Project 8: A graphing calculator

The goal of this project is to practice writing programs that have a graphical user interface (GUI) and use graphics. This project will also tie together many threads from the course of the semester and will result in an impressive product you can show your friends.

I. Introduction

You will write a program that operates as a graphing calculator. It will have a window that allows a user to enter in a function and set min and max values for x and y (to specify the viewing range); it will draw a graph of the function within the specified range.

The program I wrote to solve this problem looks like this:

You are not required to mimic this window exactly, but your program should have a window with the basic features/elements found here.

Since time in the semester is running short, it is imperative that you decide on a schedule for yourself for working on this project. This project has three distinct parts:

1. parsing and interpreting the function
2. making the window
3. drawing the actual graphs

What you need to know about these:

• Parts 1 and 2 are independent of other parts and in theory can be done in any order. They can be tested independently. Part 3, however, depends on parts 1 and 2, and cannot be tested until parts 1 and 2 are completed. You will have to do part 3 last.
• You already know how to do part 1; it's just an extended version of the interpreter you wrote in lab 13. This will be relatively easy (assuming you understood that lab).
• Part 2 you will be able to start on using what we learn on Nov 24, but we will not see other necessary pieces until Dec 1. This part isn't hard conceptually, but you'll be working with new parts of Java.
• We won't learn the material you'll need for part 3 until Dec 3 (although section 18.3&4 in Absolute Java covers it pretty well). This also will be the hardest conceptually (it will take some mathematical figuring). Since the project is due Dec 9, you'll have a week, in practice, to do this part.
• So, try to get the earlier parts done beforehand, so you can concentrate on part 3 when the time comes.
• Note that if you have both your late days left, your due date is effectively Dec 11.

II. Set up

Copy the starter files from the course public directory:

cp /homes/tvandrun/Public/cs235/proj8/* .

III. Part 1: Interpreting the function

The graphing calculator will graph functions whose bodies are defined by the following language:

expression --> integer | x | ( expression op expression)

op --> + | - | / | * | ^

Note there are two changes to the language from lab 11: the language now has variables (technically only one variable, x) and exponentiation. Remember/notice that the expression must be fully parenthesized and that there is no unary negation (ie, negative sign) in the language, so instead of

-3x^2 + 5

one must write

((0 - (3 * (x ^ 2))) + 5)

or

(((0 - 3) * (x ^ 2)) + 5)

(This might seem like an undue burden on the user, but believe me that implementing things like order of operation, implicit multiplication (ie, 3x), and unary minus would make this project severely more difficult.)

You must model expressions in this language using trees just as in lab 11 and interpret strings in the language by building appropriate trees.

A. The Tree classes

I have provided the ExprNode interface. There is one difference between this and the version from lab 11: the signature of the evaluate method is now

double evaluate(double x);

It returns a double (everything in this project will be double-valued, not int-valued), but more importantly, it also has a double parameter. This parameter indicates the value of the variable.

Your task is to write classes Number, Variable, and Operation (or similar classes; you don't have to use these exact names) which will implement ExprNode. They will be similar to those your wrote in lab 11. The interesting part is figuring out how the evaluate() method will differ. (Hint: What will the various classes do with the formal parameter x? The Variable class is the only one that will use it, the Number class will ignore it, and the Operation class will pass it along in the recursive calls.)

B. Building the trees

I have provided the class ExprStringSlicer just as with lab 11; refer to that lab description to see how it works. The class Interpreter has a static method interpret() which will be used to convert strings to ExprNode trees.

Your task is to fill-in the method interpret(). Hints:

• Make it recursive; if the input string is a operation expression, you'll have to call interpret() to build the subexpressions.
• Number and variable will be base cases.
• How do you tell which case you are in? Look at the first character. Is it x, (, or something else?

You can test it using the main() method of Interpreter, giving the expression (in quotes) and the x-value on the command line, for example

java Interpreter "((0 - (x ^ 2)) + 5)" 3.5

Don't worry yet about handling erroneous input. At this point it is ok if your program crashed on unparsable text.

IV. Part 2: Displaying the window

In this part, you will design and implement the window that will be shown to the user. The class GraphCalc has a main() method which is the main method of the whole program, and its primary purpose is to build the window.

I am providing for you a class called PaintPanel which will make doing graphics easier. It is a component which you can include in the window; it will be the space in the window where the graph appears. More details of this class will be given in part 3.

Your task is to finish the main() method of GraphCalc. I have included the parts that need to be somewhere in the window: JTextFields for the function and the x and y min and max, a button, and a PaintPanel. You may decide to rearrange these. At any rate, you need to add them to the window, plus any panels, layout managers, etc.

Don't worry about the fact that the window doesn't do anything. In this part, your only concern is the window's appearance.

V. Part 3: Drawing the graph

Finally, you need to make a graph appear on the PaintPanel whenever the button is pressed. This will require a class that implements ActionListener which is attached to the button and triggers the graphing when the button is pressed and a class that implements Painter and draws the graph.

(In my solution, I wrote one class that does both-- it implements both ActionListener and Painter. Its actionPerformed() method calls the panel's repaint() method, and its paint() method reads from the JTextFields and does most of the work.)

Here are the things that need to be done whenever the button is pressed.

• Read from the textfields to build the parse tree and find out the x and y ranges.
• Figure out the scale of graph so that you can associate pixels on the panel with points in the plane. For example, if the x range were -10 to 10 and the width of the panel were 200, then the x value -9 corresponds to the coordinate 10 on the vertical axis of the panel. Don't forget that the "origin" in the Graphics class is in the upper lefthand corner. This means that the y value -9 would correspond to coordinate 190.
• If 0 is within the x range, then draw the y axis; if 0 is within the y range, then draw the x axis.
• Draw the curve: For each horizontal pixel coordinate, find the corresponding x value; find the value of the function at that x value; if that value is within the y range, then fill-in the pixel that corresponds to (x, f(x)) by drawing a filled rectangle of area 1 pixel.
• If the input the user gives is bad (the function can't be parsed, the min and max values aren't legitimate numbers, the ranges are empty), your program should handle it gracefully. You will need some exception handling here. You may deal with bad input any way you like (ignore it, guess at a default value, display an error message), but your program must not crash.

Your task is to write a class or classes that does this, and update GraphCalc so that the new class or classes will interact with the window.

VI. Turn in

Please email the files you wrote or changed to me.

DUE: Wednesday, Dec 9, at 5:00 pm.