Assignment 2: Turtle Graphics

In this assignment, you will explore another way of thinking about graphics, inspired by the robotic “turtles” that some of you might associate with the LOGO programming language . You can think of the turtle as a machine with a pen, that sits on a sheet of paper. As it moves around the page, it drags the pen along the paper to draw pictures. You will be writing Haskell to generate instructions for a virtual turtle, and writing more Haskell to interpret these instructions into a CodeWorld Picture .

This assignment is worth 12% of your final grade.

Overview of Tasks

You will be required to complete different tasks depending on your enrolled course. This assignment is marked out 100 (for COMP1100) or 120 (for COMP1130):

	COMP1100	COMP1130
Task 1: Drawing Shapes	10 Marks	10 Marks
Task 2: Interpreting Turtle Commands	30 Marks	30 Marks
Task 3A: Sierpinski’s Triangle (Direct Drawing)	25 Marks	N/A
Task 3B: L-Systems	N/A	40 Marks
Unit Tests	10 Marks	10 Marks
Style	10 Marks	10 Marks
Technical Report	15 Marks	20 Marks

From this assignment onward, code that does not compile will be penalised heavily. It is essential that you can write code that compiles and runs. If you have a partial solution that you cannot get to compile, you should comment it out and write an additional comment directing your tutor’s attention to it.

Getting Started

Fork the assignment repository and create a project for it in IntelliJ IDEA, following the same steps as in Lab 2 . The assignment repository is at https://gitlab.cecs.anu.edu.au/comp1100/comp1100-assignment2 .

Overview of the Repository

Most of your code will be written in src/Turtle.hs . You will also need to write tests in test/TurtleTest.hs , which contains some example tests for you to study.

Other Files

test/Testing.hs is the same testing library we used in Assignment 1. You should read this file as well as test/TurtleTest.hs , and make sure you understand how to write tests.
app/Main.hs is a small test program that uses your turtle code. We discuss its features in “Overview of the Test Program”.
comp1100-assignment2.cabal tells the cabal build tool how to build your assignment. You are not required to understand this file, and we will discuss how to use cabal below.
Setup.hs tells cabal that this is a normal package with no unusual build steps. Some complex packages (that we won’t see in this course) need to put more complex code here. You are not required to understand it.

Overview of Cabal

As before, we are using the cabal tool to build the assignment code. The commands provided are very similar to last time:

cabal build : Compile your assignment.
cabal run turtle : Build your assignment (if necessary), and run the test program.
cabal repl comp1100-assignment2 : Run the GHCi interpreter over your project.
cabal test : Build and run the tests. This assignment is set up to run a unit test suite like in Assignment 1, but this time you will be writing the tests. The unit tests will abort on the first failure, or the first call to a function that is undefined .

You should execute these cabal commands in the top-level directory of your project: ~/comp1100/assignment2 (i.e., the directory you are in when you launch the IntelliJ Terminal tool for your project).

Overview of the Test Program

The test program in app/Main.hs uses CodeWorld, just like Assignment 1, and responds to the following keys:

Key	Effect
`T`	Display a triangle (from Task 1)
`P`	Display a polygon (from Task 1)
`=` / `-`	Increase/decrease the number of sides (polygon mode only, from Task 1)
`C`	Display a test pattern (a way to test your Task 2 code)
`S`	Display Sierpinski’s Triangle (from Task 3A or 3B)
`L`	Display a picture generated from an L-System (from Task 3B)

If you try to use the test program without completing Task 2, or you try to draw something you haven’t implemented yet, the test program will crash with the following error:

"Exception in blank-canvas application:" Prelude.undefined

If this happens, refresh the browser to continue using the test program.

Turtles and the `TurtleCommand` Type

We are going to imagine a turtle as a point-sized robot that sits on a canvas. This robot has:

a pen, which can be either up or down;
a position on the canvas; and
an angle called its facing .

There are four classes of commands that we can send to the turtle, and we represent those commands with the constructors of the TurtleCommand type:

type Radians = Double data TurtleCommand = Forward Double | Turn Radians | PenUp | PenDown deriving Show

The commands have the following meaning:

Command	Meaning
`Forward d`	Drive forward `d` units from the current position , along the current facing . If the pen is down, draw a line between the old and new positions .
`Turn t`	Turn `t` radians (360 degrees = `2 * pi` radians) from the current facing . This changes the direction that the turtle will drive in response to future `Forward` commands. Anticlockwise turns are represented by positive values of `t` ; clockwise turns are represented by negative values of `t` .
`PenUp`	Lift up the pen. Future calls to `Forward` will not draw lines.
`PenDown`	Put the pen on the canvas. Future calls to `Forward` will draw lines.

Task 1: Drawing Shapes (10 marks)

To draw a (CodeWorld) Picture with turtle graphics, we need two things: the commands to draw, and a way of interpreting those commands. In this task, you will define some functions that generate lists of turtle commands. When you have built the interpreter in Task 2, these functions will be a source of test data that you can use to check your interpreter.

Your Task

Define the following two functions in src/Turtle.hs :

triangle :: Double -> [TurtleCommand]

Returns a list of commands that will draw an equilateral triangle with side length equal to the argument. The turtle should finish with the same position and facing as when it started.
polygon :: Int -> Double -> [TurtleCommand]

polygon n s should return a list of commands that will draw a regular n -sided polygon, with side length equal to s . The turtle should finish with the same position and facing as when it started. If n < 3 , raise an error.

Hints

You won’t yet have an interpreter to test your generated [TurtleCommand] results. You can read ahead to the section on Unit Tests and write tests for these functions, or try working through a list of commands with a ruler and graph paper.
Try drawing a regular triangle, square or regular hexagon on a sheet of graph paper. Then place your pen on one corner and pretend that it is the turtle. What commands do you have to tell your turtle to make it trace the figure you drew on the graph paper?
The two points above are very similar, but work in opposite directions: the first one is asking you to check the result of your code by interpreting the results literally. The second point is looking at a correct result and asking yourself “what needed to happen to produce this?”. Being able to think in both directions is very useful.

Task 2: Interpreting Turtle Commands (30 marks)

Lists of TurtleCommand values are just data, but are useful because we can interpret them into a (CodeWorld) Picture . This is morally the same as the programming you are doing right now - a .hs file is just textual data, but becomes more useful because we can interpret it as a Haskell program. The difference is only in degree, not kind.

Your Task

Define a function runTurtle :: [TurtleCommand] -> Picture in src/Turtle.hs , which interprets the [TurtleCommand] according to the rules laid out in the “Turtles and the TurtleCommand ” section above. Assume that the turtle starts at (0, 0) , facing north (straight up), with the pen down (on the paper).

If you have completed this task correctly, the test pattern you get by pressing C in the test program will look like this (click for larger version):

Hints

You cannot consider a turtle command on its own; you need to know what the turtle has already done. For example, you need to know whether the pen is up or down to determine whether Forward should draw a line. We recommend defining:
- a type TurtleState , which tracks the turtle’s position , facing , and whether the pen is up or down, and
- a value initialState :: TurtleState , for the turtle’s initial position, facing, etc.
Work through a simple [TurtleCommand] on paper, to see what your program needs to do.
Break your solution apart into several functions, and test each in isolation. If you find that function is not behaving like you expect, you will have smaller units of code to debug, which is easier to get your head around.

Task 3A: Sierpinski’s Triangle - Direct Drawing (COMP1100 only: 25 marks)

Sierpinski’s Triangle is a famous fractal (self-similar structure). We can generate approximations to Sierpinski’s Triangle using the following rules:

An approximation at depth 1 is a single equilateral triangle.
An approximation at depth n is made up of three approximations at depth n - 1 , with their side length reduced by half. These approximations are arranged to cover the original triangle.

We can draw approximations to Sierpinski’s triangle using our turtle system (click for larger versions):

Your Task

Define a function sierpinski :: Int -> Double -> [TurtleCommand] in src/Turtle.hs , which generates the necessary commands to draw an approximation to Sierpinski’s Triangle. The first argument specifies the depth, and the second specifies the side length. The turtle should finish with the same position and facing as when it started.