Lab 9: Local State and Hilbert Space Filling Curves

Related files:

• gdraw.stk - Download this file to the same directory as your Lab 9 template. This lab requires you to use STk scheme.
  When using the graphics package on STk, please remember the following:
• The coordinate system starts in the graphics window with the origin in the upper left corner and extends across in the x and down in the y directions.
• The extent of the graphics window can be adjusted by using a call of the form: (set-width! 0 600 600).
• To clear the graphics window use (clear-graphics!)
• The "draw" function returns a positive numerical ID affiliated with the object just created. By referring to that numerical ID, one can access and modify many properties of that object using the following functions: Using ID = 0 refers to the underlying canvas. (set-color! ID color) set color for item Sample legal colors: red white green blue black yellow cyan magenta orange purple magenta brown pink ; the empty string "" clears the color.
• Lab 9 Template

1. Step 1: A simple procedure with local state 2 points

   Below is a small procedure called make-withdraw from the book.

   (define (make-withdraw balance)
     (lambda (amount)
       (if (>= balance amount)
           (begin (set! balance (- balance amount))
                  balance)
           "Insufficient funds")))
   

   Modify the above code so that it does not take in a balance parameter. In doing this assume every account begins with an initial balance of 300 dollars. The code should then work as follows:

   STk> (define a1 (make-withdraw))
   STk> (a1 50)
   250
   STk> (define a2 (make-withdraw))
   STk> (a2 40)
   260
   STk> (a1 40)
   210
   STk> (a1 250)
   "Insufficient funds"   
   

2. Step 2: A line drawing procedure with local state - 4 points

   The gdraw file you are given contains a procedure, (draw-line x1 y1 x2 y2), that draws a line on the gdraw canvas from coordinates (x1, y1) to (x2, y2). Using this procedure the following sequence of calls would draw a rectangle on the screen.

   STk> (draw-line 0 0 20 0)
   STk> (draw-line 20 0 20 30)
   STk> (draw-line 20 30 0 30)
   STk> (draw-line 0 30 0 0) 
   

   In many applications it nice to have an easy way to draw lines like the above example where each line is assumed to start where the last line ended. This allows you to easily specify continous line structures one coordinate at a time. If you had a procedure that did this, say line-drawer, the above rectangle could be drawn with the sequence of calls:

    
   STk> (line-drawer 0 0)   ;; First call specifies where to start
   STk> (line-drawer 20 0)  ;; Draws line from (0,0) to (20,0)
   STk> (line-drawer 20 30) ;; Draws line from (20,0) to (20,30)
   STk> (line-drawer 0 30)  ;; etc
   STk> (line-drawer 0 0)    
   

   line-drawer can be implemented as procedure with local state. Write a procedure (make-line-drawer) that returns a procedure with local state the operate like line-drawer in the above example. If your code works, the following calls should draw a square and a rectangle to the screen.

   STk> (define line-drawer (make-line-drawer))
   STk> (line-drawer 0 0)   
   STk> (line-drawer 20 0)  
   STk> (line-drawer 20 30) 
   STk> (line-drawer 0 30)  
   STk> (line-drawer 0 0)
   

3. Step 3: Drawing Hilbert Curves - 4 points

   Read through the information on Hilbert curves found here, and use the pseudo code found halfway down the page to implement a scheme procedure, called hilbert, that draws Hilbert space filling curves. Your hilbert procedure should take in a line drawing procedure created with make-line-drawer to implement the LineTo pseudo code call described in the link above. An outline of your procedure should look like:

   (define (hilbert x0 y0 xis xjs yis yjs n line-drawer)
     ;; Use line-drawer for the LineTo commmand
     ...
   )
   

   After running the test cases in the lab template, four Hilbert curves should be drawn on the gdraw canvas that look like the image at the top of this file, or some rotation of it.

Bonus Questions

• Bonus Question 1 -- 1 Bonus Point
  If you want to write the various Hilbert curves you have created in Step 5, so that instead of each using only a part of the canvas the curves are drawn on top of each other, how do you need to change the calls to the procedure hilbert that you used in Step 5?
• Bonus Question 2 -- 1 Bonus Point
  Use the set-color! procedure described above to assign a color to the lines drawn by the hilbert procedure. Choose the colors from the following: red white green blue black yellow cyan magenta orange purple brown pink. You'll need something like (set-color! (draw-line 0 0 20 0) 'green) to set the color of the line to green.
• Bonus Question 3 -- 2 Bonus Points
  Write a procedure that given the list of colors above, allows one to select a random color from that list. Use your procedure to draw hilbert functions with different colors. Tip: The procedure (random n) returns a random number in the interval 0 to n.

Congratulations on completing Lab 9!
Lab 9 total: 10 pts

This is what you will learn in this lab

• How to create procedures with local state.
• How to draw Hilbert space filling curves.