Exercise 13.8
- Assuming that g is a Graphics object, state the error in each statement.
(a) g.setColor(Color.Red);
(b) g.setFont("Serif");
- Write a program that will display a window that is 500 pixels wide
and 400 pixels high. The window should contain the following, drawn
as indicated:
- In the upper left quadrant, the name Joanne, in a monospaced
font, inside a solid blue circle
- In the lower left quadrant, the name Man-Kwan, in a serif font,
inside an outlined red square
- In the upper right quadrant, the name John, in a sans serif font,
inside a solid magenta rectangle
- In the lower right quadrant, the name Kevin, in an italic font,
inside an outlined cyan ellipse
- In the centre, the name Vaughn, in a bold italic font, inside a
solid yellow isosceles triangle
- Write a program that allows the user to click on two points within
a blank window and then draws the rectangle that has those points
as the endpoints of one of its diagonals. If the points are aligned
vertically or horizontally, the program should simply join the two
points with a line segment.
- Write a program that allows a user to click on three non-collinear
points in a window and then draws the circle that passes through
those points. If the user selects three collinear points, the program
should draw a message that indicates this.
Projects
- Write a program that asks the user to submit the time in hours
and minutes in two text fields. The program should then draw a representation of the given time as it would appear on an analog
clock. The "clock" should consist only of a circular region containing
two line segments - a short one for the hour hand and a longer one
for the minute hand.
- Write a program that first presents the user with a window that
contains a blank square area with labelled text at the bottom. The
label should direct the user to enter an integer value n in the range 2 <=
n <= 100. After the user enters the number and presses < enter >, the
program should draw n filled circles, each of radius four pixels. These
circles should be arranged at equal intervals around the perimeter of
a large circle. The diameter of the large circle should be determined
by the size of the region; it should have a diameter equal to 90% of
the lesser of the width and height of the region.
- Although we can draw a filled circle fairly easily using the fillOval
method, this question asks you to draw such a figure the hard way,
one pixel at a time. Specifically, you are to draw the graph of the
relation x^2 + y^2 <= 4 (a circular disk with radius 2 and centre at
the origin). In making your drawing, position the point (0,0) at the
centre of the display area and try using a scale of one unit = 200
pixels. Set the scale by defining a constant:
final int SCALE = 200; // pixels per unit
This should produce a drawing that will fit nicely on the screen of
your computer but, if it does not, write the program so that you
can change the size of the image easily by changing the value of the
constant.
To draw the disk, for each pixel corresponding to a point in the
square region in which -2 <= x <= 2 and -2 <= y <= 2, test whether
the sum of the squares of the coordinates of the point is less than or
equal to 4. If so, the point lies in the disk. If the point lies in the
disk, fill in the pixel by invoking the method fillOval with a width
and height of 1.
- Modify the program of the previous question to draw the graph of the
Mandelbrot set. This is a set of points on an Argand diagram, a coordinate
system in which the complex number z = a + ib is represented
by the point (a, b). To determine whether or not a complex number
c is in the Mandelbrot set, we examine the terms of the following sequence.
z1 = c
zk = zk - 1^2 + c, if k > 1
The value c is in the Mandelbrot set if and only if the terms of
the sequence never get "large". To determine whether or not this
sequence will ever get large, look at up to thirty terms, testing each
one to see whether or not |Zk| > 2. (In geometric terms, this checks
to see if the point lies outside the circle of radius 2, centred at the
origin.) If any term of the sequence ever satisfies this condition, the
sequence is guaranteed to get large. (What we mean by this is that,
as k gets large, the value of Zk is guaranteed to eventually become
larger than any given value you care to name. As an example, the
sequence 1,2,4, ... gets large in this sense.) If the sequence has not
produced a point that is more than two units from the origin after
thirty iterations, you can depend on it never growing large. In this
case, the point c is part of the graph of the Mandelbrot set on an
Argand diagram. If a point is in the set, use the drawOval method
to add it to the set, as in the previous question. The domain of your
graph should be from -2 to 1 (along the real axis) while the range
should be from -1 to 1 (along the imaginary axis).
- Write a program that allows two people to play tic-tac-toe against
each other. The program should present a square area that is divided
into nine smaller squares by vertical and horizontal lines. If a user
clicks the mouse in an empty region, the program should place a large
X or a large O (on alternate turns) into the middle of that area. The
program should not permit any move after a player has won the game.
The window should also have a "Restart" button at the bottom to
allow users to start a new game at any time.
- Modify the program in the previous question so that a user can play
against the computer. Try to make the computer's moves reasonably
intelligent.
- The game called Life was invented in 1970 by the British mathematician
John Conway. It is played by one person on a (theoretically)
unbounded grid of squares. Each cell on the grid represents
an organism which can, at any time, be either alive or dead. Which
organisms are alive changes from generation to generation according to the number of neighbouring eels that are alive. Births and deaths
take place according to the following rules:
- The neighbours of a given cell are the eight cells that are adjacent
to it vertically, horizontally, or diagonally.
- If a cell is alive but has only zero or one neighbours that are
alive, then in the next generation the cell dies of loneliness.
- If a cell is alive and has four or more neighbours that are alive,
then in the next generation the cell dies of overcrowding.
- A living cell with either two or three living neighbours remains
alive in the next generation.
- If a cell is dead, then in the next generation it will become alive
if it has exactly three neighbours that are already alive in this
generation.
- All births and deaths take place at exactly the same time so that
dying cells can help give birth to other cells but cannot prevent
the deaths of others by reducing overcrowding. Similarly, cells
about to be born can neither preserve nor kill cells living in
the current generation. In order to follow this rule, one must
determine all births and deaths before creating or destroying
any cells.
Write a program that will play the game of Life on a bounded grid.
The program should allow the user to specify a starting pattern and
should then continue to create new generations periodically until the
user stops the action. The user should be able to control the time between
generations. Java's Timer and TimerTask classes in the package
java.util provide methods for controlling time between events.
Despite the simplicity of the rules of the game, many quite interesting
patterns and dynamics are possible. Some of the "creatures"
composed of collections of living cells can blink, glide, and even produce
offspring. For some of the possibilities, take a look at some of
the many web sites devoted to this subject or see the book Wheels,
Life and Other Mathematical Amusements by Martin Gardner.
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