The following question uses a program called DrRacket The te

The following question uses a program called Dr.Racket. The textbook is called \"how to design programs\" http://www.htdp.org/

Question 1:

Exercise 27.1.1.   Develop the functions

;; draw-triangle : posn posn posn  -> true

;; too-small? : posn posn posn  ->  bool

to complete the definitions in figure 72.

Use the teachpack draw.ss to test the code. For a first test of the complete function, use the following definitions:

Create a canvas with (start 400 400). Experiment with other end points and canvas dimensions.

Solution

#lang racket (require lang/htdp-intermediate-lambda) (require htdp/draw) ;; sierpinski : posn posn posn -> true ;; to draw a Sierpinski triangle down at a, b, and c, ;; assuming it is large enough (define (sierpinski a b c) (cond [(too-small? a b c) true] [else (local ((define a-b (mid-point a b)) (define b-c (mid-point b c)) (define c-a (mid-point a c))) (and (draw-triangle a b c) (sierpinski a a-b c-a) (sierpinski b a-b b-c) (sierpinski c c-a b-c)))])) ;; mid-point : posn posn -> posn ;; to compute the mid-point between a-posn and b-posn (define (mid-point a-posn b-posn) (make-posn (mid (posn-x a-posn) (posn-x b-posn)) (mid (posn-y a-posn) (posn-y b-posn)))) ;; mid : number number -> number ;; to compute the average of x and y (define (mid x y) (/ (+ x y) 2)) ;; draw-triangle : posn posn posn -> true (define (draw-triangle a b c) (and (draw-solid-line a b \'red) (draw-solid-line b c \'red) (draw-solid-line c a \'red))) ;; too-small? : posn posn posn -> bool (define (too-small? a b c) (local ((define THRESHOLD 5) (define (distance p1 p2) (sqrt (+ (sqr (- (posn-x p1) (posn-x p2))) (sqr (- (posn-y p1) (posn-y p2))))))) (or (< (distance a b) THRESHOLD) (< (distance b c) THRESHOLD) (< (distance c a) THRESHOLD)))) (define A (make-posn 200 50)) (define B (make-posn 27 350)) (define C (make-posn 373 350)) (define DELAY 2) ;; 2 secs (start 400 400) (sierpinski A B C) (sleep-for-a-while DELAY) (stop)