Graphics and Rendering

This is an overview of the process of rendering. Do not worry if you do not understand everything right away; every step will be covered in lavish detail in later tutorials.

Everything you see on your computer's screen, even the text you are reading right now (assuming you are reading this on an electronic display device, rather than a printout) is simply a two-dimensional array of pixels. If you take a screenshot of something on your screen, and blow it up, it will look very blocky.

Figure 8. An Image

An Image

Each of these blocks is a pixel. The word pixel is derived from the term Picture Element. Every pixel on your screen has a particular color. A two-dimensional array of pixels is called an image.

The purpose of graphics of any kind is therefore to determine what color to put in what pixels. This determination is what makes text look like text, windows look like windows, and so forth.

Since all graphics are just a two-dimensional array of pixels, how does 3D work? 3D graphics is thus a system of producing colors for pixels that convince you that the scene you are looking at is a 3D world rather than a 2D image. The process of converting a 3D world into a 2D image of that world is called rendering.

There are several methods for rendering a 3D world. The process used by real-time graphics hardware, such as that found in your computer, involves a very great deal of fakery. This process is called rasterization, and a rendering system that uses rasterization is called a rasterizer.

In rasterizers, all objects that you see are empty shells. There are techniques that are used to allow you to cut open these empty shells, but this simply replaces part of the shell with another shell that shows what the inside looks like. Everything is a shell.

All of these shells are made of triangles. Even surfaces that appear to be round are merely triangles if you look closely enough. There are techniques that generate more triangles for objects that appear closer or larger, so that the viewer can almost never see the faceted silhouette of the object. But they are always made of triangles.


Some rasterizers use planar quadrilaterals: four-sided objects, where all of the points lie in the same plane. One of the reasons that hardware-based rasterizers always use triangles is that all of the lines of a triangle are guaranteed to be in the same plane. Knowing this makes the rasterization process less complicated.

An object is made out of a series of adjacent triangles that define the outer surface of the object. Such series of triangles are often called geometry, a model or a mesh. These terms are used interchangeably.

The process of rasterization has several phases. These phases are ordered into a pipeline, where triangles enter from the top and a 2D image is filled in at the bottom. This is one of the reasons why rasterization is so amenable to hardware acceleration: it operates on each triangle one at a time, in a specific order. Triangles can be fed into the top of the pipeline while triangles that were sent earlier can still be in some phase of rasterization.

The order in which triangles and the various meshes are submitted to the rasterizer can affect its output. Always remember that, no matter how you submit the triangular mesh data, the rasterizer will process each triangle in a specific order, drawing the next one only when the previous triangle has finished being drawn.

OpenGL is an API for accessing a hardware-based rasterizer. As such, it conforms to the model for rasterization-based 3D renderers. A rasterizer receives a sequence of triangles from the user, performs operations on them, and writes pixels based on this triangle data. This is a simplification of how rasterization works in OpenGL, but it is useful for our purposes.

Triangles and Vertices. Triangles consist of 3 vertices. A vertex is a collection of arbitrary data. For the sake of simplicity (we will expand upon this later), let us say that this data must contain a point in three dimensional space. It may contain other data, but it must have at least this. Any 3 points that are not on the same line create a triangle, so the smallest information for a triangle consists of 3 three-dimensional points.

A point in 3D space is defined by 3 numbers or coordinates. An X coordinate, a Y coordinate, and a Z coordinate. These are commonly written with parenthesis, as in (X, Y, Z).

Rasterization Overview

The rasterization pipeline, particularly for modern hardware, is very complex. This is a very simplified overview of this pipeline. It is necessary to have a simple understanding of the pipeline before we look at the details of rendering things with OpenGL. Those details can be overwhelming without a high level overview.

Clip Space Transformation. The first phase of rasterization is to transform the vertices of each triangle into a certain region of space. Everything within this volume will be rendered to the output image, and everything that falls outside of this region will not be. This region corresponds to the view of the world that the user wants to render.

The volume that the triangle is transformed into is called, in OpenGL parlance, clip space. The positions of the triangle's vertices in clip space are called clip coordinates.

Clip coordinates are a little different from regular positions. A position in 3D space has 3 coordinates. A position in clip space has four coordinates. The first three are the usual X, Y, Z positions; the fourth is called W. This last coordinate actually defines what the extents of clip space are for this vertex.

Clip space can actually be different for different vertices within a triangle. It is a region of 3D space on the range [-W, W] in each of the X, Y, and Z directions. So vertices with a different W coordinate are in a different clip space cube from other vertices. Since each vertex can have an independent W component, each vertex of a triangle exists in its own clip space.

In clip space, the positive X direction is to the right, the positive Y direction is up, and the positive Z direction is away from the viewer.

The process of transforming vertex positions into clip space is quite arbitrary. OpenGL provides a lot of flexibility in this step. We will cover this step in detail throughout the tutorials.

Because clip space is the visible transformed version of the world, any triangles that fall outside of this region are discarded. Any triangles that are partially outside of this region undergo a process called clipping. This breaks the triangle apart into a number of smaller triangles, such that the smaller triangles are all entirely within clip space. Hence the name clip space.

Normalized Coordinates. Clip space is interesting, but inconvenient. The extent of this space is different for each vertex, which makes visualizing a triangle rather difficult. Therefore, clip space is transformed into a more reasonable coordinate space: normalized device coordinates.

This process is very simple. The X, Y, and Z of each vertex's position is divided by W to get normalized device coordinates. That is all.

The space of normalized device coordinates is essentially just clip space, except that the range of X, Y and Z are [-1, 1]. The directions are all the same. The division by W is an important part of projecting 3D triangles onto 2D images; we will cover that in a future tutorial.

Figure 9. Normalized Device Coordinate Space

Normalized Device Coordinate Space

The cube indicates the boundaries of normalized device coordinate space.

Window Transformation. The next phase of rasterization is to transform the vertices of each triangle again. This time, they are converted from normalized device coordinates to window coordinates. As the name suggests, window coordinates are relative to the window that OpenGL is running within.

Even though they refer to the window, they are still three dimensional coordinates. The X goes to the right, Y goes up, and Z goes away, just as for clip space. The only difference is that the bounds for these coordinates depends on the viewable window. It should also be noted that while these are in window coordinates, none of the precision is lost. These are not integer coordinates; they are still floating-point values, and thus they have precision beyond that of a single pixel.

The bounds for Z are [0, 1], with 0 being the closest and 1 being the farthest. Vertex positions outside of this range are not visible.

Note that window coordinates have the bottom-left position as the (0, 0) origin point. This is counter to what users are used to in window coordinates, which is having the top-left position be the origin. There are transform tricks you can play to allow you to work in a top-left coordinate space if you need to.

The full details of this process will be discussed at length as the tutorials progress.

Scan Conversion. After converting the coordinates of a triangle to window coordinates, the triangle undergoes a process called scan conversion. This process takes the triangle and breaks it up based on the arrangement of window pixels over the output image that the triangle covers.

Figure 10. Scan Converted Triangle

Scan Converted Triangle

The center image shows the digital grid of output pixels; the circles represent the center of each pixel. The center of each pixel represents a sample: a discrete location within the area of a pixel. During scan conversion, a triangle will produce a fragment for every pixel sample that is within the 2D area of the triangle.

The image on the right shows the fragments generated by the scan conversion of the triangle. This creates a rough approximation of the triangle's general shape.

It is very often the case that triangles are rendered that share edges. OpenGL offers a guarantee that, so long as the shared edge vertex positions are identical, there will be no sample gaps during scan conversion.

Figure 11. Shared Edge Scan Conversion

Shared Edge Scan Conversion

To make it easier to use this, OpenGL also offers the guarantee that if you pass the same input vertex data through the same vertex processor, you will get identical output; this is called the invariance guarantee. So the onus is on the user to use the same input vertices in order to ensure gap-less scan conversion.

Scan conversion is an inherently 2D operation. This process only uses the X and Y position of the triangle in window coordinates to determine which fragments to generate. The Z value is not forgotten, but it is not directly part of the actual process of scan converting the triangle.

The result of scan converting a triangle is a sequence of fragments that cover the shape of the triangle. Each fragment has certain data associated with it. This data contains the 2D location of the fragment in window coordinates, as well as the Z position of the fragment. This Z value is known as the depth of the fragment. There may be other information that is part of a fragment, and we will expand on that in later tutorials.

Fragment Processing. This phase takes a fragment from a scan converted triangle and transforms it into one or more color values and a single depth value. The order that fragments from a single triangle are processed in is irrelevant; since a single triangle lies in a single plane, fragments generated from it cannot possibly overlap. However, the fragments from another triangle can possibly overlap. Since order is important in a rasterizer, the fragments from one triangle must all be processed before the fragments from another triangle.

This phase is quite arbitrary. The user of OpenGL has a lot of options of how to decide what color to assign a fragment. We will cover this step in detail throughout the tutorials.

Direct3D Note

Direct3D prefers to call this stage pixel processing or pixel shading. This is a misnomer for several reasons. First, a pixel's final color can be composed of the results of multiple fragments generated by multiple samples within a single pixel. This is a common technique to remove jagged edges of triangles. Also, the fragment data has not been written to the image, so it is not a pixel yet. Indeed, the fragment processing step can conditionally prevent rendering of a fragment based on arbitrary computations. Thus a pixel in D3D parlance may never actually become a pixel at all.

Fragment Writing. After generating one or more colors and a depth value, the fragment is written to the destination image. This step involves more than simply writing to the destination image. Combining the color and depth with the colors that are currently in the image can involve a number of computations. These will be covered in detail in various tutorials.


Previously, a pixel was stated to be an element in a 2D image that has a particular color. A color can be described in many ways.

In computer graphics, the usual description of a color is as a series of numbers on the range [0, 1]. Each of the numbers corresponds to the intensity of a particular reference color; thus the final color represented by the series of numbers is a mix of these reference colors.

The set of reference colors is called a colorspace. The most common color space for screens is RGB, where the reference colors are Red, Green and Blue. Printed works tend to use CMYK (Cyan, Magenta, Yellow, Black). Since we're dealing with rendering to a screen, and because OpenGL requires it, we will use the RGB colorspace.


You can play some fancy games with programmatic shaders (see below) that allow you to work in different colorspaces. So technically, we only have to output to a linear RGB colorspace.

So a pixel in OpenGL is defined as 3 values on the range [0, 1] that represent a color in a linear RGB colorspace. By combining different intensities of this 3 colors, we can generate millions of different color shades. This will get extended slightly, as we deal with transparency later.


A shader is a program designed to be run on a renderer as part of the rendering operation. Regardless of the kind of rendering system in use, shaders can only be executed at certain points in that rendering process. These shader stages represent hooks where a user can add arbitrary algorithms to create a specific visual effect.

In term of rasterization as outlined above, there are several shader stages where arbitrary processing is both economical for performance and offers high utility to the user. For example, the transformation of an incoming vertex to clip space is a useful hook for user-defined code, as is the processing of a fragment into final colors and depth.

Shaders for OpenGL are run on the actual rendering hardware. This can often free up valuable CPU time for other tasks, or simply perform operations that would be difficult if not impossible without the flexibility of executing arbitrary code. A downside of this is that they must live within certain limits that CPU code would not have to.

There are a number of shading languages available to various APIs. The one used in this tutorial is the primary shading language of OpenGL. It is called, unimaginatively, the OpenGL Shading Language, or GLSL. for short. It looks deceptively like C, but it is very much not C.