Develop a function named
counterchange which takes in two images and returns a 2x2
arrangement of them, as shown at right. (Click on the image for a
full-scale view.)
Hint: Use the tiles.ss teachpack.
Develop a function named checkerboard
which takes in two colors (e.g. strings) and returns a 2x2 arrangement
of them, as shown at right. Hint: This is extremely
easy if you re-use a previously-written function!
Develop a function that does something fun with images,
using some combination of image-above,
image-beside, reflect-vert,
reflect-horiz, rotate-cw,
rotate-ccw, and rotate-180.
Develop a function named
smallest-of-3
which takes in 3 numbers and returns the smallest of them.
Three candidates (Anne, Bob, and Charlie) are running for mayor
of Schemeville, which, by court order, has a new computerized
voting system. Develop a function named
who-won which takes in three numbers (the
number of votes for Anne, the number of votes for Bob, and the number of
votes for Charlie, respectively) and returns a string indicating the
name of the person who won -- either "Anne",
"Bob", or "Charlie".
For example,
(who-won 7 4 5) "should be" "Anne"
(who-won 5 11 36) "should be" "Charlie"
For now, you may assume that there are no ties.
Recall the traffic-light animation we did in class, with a single disk changing colors (green, yellow, red, green, ...). In this exercise we'll develop something that looks more like a real traffic light.
Write an expression that returns an image of a
rectangle with three circles outlined in black positioned inside it
vertically, something like the one at right. (Use the
empty-scene
function, described in the Help Desk, to get the background rectangle.)
Store the result in a variable for future use.
Develop a function choose-y which takes
in a color (however you choose to represent that) and returns the
y-coordinate of the center of that light in this picture.
The red one should be on top, yellow in the middle, green on the bottom.
Develop a function show-world which will
return an image of a traffic light with either the red, yellow, or
green light illuminated, as in the example at right. Be sure to use
the previous two problems to help!
Develop a handle-tick function and
whatever else is necessary to create an animation of a traffic light
that changes colors every second.
Develop an animation of a ball that starts at
location (3, 10) and moves by 2 in the x dimension and 1 in the y
dimension every half second. This will require, as usual,
- identifying a data type to represent the "current world";
- writing and testing a
show-worldfunction to display the world; - writing and testing a
handle-tickfunction to modify the world; - starting everything off using
big-bang; and - installing the callback functions with
on-redrawandon-tick-eventrespectively.
Don't start on this until we've gotten to section 6.3 in the textbook! In some countries, after the traffic light has been red for a while, it switches to red-and-yellow before switching to green. We can't do that if our representation of a world is just a color, so let's come up with a more flexible representation. In fact, this representation will also allow us to build traffic lights that flash the red light on and off (with the green and yellow lights never on), or flash the yellow light on and off (with the green and red lights never on), or light up the red and green at the same time for Christmas, or light up all three lights at once, etc.
Develop an animation of a light that switches from green, to yellow, to red, to red-and-yellow, to green, etc. To do this, you'll need to first...
Define a data type light
which consists of three booleans: green?,
yellow?, and red?. These will indicate
whether each of the respective lights is on or not; since they're all
independent of one another, we should be able to turn on or off
whichever combination we wish. As usual in defining a struct, you
must give several examples of constructing instances of the struct,
write down contracts for all the functions you get "for
free", and write two function templates: one for functions that
take in a light, and one for functions that
return a light. (Since these function
templates aren't complete function definitions, they should be
written in a comment in your Definitions window.)
Hint: The show-world function may
require an auxiliary function or two (or three), and will presumably
re-use some of the things you wrote for the previous traffic-light
problem.
Don't start on this until we've gotten to section 6.3 in the textbook! Modify your animation from problem 7 to act sorta like a space ship: the ball moves at a fixed velocity in both x and y dimensions, and pressing an arrow key changes the velocity, not the position. For example, if the ship is currently at position (50, 30) and moving at velocity (3,1), a second later it would be at position (53, 31). If the user then pressed the left-arrow key, it would change the velocity to (2,1), so that a second later the ship would be at position (55,32). Three more quick left-arrow presses, and the velocity becomes (-1, 1), and a second later the position would be (54, 33).
To do this, you'll need to first define a data type
space-ship
to represent both the position and the velocity of a
space ship, since both of these things can change. As usual, you must
give several examples of constructing instances of the struct, write
down contracts for all the functions you get "for free", and
write two function templates: one for functions that take in a
space-ship and one for functions that return a
space-ship. These templates should be in comments.
Hint: You'll need both a
handle-tick function, which changes the position, and a
handle-key function, which changes the velocity.
Be careful of your function contracts!
Hint: It may be helpful to write several auxiliary functions, such as
move-ship which moves the location of a ship by its current
velocity, and accelerate-ship which adjusts the velocity of a
ship by specified amounts in the x and y dimensions.
Extra credit: modify the animation from problem 9 with either or both of the following features:
-
There's a planet at a fixed location in the center of the screen. Every second, not only does the space ship's position change according to its current velocity, but its velocity also changes due to gravity. The formula for gravitational attraction is
change in x velocity = x distance to planet * G / sqr(total distance to planet)
where G is a constant. (I found that a value of 20 worked well: by adjusting the initial position and velocity of the ship, I was able to get it to orbit the planet.)
change in y velocity = y distance to planet * G / sqr(total distance to planet)Doing this will require writing several auxiliary functions.
When the user presses an arrow key, a small red triangle appears momentarily next to the space ship (on the left, right, top, or bottom as appropriate) to indicate rocket exhaust. This will require redefining the
space-shipdata structure to contain not only the location and velocity of the ship, but also the direction of the most recent rocket blast --right,left,up,down, ornone. Theshow-worldfunction will have to take this into consideration in drawing the rocket ship, thehandle-keyfunction will have to modify the direction, and thehandle-tickfunction will have to reset the direction tononeso that the exhaust disappears after a second.