This is an archive of a past semester of this course. Go to the current semester.
Project 1: Rasterizer

In this assignment you will implement a simple rasterizer, including features like supersampling, hierarchical transforms, and texture mapping with antialiasing. At the end, you'll have a functional vector graphics renderer that can take in modified SVG (Scalable Vector Graphics) files, which are widely used on the internet.



  • Project 1 is due Monday, February 5th at 11:59pm. Assignments which are turned in after 11:59pm are a full day late -- there are no late minutes or late hours.

Getting started

You can either download the zipped assignment straight to your computer or clone it from GitHub using the command

$ git clone <YOUR_PRIVATE_REPO>

Also ensure GitHub Pages is enabled for your assignment.

Please consult this article on how to build and submit assignments for CS 184.

As you go through the assignment, refer to the write-up guidelines and deliverables section below. It is recommended that you accumulate deliverables into sections in your webpage write-up as you work through the project.

Note: Do not squander all your hard work on this assignment by converting your png files into jpg or any other format! Leave the screenshots as they are saved by the 'S' key in the GUI, otherwise you will introduce artifacts that will ruin your rasterization efforts.

Using the GUI

You can run the executable with the command

./draw ../svg/basic/test1.svg

A flower should show up on your screen (after you do some work in Part 1). After finishing Part 3, you will be able to change the viewpoint by dragging your mouse to pan around or scrolling to zoom in and out. Here are all the keyboard shortcuts available (some depend on you implementing various parts of the assignment):

Key Action
' ' return to original viewpoint
'-' decrease sample rate
'=' increase sample rate
'Z' toggle the pixel inspector
'P' switch between texture filtering methods on pixels
'L' switch between texture filtering methods on mipmap levels
'S' save a png screenshot in the current directory
'1'-'9' switch between svg files in the loaded directory

The argument passed to draw can either be a single file or a directory containing multiple svg files, as in

./draw ../svg/basic/

If you load a directory with up to 9 files, you can switch between them using the number keys 1-9 on your keyboard.

Project structure

The project has 7 parts, divided into 3 sections, worth a total of 100 possible points. Some require only a few lines of code, while others are more substantial.

Section I: Rasterization (suggested completion checkpoint: Sunday 1/29)

  • Part 1: Rasterizing single-color triangles (20 pts)
  • Part 2: Antialiasing triangles (20 pts)
  • Part 3: Transforms (10 pts)

Section II: Sampling

  • Part 4: Barycentric coordinates (10 pts)
  • Part 5: "Pixel sampling" for texture mapping (15 pts)
  • Part 6: "Level sampling" with mipmaps for texture mapping (25 pts)

Section III: (optional, possible extra credit) Art Competition

  • Part 7: Draw something interesting!

There is a fair amount of code in the CGL library, which we will be using for future assignments. The relevant header files for this assignment are vector2D.h, matrix3x3.h, color.h, and renderer.h.

Here is a very brief sketch of what happens when you launch draw: An SVGParser (in svgparser.*) reads in the input svg file(s), launches a OpenGL Viewer containing a DrawRend renderer, which enters an infinite loop and waits for input from the mouse and keyboard. DrawRend (drawrend.*) contains various callback functions hooked up to these events, but its main job happens inside the DrawRend::redraw() function. The high-level drawing work is done by the various SVGElement child classes (svg.*), which then pass their low-level point, line, and triangle rasterization data back to the three DrawRend rasterization functions.

Here are the files you will be modifying throughout the project:

  1. drawrend.cpp, drawrend.h
  2. texture.cpp
  3. transforms.cpp
  4. svg.cpp

In addition to modifying these, you will need to reference some of the other source and header files as you work through the project.

Section I: Rasterization

Part 1: Rasterizing single-color triangles (20 pts)

Relevant lecture: 2

Triangle rasterization is a core function in the graphics pipeline to convert input triangles into framebuffer pixel values. In Part 1, you will implement triangle rasterization using the methods discussed in lecture 2 to fill in the DrawRend::rasterize_triangle(...) function in drawrend.cpp.


  • It is recommended that you implement SampleBuffer::fill_color() function first, so that you can see rasterized points and lines for basic/test[1/2/3].svg.
  • Remember to do point-in-triangle tests with the point exactly at the center of the pixel, not the corner. Your coordinates should be equal to some integer point plus (.5,.5).
  • For now, ignore the Triangle *tri input argument to the function. We will come back to this in Part 4.
  • You are encouraged but not required to implement the edge rules for samples lying exactly on an edge.
  • Make sure the performance of your algorithm is no worse than one that checks each sample within the bounding box of the triangle.

When finished, you should be able to render many more test files, including those with rectangles and polygons, since we have provided the code to break these up into triangles for you. In particular, basic/test3.svg, basic/test4.svg, and basic/test5.svg should all render correctly.

For convenience, here is a list of functions you will need to modify:

  1. DrawRend::rasterize_triangle
  2. SampleBuffer::fill_color

Extra Credit: Make your triangle rasterizer super fast (e.g., by factoring redundant arithmetic operations out of loops, minimizing memory access, and not checking every sample in the bounding box). Write about the optimizations you used. Use clock() to get timing comparisons between your naive and speedy implementations.

Part 2: Antialiasing triangles (20 pts)

[Relevant lecture: 3(

Use supersampling to antialias your triangles. The sample_rate parameter in DrawRend (adjusted using the - and = keys) tells you how many samples to use per pixel.

The image below shows how sampling four times per pixel produces a better result than just sampling once, since some of the supersampled pixels are partially covered and will yield a smoother edge.

To do supersampling, each pixel is now divided into sqrt(sample_rate) * sqrt(sample_rate) sub-pixels. In other words, you still need to keep track of height * width pixels, but now each pixel has sqrt(sample_rate) * sqrt(sample_rate) sampled colors. You will need to do point-in-triangle tests at the center of each of these sub-pixel squares.

We provide a SampleBuffer class to store the sub-pixels. Each SampleBuffer instance stores one pixel. Your task is to (1) fill every sub-pixel with its correctly sampled color for every SampleBuffer instance, and (2) average all sub-pixels' colors within a samplebuffer to get a pixel's color. Since you've finished Part 1, you can use SampleBuffer::fill_color() function to write color to a sub-pixel for (1).

However, filling in the correct sub-pixel colors is only the first half. In order to properly rasterize the correct color based on each SampleBuffer instance's subpixels' colors, you will need to implement SampleBuffer::get_pixel_color to perform (2). This function looks at all of the SampleBuffer instance's subpixels and averages their colors together into a single color value which is then the SampleBuffer instance's "true" color. This function is called in DrawRend::resolve in order to render the svg.

Your triangle edges should be noticeably smoother when using > 1 sample per pixel! You can examine the differences closely using the pixel inspector. Also note that, it may take several seconds to switch to a higher sampling rate.

For convenience, here is a list of functions you will need to modify:

  1. DrawRend::rasterize_triangle
  2. SampleBuffer::get_pixel_color

Extra Credit: Implement an alternative sampling pattern, such as jittered or low-discrepancy sampling. Create comparison images showing the differences between grid supersampling and your new pattern. Try making a scene that contains aliasing artifacts when rendered using grid supersampling but not when using your pattern. You can also try to implement more efficient storage types for supersampled framebuffers, instead of using one samplebuffer per pixel.

Part 3: Transforms (10 pts)

Relevant lecture: 4

Implement the three transforms in the transforms.cpp file according to the SVG spec. The matrices are 3x3 because they operate in homogeneous coordinates -- you can see how they will be used on instances of Vector2D by looking at the way the * operator is overloaded in the same file.

Once you've implemented these transforms, svg/transforms/robot.svg should render correctly, as follows:

For convenience, here is a list of functions you will need to modify:

  1. translate
  2. scale
  3. rotate

Extra Credit: Add an extra feature to the GUI. For example, you could make two unused keys to rotate the viewport. Save an example image to demonstrate your feature, and write about how you modified the SVG to NDC and NDC to screen-space matrix stack to implement it.

Section II: Sampling

Part 4: Barycentric coordinates (10 pts)

Relevant lecture: 6

Familiarize yourself with the ColorTri struct in svg.h. Modify your implementation of DrawRend::rasterize_triangle(...) so that if a non-NULL Triangle *tri pointer is passed in, it computes barycentric coordinates of each sample hit and passes them to tri->color(...) to request the appropriate color. Note that the barycentric coordinates are stored with type Vector3D, so you should use p_bary[i] to store the barycentric coordinate corresponding to triangle vertex $P_i$ for $i=0,1,2$.

Implement the ColorTri::color(...) function in svg.cpp so that it interpolates the color at the point p_bary. This function is very simple: it does not need to make use of p_dx_bary or p_dy_bary, which are for texture mapping. Note that this color() function plays the role of a very primitive shader.

Once Part 4 is done, you should be able to see a color wheel in svg/basic/test7.svg.

For convenience, here is a list of functions you will need to modify:

  1. DrawRend::rasterize_triangle
  2. ColorTri::color

Part 5: "Pixel sampling" for texture mapping (15 pts)

Relevant lecture: 6

Familiarize yourself with the TexTri struct in svg.h. This is the primitive that implements texture mapping. For each vertex, you are given corresponding uv coordinates that index into the Texture pointed to by *tex.

To implement texture mapping, DrawRend::rasterize_triangle should fill in the psm and lsm members of a SampleParams struct and pass it to tri->color(...). Then TexTri::color(...) should fill in the correct uv coordinates in the SampleParams struct, and pass it on to tex->sample(...). Then Texture::sample(...) should examine the SampleParams to determine the correct sampling scheme.

The GUI toggles DrawRend's PixelSampleMethod variable psm using the 'P' key. When psm == P_NEAREST, you should use nearest-pixel sampling, and when psm == P_LINEAR, you should use bilinear sampling.

For now, you can pass in dummy Vector3D(0,0,0) values for the p_dx_bary and p_dy_bary arguments to tri->color

For this part, just pass 0 for the level parameter of the sample_nearest and sample_bilinear functions.

Once Part 5 is done, you should be able to rasterize the svg files in svg/texmap/, which rely on texture maps.

For convenience, here is a list of functions you will need to modify:

  1. DrawRend::rasterize_triangle
  2. TexTri::color
  3. Texture::sample
  4. Texture::sample_nearest
  5. Texture::sample_bilinear

Part 6: "Level sampling" with mipmaps for texture mapping (25 pts)

Relevant lecture: 6

Finally, add support for sampling different MipMap levels. The GUI toggles DrawRend's LevelSampleMethod variable lsm using the 'L' key.

  • When lsm == L_ZERO, you should sample from the zero-th MipMap, as in Part 5.
  • When lsm == L_NEAREST, you should compute the nearest appropriate MipMap level using the one-pixel difference vectors du and dv and pass that level as a parameter to the nearest or bilinear sample function.
  • When lsm == L_LINEAR, You should find the appropriate MipMap level and compute a weighted sum of two samples from adjacent levels.

Implement Texture::get_level as a helper function. You will need $(\frac{du}{dx}, \frac{dv}{dx})$ and $(\frac{du}{dy},\frac{dv}{dy})$ to calculate the correct MipMap level. In order to get these values corresponding to a point $p = (x,y)$ inside a triangle, you must

  1. calculate the barycentric coordinates of $(x+1,y)$ and $(x,y+1)$ in rasterize_triangle, passing these to tri->color as the variables p_dx_bary and p_dy_bary,
  2. calculate the uv coordinates sp.p_dx_uv and sp.p_dy_uv inside tri_color,
  3. calculate the difference vectors sp.p_dx_uv - sp.p_uv and sp.p_dy_uv - sp.p_uv inside Texture::get_level, and finally
  4. scale up those difference vectors respectively by the width and height of the full-resolution texture image.

With these, you can proceed with the calculation from the lecture slides.

For convenience, here is a list of functions you will need to modify:

  1. DrawRend::rasterize_triangle
  2. TexTri::color
  3. Texture::sample
  4. Texture::get_level

Extra Credit: Implement anisotropic filtering or summed area tables. Show comparisons of your method to nearest, bilinear, and trilinear sampling. Use clock() to measure the relative performance of the methods.

Section III: (optional, possible extra credit) Art Competition

Part 7: Draw something interesting!

Use your newfound powers to render something fun. You can look up the svg specifications online for matrix transforms and for Point, Line, Polyline, Rect, Polygon, and Group classes. The ColorTri and TexTri are our own inventions, so you can intuit their parameters by looking at the svgparser.cpp file. You can either try to draw something "by hand" or try to output an interesting pattern programmatically. For example, we wrote some simple programs to generate the texture mapped svg files in the texmap directory as well as the color wheel in basic/test7.svg.

Flex your right or left brain -- either show us your artistic side, or generate awesome procedural patterns with code. This could involve a lot of programming either inside or outside of the codebase! If you write a script to generate procedural svg files, include it in your submission and briefly explain how it works.

Tips and guidelines for your submission:

  • Your resulting png screenshot should be 800x800 resolution. Keep this in mind when writing your svg file.
  • Use the GUI's 'S' functionality to save your screenshot as a png. Don't take your own screenshot of your rasterized result, or you'll ruin the quality of your hard work!

Students will vote on their favorite submissions and the top voted submission(s) will receive extra credit!


Please consult this article on how to build and submit assignments for CS 184.

You will submit your code as well as some deliverables (see below) in a webpage project write-up.

Project write-up guidelines and instructions

We have provided a simple HTML skeleton in index.html found within the docs directory to help you get started and structure your write-up.

You are also welcome to create your own webpage report from scratch using your own preferred frameworks or tools. However, please follow the same overall structure as described in the deliverables section below.

The goals of your write-up are for you to (a) think about and articulate what you've built and learned in your own words, (b) have a write-up of the project to take away from the class. Your write-up should include:

  • An overview of the project, your approach to and implementation for each of the parts, and what problems you encountered and how you solved them. Strive for clarity and succinctness.
  • On each part, make sure to include the results described in the corresponding Deliverables section in addition to your explanation. If you failed to generate any results correctly, provide a brief explanation of why.
  • The final (optional) part for the art competition is where you have the opportunity to be creative and individual, so be sure to provide a good description of what you were going for and how you implemented it.
  • Clearly indicate any extra credit items you completed, and provide a thorough explanation and illustration for each of them.

The write-up is one of our main methods of evaluating your work, so it is important to spend the time to do it correctly and thoroughly. Plan ahead to allocate time for the write-up well before the deadline.

Project write-up deliverables


Give a high-level overview of what you implemented in this project. Think about what you've built as a whole. Share your thoughts on what interesting things you've learned from completing the project.

Part 1

  • Walk through how you rasterize triangles in your own words. Explain how your algorithm is no worse than one that checks each sample within the bounding box of the triangle.
  • Show a png screenshot of basic/test4.svg with the default viewing parameters and with the pixel inspector centered on an interesting part of the scene.
  • Extra credit: Explain any special optimizations you did beyond simple bounding box triangle rasterization, with a timing comparison table (we suggest using the c++ clock() function around the svg.draw() command in DrawRend::redraw() to compare millisecond timings with your various optimizations off and on).

Part 2

  • Walk through how you implemented supersampling and what modifications you made to the rasterization pipeline in the process. Explain how you used supersampling to antialias your triangles.
  • Show png screenshots of basic/test4.svg with the default viewing parameters and sample rates 1, 4, and 16 to compare them side-by-side. Position the pixel inspector over an area that showcases the effect dramatically; for example, a very skinny triangle corner.
  • Extra credit: If you implemented alternative antialiasing methods, describe them and include comparison pictures demonstrating the difference between your method and grid-based supersampling.

Part 3

  • Create an updated version of svg/transforms/robot.svg with cubeman doing something more interesting, like waving or running. Feel free to change his colors or proportions to suit your creativity.
  • Save your svg file as my_robot.svg in your docs/ directory and show a png screenshot of your rendered drawing in your write-up. Explain what you were trying to do with cubeman in words.

Part 4

  • Explain barycentric coordinates in your own words and use an image to aid you in your explanation. One idea is to use a svg file that plots a single triangle with one red, one green, and one blue vertex, which should produce a smoothly blended color triangle.
  • Show a png screenshot of svg/basic/test7.svg with default viewing parameters and sample rate 1. If you make any additional images with color gradients, include them.

Part 5

  • Explain pixel sampling in your own words and describe how you implemented it to perform texture mapping. Briefly discuss the two different pixel sampling methods, nearest and bilinear.
  • Check out the svg files in the svg/texmap/ directory. Use the pixel inspector to find a good example of where bilinear sampling clearly defeats nearest sampling. Show and compare four png screenshots using nearest sampling at 1 sample per pixel, nearest sampling at 16 samples per pixel, bilinear sampling at 1 sample per pixel, and bilinear sampling at 16 samples per pixel.
  • Comment on the relative differences. Discuss when there will be a large difference between the two methods and why.

Part 6

  • Explain level sampling in your own words and describe how you implemented it for texture mapping.
  • You can now adjust choose between pixel sampling and level sampling as well as adjust the number of samples per pixel. Analyze the tradeoffs between speed, memory usage, and antialiasing power between the various techniques at different zoom levels.
  • Show at least one example (using a png file you find yourself) comparing all four combinations of one of L_ZERO and L_NEAREST with one of P_NEAREST and P_LINEAR at a zoomed out viewpoint.
    • To use your own png, make a copy of one of the existing svg files in svg/texmap/ (or create your own modelled after one of the provided svg files). Then, near the top of the file, change the texture filename to point to your own png. From there, you can run ./draw and pass in that svg file to render it and then save a screenshot of your results.
  • Extra credit: If you implemented any extra filtering methods, describe them and show comparisons between your results with the other above methods.

Part 7

  • Save your best svg file as competition.svg in your docs/ directory, and show us a 800x800 png screenshot of it in your write-up!
  • Explain how you did it. If you wrote a script to generate procedural svg files, include it in your submission in the src/ directory and briefly explain how it works.

Website tips and advice

  • Your main report page should be called index.html.
  • Be sure to include and turn in all of the other files (such as images) that are linked in your report!
  • Use only relative paths to files, such as "./images/image.jpg"
  • Do NOT use absolulte paths, such as "/Users/student/Desktop/image.jpg"
  • Pay close attention to your filename extensions. Remember that on UNIX systems (such as the instructional machines), capitalization matters. .png != .jpeg != .jpg != .JPG
  • Be sure to adjust the permissions on your files so that they are world readable. For more information on this please see this tutorial.
  • Start assembling your webpage early to make sure you have a handle on how to edit the HTML code to insert images and format sections.