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1 Introduction

In GPipe, you'll primary work with these four types of data on the GPU:

Let's walk our way through an simple example as I explain how you work with these types. This example requires GPipe version 1.2.1 or later. This page is formatted as a literate Haskell page, simply save it as "box.lhs" and then type

ghc --make –O box.lhs

at the prompt to see a spinning box. You’ll also need an image named "myPicture.jpg" in the same directory (I used a picture of some wooden planks).

> module Main where
> import Graphics.GPipe
> import Graphics.GPipe.Texture.Load
> import qualified Data.Vec as Vec
> import Data.Vec.Nat
> import Data.Vec.LinAlg.Transform3D
> import Data.Monoid
> import Data.IORef
> import Graphics.UI.GLUT
>     (Window,
>     mainLoop,
>     postRedisplay,
>     idleCallback,
>     getArgsAndInitialize,
>     ($=))

Besides GPipe, this example also uses the Vec-Transform package for the transformation matrices, and the GPipe-TextureLoad package for loading textures from disc. GLUT is used in GPipe for window management and the main loop.

2 Creating a window

We start by defining the
> main :: IO ()
> main = do
>     getArgsAndInitialize
>     tex <- loadTexture RGB8 "myPicture.jpg"
>     angleRef <- newIORef 0.0
>     newWindow "Spinning box" (100:.100:.()) (800:.600:.()) (renderFrame tex angleRef) initWindow
>     mainLoop       
> renderFrame :: Texture2D RGBFormat -> IORef Float -> Vec2 Int -> IO (FrameBuffer RGBFormat () ())
> renderFrame tex angleRef size = do
>     angle <- readIORef angleRef
>     writeIORef angleRef ((angle + 0.005) `mod'` (2*pi))
>     return $ cubeFrameBuffer tex angle size
> initWindow :: Window -> IO ()
> initWindow win = idleCallback $= Just (postRedisplay (Just win))
First we set up GLUT, and load a texture from disc via the GPipe-TextureLoad package function
. In this example we're going to animate a spinning box, and for that we put an angle in an
so that we can update it between frames. We then create a window with newWindow. When the window is created,
registers this window as being continously redisplayed in the idle loop. At each frame, the
renderFrame tex angleRef size
is run. In this function the angle is incremented with 0.005 (reseted each lap), and a
is created and returned to be displayed in the window. But before I explain
s, let's jump to the start of the graphics pipeline instead.

3 PrimitiveStreams

The graphics pipeline starts with creating primitives such as triangles on the GPU.Let's create a box with six sides, each made up of two triangles each.

> cube :: PrimitiveStream Triangle (Vec3 (Vertex Float), Vec3 (Vertex Float), Vec2 (Vertex Float))
> cube = mconcat [sidePosX, sideNegX, sidePosY, sideNegY, sidePosZ, sideNegZ]
> sidePosX = toGPUStream TriangleStrip $ zip3 [1:.0:.0:.(), 1:.1:.0:.(), 1:.0:.1:.(), 1:.1:.1:.()] (repeat (1:.0:.0:.()))    uvCoords
> sideNegX = toGPUStream TriangleStrip $ zip3 [0:.0:.1:.(), 0:.1:.1:.(), 0:.0:.0:.(), 0:.1:.0:.()] (repeat ((-1):.0:.0:.())) uvCoords
> sidePosY = toGPUStream TriangleStrip $ zip3 [0:.1:.1:.(), 1:.1:.1:.(), 0:.1:.0:.(), 1:.1:.0:.()] (repeat (0:.1:.0:.()))    uvCoords
> sideNegY = toGPUStream TriangleStrip $ zip3 [0:.0:.0:.(), 1:.0:.0:.(), 0:.0:.1:.(), 1:.0:.1:.()] (repeat (0:.(-1):.0:.())) uvCoords
> sidePosZ = toGPUStream TriangleStrip $ zip3 [1:.0:.1:.(), 1:.1:.1:.(), 0:.0:.1:.(), 0:.1:.1:.()] (repeat (0:.0:.1:.()))    uvCoords
> sideNegZ = toGPUStream TriangleStrip $ zip3 [0:.0:.0:.(), 0:.1:.0:.(), 1:.0:.0:.(), 1:.1:.0:.()] (repeat (0:.0:.(-1):.())) uvCoords
> uvCoords = [0:.0:.(), 0:.1:.(), 1:.0:.(), 1:.1:.()]

Every side of the box is created from a regular list of four elements each, where each element is a tuple with three vectors: a position, a normal and an uv-coordinate. These lists of vertices are then turned into PrimitiveStreams on the GPU by toGPUStream that in our case creates triangle strips from the vertices, i.e 2 triangles from 4 vertices. Refer to the OpenGl specification on how triangle strips and the other topologies works.

All six sides are then concatenated together into a cube. We can see that the type of the cube is a
of Triangles where each vertex is a tuple of three vectors, just as the lists we started with. One big difference is that those vectors now are made up of
Vertex Float
s instead of
s since they are now on the GPU.

The cube is defined in model-space, i.e where positions and normals are relative the cube. We now want to rotate that cube using a variable angle and project the whole thing with a perspective projection, as it is seen through a camera 2 units down the z-axis.

> transformedCube :: Float -> Vec2 Int -> PrimitiveStream Triangle (Vec4 (Vertex Float), (Vec3 (Vertex Float), Vec2 (Vertex Float)))
> transformedCube angle size = fmap (transform angle size) cube
> transform angle (width:.height:.()) (pos, norm, uv) = (transformedPos, (transformedNorm, uv))
>     where
>         modelMat = rotationVec (normalize (1:.0.5:.0.3:.())) angle `multmm` translation (-0.5)
>         viewMat = translation (-(0:.0:.2:.())) 
>         projMat = perspective 1 100 (pi/3) (fromIntegral width / fromIntegral height)
>         viewProjMat = projMat `multmm` viewMat
>         transformedPos = toGPU (viewProjMat `multmm` modelMat) `multmv` (homPoint pos :: Vec4 (Vertex Float))
>         transformedNorm = toGPU ( (Vec.take n3) $ Vec.take n3 $ modelMat) `multmv` norm
When applying a function on the
, that function will be executed on the GPU using vertex shaders. The toGPU function transforms normal values like
s into GPU-values like
Vertex Float
so it can be used with the vertices of the

4 FragmentStreams

To render the primitives on the screen, we must first turn them into pixel fragments. This called rasterization and in our example done by the function rasterizeFront, which transforms
s into FragmentStreams.
> rasterizedCube :: Float -> Vec2 Int -> FragmentStream (Vec3 (Fragment Float), Vec2 (Fragment Float))
> rasterizedCube angle size = rasterizeFront $ transformedCube angle size
In the rasterization process, values of type
Vertex Float
are turned into values of type
Fragment Float

For each fragment, we now want to give it a color from the texture we initially loaded, as well as light it with a directional light coming from the camera.

> litCube :: Texture2D RGBFormat -> Float -> Vec2 Int -> FragmentStream (Color RGBFormat (Fragment Float))
> litCube tex angle size = fmap (enlight tex) $ rasterizedCube angle size
> enlight tex (norm, uv) = RGB (c * Vec.vec (norm `dot` toGPU (0:.0:.1:.())))
>     where RGB c = sample (Sampler Linear Wrap) tex uv
on a
will execute a function on the GPU using fragment shaders. The function sample is used for sampling the texture we have loaded, using the fragment's interpolated uv-coordinates and a sampler state. Once we have a
s, we can paint those fragments onto a

5 FrameBuffers

A FrameBuffer is a 2D image in which fragments from
s are painted. A
may contain any combination of a color buffer, a depth buffer and a stencil buffer. Besides being shown in windows,
s may also be saved to memory or converted to textures, thus enabling multi pass rendering. A
has no defined size, but take the size of the window when shown, or are given a size when saved to memory or converted to a texture. And so finally, we paint the fragments we have created onto a black
. By this we use paintColor without any blending or color masking.
> cubeFrameBuffer :: Texture2D RGBFormat -> Float -> Vec2 Int -> FrameBuffer RGBFormat () ()
> cubeFrameBuffer tex angle size = paintSolid (litCube tex angle size) emptyFrameBuffer
> paintSolid = paintColor NoBlending (RGB $ Vec.vec True)
> emptyFrameBuffer = newFrameBufferColor (RGB 0)
is the one we return from the
action we defined at the top.

6 Screenshot