Below is our solution to Problem Set $3.$

;; For problem set $4$ you must improve this program in important ways. Be sure

;; not to change the program's behaviour in any other ways than we are asking.

;; Making extra improvements could cause you problems with the autograder.

;;

;; Modify the program so that instead of there being a single ball there

;; can be any number of balls. The mouse button should add a new ball.

;; Pressing space should clear all the balls.

;;

;; Again your change should be systematic and complete. All relevant

;; design elements and tags must be updated. You must name the new

;; world state type ListOfBall.

;;

;; NOTE, if you work systematically, starting from the HtDW recipe, you

;; will decide that you need a new ListOfBall type; but that the Ball

;; type does not change. Therefore you should NOT change your next$-$ball

;; function. Your render$-$ball function will also be useful when you

;; work on your place$-$ball function, although render$-$ball will have to

;; change some.

;;

$($@problem $1)$

$($@htdw Ball$)$

;; Constants:

$($define WIDTH $605)$

$($define HEIGHT $535)$

$($define BALL$-$RADIUS $10)$

$($define TOP $(+0$ BALL$-$RADIUS$))$;these constants define the "inner box"

$($define BOT $(-$ HEIGHT $1$ BALL$-$RADIUS$))$;that constrains the center of the ball

$($define LEF $(+0$ BALL$-$RADIUS$))$;

$($define RIG $(-$ WIDTH $1$ BALL$-$RADIUS$))$;

$($define BALL $($circle BALL$-$RADIUS "solid" "white"$))$

$($define MTS $($rectangle WIDTH HEIGHT "solid" "green"$))$

;; $===========================================================================$

;; $===========================================================================$

;; Data definitions:

$($@htdd Ball$)$

$($define$-$struct ball $($x y dx dy$))$

;; Ball is $($make$-$ball Number Number Number Number$)$

;; interp. $($make$-$ball x y dx dy$)$ is ball

;; $-$ position x$,$ y in screen coordinates

;; $-$ velocity dx$,$ dy in pixels$/$tick

$($define B$1($make$-$ball $(/$ WIDTH $2)(/$ HEIGHT $2)4-3))$

$($@dd$-$template$-$rules compound$)$

$($define $($fn$-$for$-$ball b$)$

$(...($ball$-$x b$)$

$($ball$-$y b$)$

$($ball$-$dx b$)$

$($ball$-$dy b$)))$

;; $===========================================================================$

;; $===========================================================================$

;; Functions:

$($@htdf main$)$

$($@signature Ball $->$ Ball$)$

;; start the game, call with $($main B$1)$

;;

$($@template$-$origin htdw$-$main$)$

$($define $($main b$)$

$($big$-$bang b

$($on$-$draw render$-$ball$)$ ;Ball $->$ Image

$($on$-$tick next$-$ball$)$ ;Ball $->$ Ball

$($on$-$mouse handle$-$mouse$)))$;Ball Integer Integer MouseEvent $->$ Ball

$($@htdf render$-$ball$)$

$($@signature Ball $->$ Image$)$

;; place BALL on image at appropriate x$,$ y coordinate

$($check$-$expect $($render$-$ball $($make$-$ball $203033))$

$($place$-$image BALL $2030$ MTS$))$

$($check$-$expect $($render$-$ball $($make$-$ball $(-$ WIDTH $4)(-$ HEIGHT $5)-2-3))$

$($place$-$image BALL $(-$ WIDTH $4)(-$ HEIGHT $5)$ MTS$))$

#;

$($define $($render$-$ball b$)$ MTS$)$

$($@template$-$origin Ball$)$

$($@template

$($define $($render$-$ball b$)$

$(...($ball$-$x b$)$

$($ball$-$y b$)$

$($ball$-$dx b$)$

$($ball$-$dy b$))))$

$($define $($render$-$ball b$)$

$($place$-$image BALL $($ball$-$x b$)($ball$-$y b$)$ MTS$))$

$($@htdf next$-$ball$)$

$($@signature Ball $->$ Ball$)$

;; produce ball at next x$,$y; checks bounces off top$/$right$/$bottom$/$left wall

$($check$-$expect $($next$-$ball $($make$-$ball $(+$ LEF $1)$ TOP $3-4))$

$($bounce$-$top $($make$-$ball $(+$ LEF $1)$ TOP $3-4)))$

$($check$-$expect $($next$-$ball $($make$-$ball $(+$ LEF $1)$ BOT $34))$

$($bounce$-$bottom $($make$-$ball $(+$ LEF $1)$ BOT $34)))$

$($check$-$expect $($next$-$ball $($make$-$ball LEF $(+$ TOP $1)-34))$

$($bounce$-$left $($make$-$ball LEF $(+$ TOP $1)-34)))$

$($check$-$expect $($next$-$ball $($make$-$ball RIG $(+$ TOP $1)34))$

$($bounce$-$right $($make$-$ball RIG $(+$ TOP $1)34)))$

$($check$-$expect $($next$-$ball $($make$-$ball $(/$ WIDTH $2)(/$ HEIGHT $2)34))$

$($glide $($make$-$ball $(/$ WIDTH $2)(/$ HEIGHT $2)34)))$

#;

$($define $($next$-$ball b$)$ b$)$

$($@template$-$origin Number$)$ ; because b is treated as atomic

$($@template

$($define $($next$-$ball b$)$

$(...$ b$)))$

$($define $($next$-$ball b$)$

$($cond $[($touch$-$top? b$)($bounce$-$top b$)]$

$[($touch$-$bottom? b$)($bounce$-$bottom b$)]$

$[($touch$-$right? b$)($bounce$-$right b$)]$

$[($touch$-$left? b$)($bounce$-$left b$)]$

$[$else

$($glide b$)]))$

$($@htdf handle$-$mouse$)$

$($@signature Ball Integer Integer MouseEvent $->$ Ball$)$

;; replace ball with new ball on mouse click

;; NOTE: uses random, so testing has to use check$-$random

$($check$-$random $($handle$-$mouse $($make$-$ball $1234)100200$ "button$-$down"$)$

$($make$-$ball $100200(-5($random $11))(-5($random $11))))$

$($check$-$random $($handle$-$mouse $($make$-$ball $1234)100200$ "button$-$up$")$

$($make$-$ball $1234))$

#;

$($define $($handle$-$mouse b x y me$)$ b$)$

$($@template$-$origin MouseEvent$)$

$($@template

$($define $($handle$-$mouse b x y me$)$

$($cond $[($mouse$=?$ me "button$-$down"$)(...$ b x y$)]$

$[$else

$(...$ b x y$)])))$

$($define $($handle$-$mouse b x y me$)$

$($cond $[($mouse$=?$ me "button$-$down"$)$