Portability | tested on GHC only |
---|---|

Stability | experimental |

Maintainer | Luke Palmer <lrpalmer@gmail.com> |

Drawing combinators as a functional interface to 2D graphics using OpenGL.

This module is intended to be imported `qualified`

, as in:

import qualified Graphics.DrawingCombinators as Draw

Whenever possible, a *denotational semantics* for operations in this library
is given. Read `[[x]]`

as "the meaning of `x`

".

Intuitively, an `Image`

`a`

is an infinite plane of pairs of colors *and*
`a`

's. The colors are what are drawn on the screen when you `render`

, and
the `a`

's are what you can recover from coordinates using `sample`

. The
latter allows you to tell, for example, what a user clicked on.

The following discussion is about the associated data. If you are only
interested in drawing, rather than mapping from coordinates to values, you
can ignore the following and just use `mappend`

and `mconcat`

to overlay images.

Wrangling the `a`

's -- the associated data with each "pixel" -- is done
using the `Functor`

, `Applicative`

, and `Monoid`

instances.

The primitive `Image`

s such as `circle`

and `text`

all return `Image Any`

objects. `Any`

is just a wrapper around `Bool`

, with `(||)`

as its monoid
operator. So e.g. the points inside the circle will have the value ```
Any
True
```

, and those outside will have the value `Any False`

. Returning `Any`

instead of plain `Bool`

allows you to use `Image`

s as a monoid, e.g.
`mappend`

to overlay two images. But if you are doing anything with
sampling, you probably want to map this to something. Here is a drawing
with two circles that reports which one was hit:

twoCircles :: Image String twoCircles = liftA2 test (translate (-1,0) %% circle) (translate (1,0) %% circle) where test (Any False) (Any False) = "Miss!" test (Any False) (Any True) = "Hit Right!" test (Any True) (Any False) = "Hit Left!" test (Any True) (Any True) = "Hit Both??!"

The last case would only be possible if the circles were overlapping.

Note, the area-less shapes such as `point`

, `line`

, and `bezierCurve`

*always* return `Any False`

when sampled, even if the exact same
coordinates are given. This is because miniscule floating-point error
can make these shapes very brittle under transformations. If you need
a point to be clickable, make it, for example, a very small box.

- module Graphics.DrawingCombinators.Affine
- data Image a
- render :: Image a -> IO ()
- clearRender :: Image a -> IO ()
- sample :: Image a -> R2 -> a
- point :: R2 -> Image Any
- line :: R2 -> R2 -> Image Any
- regularPoly :: Int -> Image Any
- circle :: Image Any
- convexPoly :: [R2] -> Image Any
- (%%) :: Affine -> Image a -> Image a
- bezierCurve :: [R2] -> Image Any
- data Color = Color !R !R !R !R
- modulate :: Color -> Color -> Color
- tint :: Color -> Image a -> Image a
- data Sprite
- openSprite :: FilePath -> IO Sprite
- sprite :: Sprite -> Image Any
- data Font
- openFont :: String -> IO Font
- text :: Font -> String -> Image Any
- textWidth :: Font -> String -> R
- class Monoid a where
- newtype Any = Any {}

# Documentation

# Basic types

The type of images.

[[Image a]] = R2 -> (Color, a)

The semantics of the instances are all consistent with *type class morphism*.
I.e. Functor, Applicative, and Monoid act point-wise, using the `Color`

monoid
described below.

render :: Image a -> IO ()Source

Draw an Image on the screen in the current OpenGL coordinate system (which, in absense of information, is (-1,-1) in the lower left and (1,1) in the upper right).

clearRender :: Image a -> IO ()Source

Like `render`

, but clears the screen first. This is so
you can use this module and pretend that OpenGL doesn't
exist at all.

# Selection

sample :: Image a -> R2 -> aSource

Sample the value of the image at a point.

[[sample i p]] = snd ([[i]] p)

# Geometry

point :: R2 -> Image AnySource

A single "pixel" at the specified point.

[[point p]] r | [[r]] == [[p]] = (one, Any True) | otherwise = (zero, Any False)

regularPoly :: Int -> Image AnySource

A regular polygon centered at the origin with n sides.

An (imperfect) unit circle centered at the origin. Implemented as:

circle = regularPoly 24

convexPoly :: [R2] -> Image AnySource

A convex polygon given by the list of points.

(%%) :: Affine -> Image a -> Image aSource

Transform an image by an `Affine`

transformation.

[[tr % im]] = [[im]] . inverse [[tr]]

bezierCurve :: [R2] -> Image AnySource

A Bezier curve given a list of control points. It is a curve
that begins at the first point in the list, ends at the last one,
and smoothly interpolates between the rest. It is the empty
image (`mempty`

) if zero or one points are given.

# Colors

Color is defined in the usual computer graphics sense: a 4 vector containing red, green, blue, and alpha.

The Monoid instance is given by alpha composition, described
at `http://lukepalmer.wordpress.com/2010/02/05/associative-alpha-blending/`

In the semantcs the values `zero`

and `one`

are used, which are defined as:

zero = Color 0 0 0 0 one = Color 1 1 1 1

modulate :: Color -> Color -> ColorSource

Modulate two colors by each other.

modulate (Color r g b a) (Color r' g' b' a') = Color (r*r') (g*g') (b*b') (a*a')

tint :: Color -> Image a -> Image aSource

Tint an image by a color; i.e. modulate the colors of an image by a color.

[[tint c im]] = first (modulate c) . [[im]] where first f (x,y) = (f x, y)

# Sprites (images from files)

openSprite :: FilePath -> IO SpriteSource

Load an image from a file and create a sprite out of it.

sprite :: Sprite -> Image AnySource

The image of a sprite at the origin.

[[sprite s]] p | p `elem` [-1,1]^2 = ([[s]] p, Any True) | otherwise = (zero, Any False)

# Text

text :: Font -> String -> Image AnySource

The image representing some text rendered with a font. The baseline is at y=0, the text starts at x=0, and the height of a lowercase x is 1 unit.

class Monoid a where

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

`mappend mempty x = x`

`mappend x mempty = x`

`mappend x (mappend y z) = mappend (mappend x y) z`

`mconcat =`

`foldr`

mappend mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Minimal complete definition: `mempty`

and `mappend`

.

Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define `newtype`

s and make those instances
of `Monoid`

, e.g. `Sum`

and `Product`

.

mempty :: a

Identity of `mappend`

mappend :: a -> a -> a

An associative operation

mconcat :: [a] -> a

Fold a list using the monoid.
For most types, the default definition for `mconcat`

will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.

Monoid Ordering | |

Monoid () | |

Monoid All | |

Monoid Any | |

Monoid ByteString | |

Monoid Affine | |

Monoid Color | |

Monoid [a] | |

Monoid a => Monoid (Dual a) | |

Monoid (Endo a) | |

Num a => Monoid (Sum a) | |

Num a => Monoid (Product a) | |

Monoid (First a) | |

Monoid (Last a) | |

Monoid a => Monoid (Maybe a) | |

Monoid m => Monoid (Image m) | |

Monoid b => Monoid (a -> b) | |

(Monoid a, Monoid b) => Monoid (a, b) | |

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | |

(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | |

(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) |