- The screensaver is a universe program that displays a Perpetual Goofball moving around an arena.
- The Perpetual Goofball and arena behave as specified in problem 3 of Problem Set 02, with one major exception: For this screensaver, the velocity components of the Perpetual Goofball will be interpreted as cm per tick instead of cm per second.
- The arena is displayed on a canvas 400 pixels wide and 400 pixels high, with each pixel representing 1cm. The center of the arena has coordinates (0, 0). (Note that this coordinate system has a different origin from the one used by DrRacket, so you'll have to translate coordinates.)
- The Perpetual Goofball is displayed as an outline circle drawn to that 1 cm/pixel scale. If the Perpetual Goofball has its normal 20cm radius, then that circle is displayed as a blue outline. If the Perpetual Goofball's radius is less than 20cm, then that circle is displayed as a red outline.
- If the Perpetual Goofball is displayed as a blue outline circle, then its current velocity is displayed as a string of the form (vx, vy), centered within the circle, in blue, large enough to be legible but small enough to fit within the circle.
- The space bar pauses or unpauses the screensaver. The screensaver is initially paused.
- The Perpetual Goofball is initially centered at position (168,133), with a southeastern velocity of (+1, +1). (Remember that we are using computer-graphics coordinates, in which y increases as you go down the page (south).)
Here's a crude demo showing the screensaver's behavior at the southeastern corner:
You are to deliver a file named screensaver-1.rkt that provides all twelve of the following functions:
;;; screensaver : PosReal -> WorldState ;;; GIVEN: the speed of the screensaver, in seconds per tick ;;; (so larger numbers run slower) ;;; EFFECT: runs the screensaver, starting with the initial state as ;;; specified in the problem set ;;; RETURNS: the final state of the world ;;; EXAMPLES: ;;; (screensaver 1) runs the screensaver at normal speed ;;; (screensaver 1/4) runs at a faster than normal speed ;;; initial-world : Any -> WorldState ;;; GIVEN: any value (ignored) ;;; RETURNS: the initial world specified for the screensaver ;;; EXAMPLE: (initial-world -174) ;;; world-after-tick : WorldState -> WorldState ;;; GIVEN: any WorldState that's possible for the screensaver ;;; RETURNS: the WorldState that should follow the given WorldState ;;; after a tick ;;; world-after-key-event : WorldState KeyEvent -> WorldState ;;; GIVEN: a WorldState and a KeyEvent ;;; RETURNS: the WorldState that should follow the given WorldState ;;; after the given KeyEvent ;;; world-goofball1 : WorldState -> Goofball ;;; GIVEN: a WorldState ;;; RETURNS: the Goofball (as specified in Problem Set 02) ;;; that's present in the WorldState ;;; world-paused? : WorldState -> Boolean ;;; GIVEN: a WorldState ;;; RETURNS: true iff the WorldState is paused ;;; goofball-at : Integer Integer Integer Integer -> Goofball ;;; goofball-radius : Goofball -> Integer ;;; goofball-x : Goofball -> Integer ;;; goofball-y : Goofball -> Integer ;;; goofball-vx : Goofball -> Integer ;;; goofball-vy : Goofball -> Integer ;;; ;;; The six functions named above behave as specified in problem 3 ;;; of Problem Set 02, except the vx and vy components of velocity ;;; are interpreted as cm per tick instead of cm per second.
- The arena contains two Perpetual Goofballs instead of just one. (Having two real goofballs within a single arena would scare the physicists, but they say it should be okay so long as we're just running a screensaver on a computer.) The two goofballs do not interact with each other in any way (mainly because the physicists haven't yet figured out how they would interact in real life).
- The initial position and velocity of the first Goofball are as described in problem 1. The second Goofball is initially centered at position (140, 110) with a western velocity of (-1,0).
- Pressing the "1" key rotates the first Goofball's velocity clockwise by 45 degrees. Pressing the "2" key rotates the second Goofball's velocity counter-clockwise by 45 degrees. (Examples: The second Goofball's initial (-1,0) velocity would become (-1,1) when the "2" key is pressed, and would become (0,1) if the "2" were pressed a second time.) The "1" and "2" keys continue to operate even when the screensaver is paused.
- Both goofballs are selectable and draggable. Depressing the mouse button within a goofball's circle causes the goofball to be "selected". When a goofball is selected, its outline is displayed in green instead of blue or red, and its velocity is not displayed.
- The location where the mouse grabbed the goofball should be indicated by a solid orange circle of radius 4 pixels. Simply pressing the mouse button, without moving the mouse, should not cause the goofball to move on the canvas.
- Once a goofball has been selected, you should be able to drag it around the Universe canvas with the mouse. As you drag it, the position of the mouse within the goofball (as indicated by the solid orange circle), should not change relative to the goofball's center, although the circle representing the goofball may change in radius as required by its interaction with the arena walls. When the mouse button is released, the goofball should go back to its unselected state (outline blue or red, depending on its radius) in its new location.
- Selecting and dragging work regardless of whether the screensaver is paused.
- We refer to the behavior described above as "smooth dragging." We will be implementing other objects with this behavior in future problem sets.
Here's a demonstration of smooth dragging in which the decreasing radius of both dragged goofballs eventually causes the dragging mouse to lie outside a goofball's circle, which allows the goofball to escape the dragging mouse and assume its undragged (red) appearance and behavior:
You are to deliver a file named screensaver-2.rkt that
provides all the functions provided for problem 1 above, modified
to behave as specified in this problem 2.
(That means you'll probably have to change your definitions of
initial-world, world-after-tick,
and world-after-key-event.)
The goofball-at function should behave as before,
but return an unselected Goofball.
You must also define and provide the following new functions:
;;; world-goofball2 : WorldState -> Goofball ;;; GIVEN: a WorldState ;;; RETURNS: the second Goofball that's present in the WorldState ;;; world-after-mouse-event ;;; : WorldState Int Int MouseEvent -> WorldState ;;; ;;; GIVEN: A World, the x- and y-coordinates of a mouse event, and the ;;; mouse event ;;; RETURNS: the world that should follow the given world after the given ;;; mouse event. ;;; goofball-selected? : Goofball -> Boolean ;;; RETURNS: true iff the given Goofball is selected.