teaching machines

Homework 5 – Plaid Scientist – due December 1

August 22, 2019 by . Filed under cs1, fall 2019, specifications.

Your objective in this homework is to learn how to organize and process data using arrays. You will do this in the context of writing a program that generates plaid patterns.

Arrays have two features that are indispensible when building software: they help us manage large sequences of data by collecting the data into a single container, and they let us reach into the data with integer indices—which means we can write all sorts of algorithms that look up or access data indirectly.

This assignment is more involved and less easy to test in small chunks than your previous assignments. Plan accordingly.

Before we dig into the specification, let’s talk about plaid and the file formats you will be using.


Plaid patterns are generated by weaving together yarns of different colors in algorithmic patterns. One can use a rectangular frame or loom to generate these patterns. First, yarn is stretched from the top of the loom to the bottom in a series of columns or warps. Then horizontal strands of yarn are weaved through the warps. Because these horizontal strands are the active agents of the weaving, they are called wefts.


The weaver has choices about how to string the horizontal wefts through the vertical warps. One could go over one warp, under the next, over the next, under the next, and so on. This pattern is called a 1/1 twill. If the weaver goes over two warps, under one warp, over two warps, under one warp, and so on, a 2/1 twill pattern is produced. A 3/2 twill pattern goes over 3 warps, under 2, over 3, under 2, and so on.


The yarns themselves are dyed in repeating patterns. For example, a yarn might be dyed cornflower blue for 2 inches and pumpkin for 1 inch, with this pattern repeated along the whole length of the yarn.

The combination of the geometric alternation of the twill and the alternation of colors of the warps and wefts produces the comforting plaid patterns that we find in our flannel shirts, tablecloths, and other fabrics.

Plaid Pattern Specification

In this homework, we describe plaid patterns in a plain text file that has a form like the following:

hmirror true
vmirror false
twill 3 1

salmon 240 142 125
marzipan 240 200 125

salmon 2
marzipan 4

There are five possible commands: hmirror, vmirror, twill, palette, and yarn. They may appear in any order. There may be multiple palette and yarn sections—but if you follow the pseudocode suggested later, you don’t need to do anything special to support this. We will consider how these commands are interpreted in the following sections.


In the example plaid pattern shown above, we see that the yarn alternates between 2 units of salmon and 4 units of marzipan. The RGB values of these colors are defined in the palette section. The base yarn pattern looks like this:

We use this base pattern to form the colorings of the warps and wefts.


The vmirror property is false, so we use the base yarn pattern directly to form the vertical warp pattern:

When strung on the loom, the warp pattern will repeat to span the loom’s height:

If we were to string 12 of these warps on a loom, we’d see the following color pattern:

This is not how the final fabric appears. We still need to string the wefts through.


The weft is different because hmirror is true. Instead of repeating the base yarn pattern directly, we mirror it first. The base is 2 salmon and 4 marzipan, and therefore the mirrored pattern is 2 salmon, 4 marzipan, 4 marzipan, and 2 salmon:

When repeated along the width of the loom, we see this for the wefts:

If we laid out a number of wefts as we did with the warps, we might suppose we’d see a pattern like this:

To add some visual variety, however, weavers shift the pattern one step after each row, like so:

Weaving Algorithm

We now know what a fabric of all warps would look like, and we know what a fabric of all wefts would look like. But a weave is a selective combination of the warps and the wefts. The twill pattern tells us which of the two will be visible. If the twill is 2/1, we see weft-weft-warp, weft-weft-warp, and so on. If the twill is 3/1, we see weft-weft-weft-warp, weft-weft-weft-warp, and so on.

Suppose we weave the plaid patterns in an image instead of a loom, stringing the warps along its columns and the wefts along its rows. At each pixel, we must decide whether we use the color from the warp or the weft. Considering all the information above regarding the twill, warps, wefts, and shifting, we formulate this algorithm:

period = over count + under count
for each row r
  twill index = 0 for row 0, 1 for row 1, etc, with wrapping
  for each column c
    if twill index says we're in weft zone
      choose color from weft according to c, with wrapping
      choose color from warp according to r, with wrapping
    set pixel to chosen color
    advance twill index by 1, with wrapping

Though not shown in this pseudocode, the twill index must always wrap back around to 0 when it reaches the period or beyond.


To visualize the color data that we generate by our weaving algorithm, we have to write it out in a format that image editors can read. JPEG and PNG are popular formats, but they use mathematics beyond the scope of this course to shrink down the file size. We will instead use a very readable format called Portable Pixmap (PPM).

Humans can open a PPM file in a text editor and understand it with some labor. Consider this PPM, for example:

2 4
255 0 0
0 255 0
0 0 255
255 255 0
255 0 255
0 255 255
255 255 255
0 0 0

The first line is P3. Many file formats specify a magic number, a special sequence of bytes that tells applications what kind of file it is. P3 is the magic number for the PPM format. The second line (2 4) is the image’s width and height. The third line (255) is the maximum intensity found in any color. A color whose red, green, and blue components are this number will display as white. For our purposes, assume this number is always 255. The next lines are the individual pixel triplets, row by row. The first pixel in this example is red, and the second is green. Then we have blue and yellow. Then magenta and cyan. And finally white and black. The first pixel in the file is shown at the top-left of the image.

Paste the text into a file and view it with an image editor like The GIMP. Not all editors can read PPM. You should see an image that looks like this:

Tweak color values in the text file and see what happens. Make sure you understand the file structure before moving on.


Complete the classes described below. Place all classes in package hw5. Make all methods static.


Write class Main with a main method, which you are encouraged to use to test your code. Nothing in particular is required of it, but it must exist.


Write class ImageUtilities with the following methods:


Write class PlaidUtilities with the following methods:


For an extra credit participation point, identify some plaid in your life and recreate it using your program. Share a photo of the original plaid, your plaid pattern, and a resulting PNG image on Piazza under folder ec5 by the due date. The submission garnering the most votes will be honored in some way.


To check your work and submit it for grading:

  1. Run the SpecChecker by selecting hw5 SpecChecker from the run configurations dropdown in IntelliJ IDEA and clicking the run button.
  2. Fix problems until all tests pass.
  3. Commit and push your work to your repository.
  4. Verify on GitLab that your submission uploaded successfully.

A passing SpecChecker does not guarantee you credit. Your grade is conditioned on a few things: