function which takes as input a vector v, and returns the minimum distance to a separating line from the local origin in the direction of v. When composing two diagrams with atop we take the pointwise maximum of their envelopes; to place two diagrams next to each other we use their envelopes to decide how to reposition their local origins before composing them with atop. # Transforming diagrams As you would expect, there is a range of standard functions available for transforming diagrams, such as: • scale (scale uniformly) • scaleX and scaleY (scale in the X or Y axis only) • rotate (rotate by an angle in radians) • rotateBy (rotate by a fraction of a circle) • reflectX and reflectY for reflecting along the X and Y axes For example: > circleRect = circle 1 # scale 0.5 ||| square 1 # scaleX 0.3 > > circleRect2 = circle 1 # scale 0.5 ||| square 1 # scaleX 0.3 > # rotateBy (1/6) > # scaleX 0.5 (Of course, circle 1 # scale 0.5 would be better written as just circle 0.5.) ## Freezing Note that the transformed circles and squares in the examples above were all drawn with the same uniform lines. This is because by default, transformations operate on the abstract geometric ideal of a diagram, and not on its attributes. Often this is what you want; but occasionally you want scaling a diagram to have an effect on the width of its lines, and so on. This can be accomplished with the freeze combinator: whereas transformations normally do not affect a diagram’s attributes, transformations do affect the attributes of a frozen diagram. Here is an example. On the left is an untransformed circle drawn with a line 0.1 units thick. The next circle is a scaled version of the first: notice how the line thickness is the same. The third circle was produced by first freezing, then scaling the first circle, resulting in a line twice as thick. The last two circles illustrate a non-uniform scale applied to an unfrozen circle (which is drawn with a uniform line) and to a frozen one (in which the line gets thicker and thinner according to the non-uniform scale). > c = circle 1 # lw 0.1 > > circles = hcat' with {sep = 0.5} > [ c > > , c # scale 2 > , c # freeze # scale 2 > > , c # scaleX 0.2 > , c # freeze # scaleX 0.2 > ] > # centerXY > # pad 1.1 This example also illustrates the hcat' function, which takes a list of diagrams and lays them out horizontally, here with a separation of 0.5 units between each one. For more information on hcat' and similar combinators, see the Diagrams.TwoD.Combinators documentation. ## Translation Of course, there are also translation transformations like translate, translateX, and translateY. These operations translate a diagram within its local vector space — that is, relative to its local origin. > circleT = circle 1 # translate (r2 (0.5, 0.3)) # showOrigin As circleT shows, translating a diagram by (0.5, 0.3) is the same as moving its local origin by (-0.5, -0.3). Since diagrams are always composed with respect to their local origins, translation can affect the way diagrams are composed. > circleSqT = square 1 atop circle 1 # translate (r2 (0.5, 0.3)) > circleSqHT = square 1 ||| circle 1 # translate (r2 (0.5, 0.3)) > circleSqHT2 = square 1 ||| circle 1 # translate (r2 (19.5, 0.3)) As circleSqHT and circleSqHT2 demonstrate, when we place a translated circle next to a square, it doesn’t matter how much the circle was translated in the horizontal direction — the square and circle will always simply be placed next to each other. The vertical direction matters, though, since the local origins of the square and circle are placed on the same horizontal line. ## Aligning It’s quite common to want to align some diagrams in a certain way when placing them next to one another — for example, we might want a horizontal row of diagrams aligned along their top edges. The alignment of a diagram simply refers to its position relative to its local origin, and convenient alignment functions are provided for aligning a diagram with respect to its envelope. For example, alignT translates a diagram in a vertical direction so that its local origin ends up exactly on the edge of its envelope. > circlesTop = hrule (2 * sum sizes) # lw 0.1 === circles # centerX > where circles = hcat . map alignT . zipWith scale sizes > repeat (circle 1 # lw 0.1)
>         sizes   = [2,5,4,7,1,3]

See Diagrams.TwoD.Align for other alignment combinators.

# Diagrams as a monoid

As you may have already suspected if you are familiar with monoids, diagrams form a monoid under atop. The diagrams standard library provides (<>) as a convenient synonym for mappend, so (<>) can also be used to superimpose diagrams. This also means that mempty is available to construct the “empty diagram”, which takes up no space and produces no output.

Quite a few other things in the diagrams standard library are also monoids (transformations, trails, paths, styles, and colors).

# Next steps

This tutorial has really only scratched the surface of what is possible! Included among the many things not covered by this tutorial are paths, splines, text, traces, a wide array of predefined shapes, named subdiagrams, animation… Here are pointers to some resources for learning more:

• The diagrams user manual goes into much more depth on all the topics covered in this tutorial, plus many others, and includes lots of illustrative examples. If there is anything in the manual that you find unclear, confusing, or omitted, please report it as a bug!

• The diagrams-lib API is generally well-documented; start with the documentation for Diagrams.Prelude, and then drill down from there to learn about whatever you are interested in. If there is anything in the API documentation that you find unclear or confusing, please report it as a bug!

• If you run into difficulty or have any questions, join the #diagrams IRC channel on freenode.org, or the diagrams-discuss mailing list.