Due date: 1/18 @ 4:30 pm
For this problem set, you will use the design recipe to systematically
create simple functions and programs. The functions consume atomic forms
of data (numbers, symbols, images) and also use conditionals to
distinguish among various situations.
Optional: You may wish to explore the world.ss teachpack, which provides
functions for composing and animating images. We strongly recommend that
you at least make an attempt to solve these optional parts.
2.2.4, 2.3.3, 5.1.5
Additional Problem 1:
Your buddies and you have decided to develop a piece of a game based on
"Star Thaler", a fairy tale by the brothers Grimm. In this fairy tale,
stars begin to drop from the skies and the main character, a poor girl,
collects the falling stars ("thalers", "talers", "dollars") in her skirt.
A star thaler drops at the rate of five pixels per time unit. It starts
at a height of 10; its visual appearance is that of a red disk.
Make up a table that shows how far a star thaler has dropped at times t =
0, 1, 2, 3 and 4. Remember that "down" means the numbers get bigger on a
Formulate a formula for the height of the star thaler, depending on the
time. Test it on the numbers in the table.
Translate the formula into a Scheme function. Call the function
star-height. Translate the table into tests.
Define the function
place-star, which consumes a time
(number of seconds) and produces a 100 x 100 scene with the star at the
appropriate place. The star is always 20 pixels from the left.
Additional Problem 2:
Your manager asked you to develop a piece of a "space wars" game. One of
the elements of the game is a UFO that descends from the top of the
canvas to the bottom. When it reaches the bottom, it stops and just sits
there. [Okay, in a real game, there are ways to shoot and destroy the
UFO but we're not there yet.]
Design the function
ufo-height. It consumes the time (in
number of seconds) and computes the y-coordinate of the UFO. Assume that
the UFO drops at a rate of 4 pixels per second until it is close enough
to the ground; at that point it just lands. For us, "landing" means that
the UFO no longer moves; "close" means that the UFO is within 2 pixels of
the ground line. The height of the canvas is 200 pixels. The UFO is
initially 5 pixels down from the top.
Define the function
place-ufo, which consumes a time
(number of seconds) and produces a 100 x 200 scene with the UFO at the
appropriate place. The UFO is always 30 pixels from the left. Represent a
UFO as yellow flying saucer (flat rectangle plus disk).
Additional Problem 3:
Your teacher wants to play again with his one and only computer program:
Worm. You are to develop one function for this old computer game. The
purpose of the game is to move a (growing) worm around the screen. It can
move in all four directions, reacting to a player's keystrokes (on the
worm-move. The function consumes a keystroke, which is
either a character or a symbol, and the head of a worm, which we
represent as a
Posn. It outputs a new
representing the head's next position. If the keystroke is one of the
four arrow keys (represented as the symbols
'right), the worm
moves in the specified direction by 10 pixels. Otherwise, it remains on
the spot. The worm also remains on the given spot, if a move were to
bring it outside a 100 x 100 box.
Please explain any problems you had completing this assignment in no more than 30 words.