In-Class Examination 2

• Before you answer any questions, write your name and perm number.
• Read each question carefully.  Make sure that you clearly understand each question before answering it.
• Put your answer to each question on its own page.
• You may wish to work out an answer on scratch paper before writing it on your answer page; answers that are difficult to read may lose points for that reason.
• Each question is worth 25 points.

    double max(double a[][][])
    {
        double max = a[0][0][0];

        for (int i = 0; i < a.length; i++)
        for (int j = 0; j < a[i].length; j++)
        for (int k = 0; k < a[i][j].length; k++)
            if (max < a[i][j][k])
                max = a[i][j][k];

        return max;
    }

• a point, so represented
• an integer number of degrees

        x' =  x*cos(theta) + y*sin(theta)
        y' = -x*sin(theta) + y*cos(theta)

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Solution:

        p[1] = -p[0]*Math.sin(radians) + p[1]*Math.cos(radians);
        p[0] = temp;
        return;
    }

When the mouse is released in the red circle, add 150 points to int variable sum.  When the mouse is clicked in the yellow ring (the yellow circle, but not the red circle), add 100 points to sum.  When the mouse is clicked in the blue ring (the blue circle, but not the yellow circle), add 50 points to sum. (Hint: recall, for a right triangle, that the sum of the squares of the sides equals the square of the hypoteneuse.)

public class target extends Applet implements MouseListener
{
    int sum = 0, x, y;

    public void init()
    {
        addMouseListener(this);
    }

    public void paint( Graphics g)
    {
        g.setColor(Color.blue);
        g.fillOval(50, 50, 300, 300);
        g.setColor(Color.yellow);
        g.fillOval(100, 100, 200, 200);
        g.setColor(Color.red);
        g.fillOval(150, 150, 100, 100);
    }

    public void mousePressed(MouseEvent e) { }
    public void mouseClicked(MouseEvent e)  { }
    public void mouseReleased(MouseEvent e)
    {
        x = e.getX();
        y = e.getY();
        repaint();
    }
    public void mouseEntered(MouseEvent e)  { }
    public void mouseExited(MouseEvent e)   { }
}

Solution:

I said during the test that you can imagine putting your code in the paint method.  You also could have put the code in the mouseReleased method, as is done below.

The question says that the circles are centered at pixel coordinates 150, 150.  The code below has the circles centered on 200, 200.  Either center ( 150, 150 or 200, 200 ) is fine.

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import java.awt.*;
import java.applet.*;
import java.awt.event.*;

public class target extends Applet implements MouseListener
{
    int sum = 0, x, y;

    public void init()
    {
        addMouseListener(this);
    }

    public void paint( Graphics g)
    {
        g.setColor(Color.blue);
        g.fillOval(50, 50, 300, 300);
        g.setColor(Color.yellow);
        g.fillOval(100, 100, 200, 200);
        g.setColor(Color.red);
        g.fillOval(150, 150, 100, 100);
    }

    public void mousePressed(MouseEvent e) { }
    public void mouseClicked(MouseEvent e)  { }
    public void mouseReleased(MouseEvent e)
    {
        int dist;    // the square of the distance from the center

        x = e.getX();
        y = e.getY();
        dist = (200 - x)*(200 - x) + (200 - y)*(200 - y);
        if (dist < 50*50)
            sum += 150;
        else if (dist < 100*100)
            sum += 100;
        else if (dist < 150*150)
            sum += 50;
        repaint();
    }
    public void mouseEntered(MouseEvent e)  { }
    public void mouseExited(MouseEvent e)   { }
}

4. Characterize a square in the 2-dimensional plane by its lower left corner and its edge length.  For example, the square whose 4 corners are (-1, -1), (1, -1), (-1, 1), (1, 1) would be represented by its lower left corner, (-1, -1), and its edge length of 2.  For this question, represent the lower left corner with 2 doubles (xLL, yLL), and the edge length with another double:

    double xLL = -1.0, yLL = -1.0, edge = 2.0;

This square in the 2-dimensional plane is "displayed"on the applet's graphic object as a 100 x 100 pixel square whose upper left corner has pixel coordinates (0,0).

The mouse release coordinates (x, y) are in applet int variables x and y.

    int x,y;   // mouse coordinates in pixels

We say that the mouse coordinates refer to the corresponding point in the 2-dimensional plane. In the example above, if mouse coordinates (x,y) were pixel coordinates (0,0) (i.e., the upper left corner of the square), then they would refer to 2-dimensional plane coordinates (-1, 1).

Give Java statements that compute the lower left corner of the square in the 2-dimensional plane (i.e., compute the values of xLL and yLL) whose edge length is the same as the current square, but whose center is the point in the 2-dimensional plane referred to by the mouse coordinates.   In the example above, the new lower left point is (-2, 0) (i.e., xLL is -2.0 and yLL is 0.0).  See Powerpoint slide.  Assume that the mouse coordinates are within the applet square.

Solution:

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        y = 100 - y;
        xLL += edge * ((x - 50) / 100.0);
        yLL += edge * ((y - 50) / 100.0);

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