For this assignment you will write a GUI for plotting functions. The user will supply the de?nition of a function in the variable x, the range of x and y values to be plotted and the number of steps in the plot. The GUI will then display the function. The user can enter any number of functions. Each will be plotted in the chosen colour. The plot information can also be changed - i.e. the x and y ranges and the number of steps. All the functions can then be redrawn using the new setup.
One way to plot a function is to construct a sequence
< (x1, y1), (x2, y2), . . . , (xn, yn) >
where x1 is the smallest value of x, xn is the largest value of x, n is the number of steps, each yi is the result of applying the function to xi and all the xi are equally spaced. The lines from (x_{i}, y_{i}) to (x_{i+1}, y_{i+1}) are then drawn to produce an approximation to the function. The larger the number of steps, the better the approximation.
Typically though, the sequence is not really constructed. All that is needed is the pairs of adjacent points so that a line can be drawn between them. The assignment support ?le de?nes an iterator that generates the required sequence.
Below is an example of plotting the function x^{2} from -5 to 5 in 6 steps. First a line from (-5, 25) to (-3, 9) is drawn followed by the line from (-3, 9) to (-1, 1), followed by the line from (-1, 1) to (1, 1), followed by the line from (1, 1) to (3, 9), followed by the line from (3, 9) to (5, 25).
For the actual plotting you will be using a canvas widget. The canvas has a given width and height while the plotting parameters specify ranges for x and y. Therefore a conversion is required that map 'real world' coordinates (i.e. the x,y values) to screen (canvas) coordinates. Remember that in the 'real world' y values increase as you move up while on a canvas they decrease as you move up. The assignment support ?le de?nes a coordinates conversion class that does this job.
Assignment Tasks
For each class and method that you write you need to provide a suitable comment giving a description and where necessary the type and any preconditions. You should use the triple-quote commenting style.