Graphics Programming

Due 11:59pm on Wednesday, November 1

1. Use nested loops to solve Program Design Exercise 14 in Chapter 8 of the text.
    
   Solution.
    
2. Do Program Design Exercise 16 in Chapter 8 of the text.  To clarify the problem, you should display one rectangle when the mouse is clicked.  Subsequently, any clicks outside of the rectangle are ignored.  But if a click occurs inside the rectangle, then the rectangle should disappear.  At that point, a subsequent click should create a new rectangle, and so on.
    
   Note: the text suggests using the "Click" property to determine the number of clicks, but this may lead to difficulties.  I suggest overriding the "OnDoubleClick" method instead.  If all else fails, you are allowed to ignore the issue of single-click vs. double-click, and just do everything using single-clicks.
    
   Solution.
    
3. Use recursion to generate a fractal snowflake.  This snowflake is an example of a fractal computation, but we don't need to know anything about fractals to solve it.

   There are several ways to describe a fractal snowflake.  The best way for this assignment is to first draw an equilateral triangle like this:
   ____________________
   \                             /
     \                         /
       \                     /
         \                 /
           \             /
             \         /
               \     /
                 \ /
   
   Then draw a second one on top of this, the same size, but rotated 180 degrees (thus generating the Star of David):

                 / \
               /     \
             /         \
   _____/________\_____
   \     /                 \    /
     \ /                    \ /
     / \                    / \
   /___\__________/___\
           \             /
             \         /
               \     /
                 \ /

   This figure is roughly drawn -- the triangles are supposed to be equilateral, having the same center point, and the six smaller triangles that this forms should also be equilateral of the same size.  Note that three of the smaller triangles are oriented like the first large triangle, and three are oriented like the second.  Indeed, the point now is to repeat this process for each of the corner triangles, and repeat again and again, until a suitably small triangle is reached.

   Draw your snowflake on a Form.  Experiment with sizes to get it to look nice (hint: make the form large!).  You may want to experiment with filled versus unfilled triangles and different colors for the successively smaller layers.

   Hint: The hardest thing about this assignment is figuring out the coordinates of the various images.  I suggest that you start with the smallest version, and then scale it up suitably.  There are two things to figure out from a given center: the new centers, and the vertices of the two triangles.  If we map this out on a 6-by-6 grid, the centers are given by:

        (3,1)
   (1,2)     (5,2)
        (3,3)
   (1,4)     (5,4)
        (3,5)

   and the vertices by:

          (3,0)
   (0,1.5)     (6,1.5)
          (3,3)
   (0,4.5)     (6,4.5)
          (3,6)

   If this doesn't make sense to you, draw a 6x6 grid on paper, and map out the above coordinates.

   Additional hints:

   Define a method:

   public void DrawTri(Graphics g, int x, int y, int m, int c, bool o)

   This method should draw a triangle on g that is centered at (x,y) and has side-length 6*m.  The parameter o determines the orientation -- if o is true, the horizontal side is on top, and if false the horizontal side is on the bottom.  The parameter c determines the color of the triangle, and is optional (I used it to index into an array of colors so that I could change the color at each level of the recursion).

   Then define a method:

   public void Flake(Graphics g, int x, int y, int m, int c, bool o)

   This method is the heart of the program, and should be recursive.  It should first draw a triangle using DrawTri, and then recursively call itself at each of the six smaller triangles.

   Final hint: the OnPaint method should make one call to DrawTri, and then one call to Flake.
    
   Solution.