Assignment 1: Software Rasterization

In this assignment, you will implement a rasterization library in software that emulates the way 3D scenes are rendered on the GPU. Your software rasterizer should support the following features that we have covered in class: triangle rasterization, supersampling, affine and perspective transformations, z-buffering, and perspective-correct interpolation.


We will use SDL2 for window management, and GLM for vector and matrix datatypes. GLM provides convenient vector and matrix operations following GLSL syntax. Go through the linked page and learn the operations, so that you can use them instead of re-implementing everything like vector addition, dot products etc. yourself. Generally all the GLSL operations on the linked page are supported in GLM, except for precision qualifiers and “swizzling”.

The code framework for this assignment is posted at I suggest you clone it using Git instead of simply downloading it, in case I update it in the future.

This code framework defines, in the file src/, a simple rasterization API for drawing objects made of triangles and displaying them in a window on the screen. You can look at examples/e1.cpp for an example of how this API can be used, and read the comments in src/ for further details.

The API is implemented by two different classes. One named COL781::Hardware::Rasterizer is defined in src/hw.*pp; it performs hardware rasterization on the GPU using OpenGL. If you compile the project right now, the executable e1 produced by examples/e1.cpp will use this class to draw the tick mark described in class.

The other implementation of the API is named COL781::Software::Rasterizer and is declared in src/sw.hpp; it is intended to perform software rasterization on the CPU. However, its implementation in src/sw.cpp is incomplete, so it cannot be used right now!


Your main job in this assignment is to add your own code to src/sw.cpp to make all the provided examples work with your software rasterizer. I suggest you do this incrementally, implementing enough methods to make examples/e1.cpp work, then do examples/e2.cpp, and so on. You can change the rasterizer used by each example by commenting/uncommenting the two namespace R = ... lines. Note that the software rasterizer class uses different types than the hardware rasterizer, but the function calls are the same, so the same example code can use either implementation.

As you modify the software rasterizer implementation, please keep a few things in mind:

Here are some further details on how to proceed:

  1. Examples e1 and e2 just require you to implement a clear method that clears the framebuffer by setting all pixels to a given colour, a triangle rasterization procedure that draws a single triangle onto the framebuffer, and a drawObject method that draws an arbitrary triangulated shape specified via vertex coordinates and triangle vertex indices. Since this example is 2D, you can ignore the w and z coordinates for now.
    • In our API, colour components (red, green, and blue) are specified with values lying between 0 and 1. However, SDL expects the components to be integers between 0 and 255, so you will have to rescale them.
  2. At this point you should also add support for supersampling, specified through the last (optional) parameter of the initialize method. You may assume that n must be a perfect square. Once supersampling is on, the user should be able to draw the scene as usual and automatically obtain anti-aliased results. Verify this by modifying the initialize calls in e1 and e2 and checking that the triangle edges look smoother.

From e3 onwards, you will have to add support for rendering 3D triangles. The modeling, viewing, and projection transformations will already be provided by the user and applied by the vertex shader. Your job is to do perspective division, perspective-correct interpolation, and depth testing.

  1. Include a perspective division stage after the vertex shader, which maps a glm::vec4(x, y, z, w) to a glm::vec3(x/w, y/w, z/w). This should not change the results of any of the 2D examples since their w is always 1, but it should make example e5 look like a rotating 3D square.
  2. Add a z-buffer to your rasterizer so that you can perform depth testing. This can just be an array of floats that you maintain yourself. Z-buffer testing should only be enabled once enableDepthTest() is called, to avoid changing the 2D examples. Then examples e3 and e4 should show correct visibility like in lecture 7. When clearing the screen, remember to clear the z-buffer as well. Also verify that this continues to work when supersampling is enabled.
  3. Make sure the attribute interpolation you perform in the rasterization step is perspective-correct, so that the gradient from blue to yellow in example e5 is drawn correctly. It should not look like the distorted gradient in lecture 8.

With this, you should be able to run all five of the provided examples with your software rasterizer, and get results comparable to those produced by the hardware.

A secondary goal in this assignment is to use this API to draw some interesting scenes. For each scene, create a new .cpp file under examples/ and add it to CMakeLists.txt.

  1. Write a program that uses affine transformations to draw an analogue clock showing the current time. For full marks, the only mesh object your code contains should be a unit square having 4 vertices and 2 triangles. By applying various scaling, rotation, and translation operations, you can stretch it into a rectangle representing the hour hand, and similarly the minute hand, the second hand, and markings at the twelve hour locations (something like this picture, ignoring the circles). On each frame, the clock hands should point according to the current time.
  2. Design an interesting 3D scene on your own, by creating a new program similar to the given examples. Your program should work with both the software and hardware backends. Feel free to make the scene as complicated as you like; it should contain at least two different meshes (not just two transformed copies of the same mesh), a perspective camera, and animated motion of at least one mesh or the camera. You could design the mesh geometry by sketching it on graph paper, or use any formulas of geometrical shapes like spheres, cones, tori, etc. that you know of.
    • Consider giving the vertices varying colours so that the shape can be seen better instead of being completely flat.
    • Try to avoid having any geometry move behind the camera; this may create rendering bugs since you have not been asked to implement clipping.
    • There will be a small amount of marks for how aesthetically pleasing your scene is.


Submit your assignment on Moodle before midnight on the due date. Your submission should be a zip file that contains your entire source code for the assignment, not including any binary object files or executables. The zip file should also contain a PDF report that includes the following:

Separately, each of you should individually submit a short response in a separate form regarding how much you and your groupmate(s) contributed to the work in this assignment.