Sample Questions for Exam 1

Evaluate each of the following:

Given the following draw() method:

    public void draw(Color color, double[] p, double[] q)
    {
       double    alpha, m;

       if (q[0] == p[0]) m = Double.POSITIVE_INFINITY;
       else              m = (q[1]-p[1])/(q[0]-p[0]);

       if ((m >= -1.0) && (m <= 1.0))
       {
          double   y;          
          int      xEnd, xStart;

          if (p[0] <= q[0])
          {
             xStart = (int)Math.round(p[0]); 
             xEnd   = (int)Math.round(q[0]); 
          }
          else
          {
             xStart = (int)Math.round(q[0]); 
             xEnd   = (int)Math.round(p[0]); 
          }
          
    
          for (int x=xStart; x<=xEnd; x++)
          {
             if (q[0] == p[0])
             {
                y = p[1];                
             }
             else
             {
                alpha = (x - p[0])/(q[0] - p[0]);
                y = p[1] + alpha * (q[1] - p[1]);          
             }
                
             fb.setPixel(x, (int)Math.round(y), color);          
          }
       }
       else
       {
          double   x;          
          int      yEnd, yStart;
       
          if (p[1] <= q[1])
          {
             yStart = (int)Math.round(p[1]); 
             yEnd   = (int)Math.round(q[1]); 
          }
          else
          {
             yStart = (int)Math.round(q[1]); 
             yEnd   = (int)Math.round(p[1]); 
          }
          
    
          for (int y=yStart; y<=yEnd; y++)
          {
             if (q[1] == p[1])
             {
                x = p[0];                
             }
             else
             {
                alpha = (y - p[1])/(q[1] - p[1]);
                x = p[0] + alpha * (q[0] - p[0]);          
             }
             
             fb.setPixel((int)Math.round(x), y, color);          
          }
       }
    }

show (in the grid below) what will be drawn if this method is called as follows:

    double[] p = { 0, 0};
    double[] q = {10, 3};
    draw(Color.RED, p, q);

You must assume that the lower-left pixel is the origin [i.e., (0,0)] and that the coordinates increase from left-to-right and bottom-to-top.

Complete the following onLine() method. Your answer must be consistent with the comments describing the method. You may use methods that were required in the VMath and MMath classes.

    /**
     * Determines if a point is on a line 
     * (represented in in explicit form)
     *
     * @param m  The slope of the line
     * @param b  The vertical intercept of the line
     * @param p  The test point
     * @return   true if p is on the line defined by h
     */
    public static boolean onLine(double m, double b, double[] p)
    {






















    }

Complete the following sameSide() method. Your answer must be consistent with the comments describing the method. You may use methods that were required in the VMath and MMath classes.

    /**
     * Determines if two 2D points are on the same side of 
     * a line segement
     *
     * The vertexes can be assumed to be ordered correctly
     * (i.e., obey the right-hand rule)
     * 
     * @param p  One point on the line
     * @param q  Another point on the line 
     * @param s  One test point
     * @param t  The other test point
     * @return   true if s and t are on the same side; false otherwise
     */
    public static boolean sameSide(double[] p, double[] q, 
                                   double[] s, double[] t)
    {






















    }

Using the sameSide() method above, write a method that determines if a given point is inside a convex polygon.