1. Section 6.1: Structures (continued)

2. Example 1: in-left-side? ; Purpose: To determine whether a point is in the leftmost 150 pixels of the screen. ; Contract : posn -> boolean "Examples of in-left-side?:" (in-left-side? (make-posn 5 7)) "should be" true (in-left-side? (make-posn 200 7)) "should be" false (in-left-side? (make-posn 150 7)) "should be" false

3. Example 1: in-left-side? ; Purpose: To determine whether a point is in the leftmost 150 pixels of the screen. ; Contract : posn -> boolean (define (in-left-side? where) … where … ) "Examples of in-left-side?:" (in-left-side? (make-posn 5 7)) "should be" true (in-left-side? (make-posn 200 7)) "should be" false (in-left-side? (make-posn 150 7)) "should be" false

4. Example 1: in-left-side? ; Purpose: To determine whether a point is in the leftmost 150 pixels of the screen. ; Contract : posn -> boolean (define (in-left-side? where) … where … ; a posn … (posn-x where) … ; a number … (posn-y where) … ; a number ) "Examples of in-left-side?:" (in-left-side? (make-posn 5 7)) "should be" true (in-left-side? (make-posn 200 7)) "should be" false (in-left-side? (make-posn 150 7)) "should be" false

5. Example 1: in-left-side? ; Purpose: To determine whether a point is in the leftmost 150 pixels of the screen. ; Contract : posn -> boolean (define (in-left-side? where) (< (posn-x where) 150) ; a boolean ) "Examples of in-left-side?:" (in-left-side? (make-posn 5 7)) "should be" true (in-left-side? (make-posn 200 7)) "should be" false (in-left-side? (make-posn 150 7)) "should be" false

6. Example 2: above-diagonal? Takes a point and determines whether it is above the diagonal. The green points return true. The red points return false.

7. Example 2: above-diagonal? ; Purpose: To determine if a point is above the diagonal. ; Contract: posn -> boolean "Examples of above-diagonal?:" (above-diagonal? (make-posn 5 7)) "should be" false (above-diagonal? (make-posn 200 7)) "should be" true (above-diagonal? (make-posn 7 7)) "should be" false

8. Example 2: above-diagonal? ; Purpose: To determine if a point is above the diagonal. ; Contract: posn -> boolean (define (above-diagonal? where) ; … where … a posn ) "Examples of above-diagonal?:" (above-diagonal? (make-posn 5 7)) "should be" false (above-diagonal? (make-posn 200 7)) "should be" true (above-diagonal? (make-posn 7 7)) "should be" false

9. Example 2: above-diagonal? ; Purpose: To determine if a point is above the diagonal. ; Contract: posn -> boolean (define (above-diagonal? where) ; … where … a posn ; … (posn-x where) … a number ; … (posn-y where) … a number ) "Examples of above-diagonal?:" (above-diagonal? (make-posn 5 7)) "should be" false (above-diagonal? (make-posn 200 7)) "should be" true (above-diagonal? (make-posn 7 7)) "should be" false

10. Example 2: above-diagonal? ; Purpose: To determine if a point is above the diagonal. ; Contract: posn -> boolean (define (above-diagonal? where) (> (posn-x where) (posn-y where)) ) "Examples of above-diagonal?:" (above-diagonal? (make-posn 5 7)) "should be" false (above-diagonal? (make-posn 200 7)) "should be" true (above-diagonal? (make-posn 7 7)) "should be" false

11. Example 3: distance-to-0 Takes a point and finds its distance from the origin. Hint: the formula is (sqrt((x 1 -x 2 ) 2 + (y 1 -y 2 ) 2 ))

12. Example 3: distance-to-0 ; Purpose: To determine how far a point is from the origin. ; Contract: posn -> number "Examples of distance-to-0” (distance-to-0 (make-posn 3 4)) "should be" 5 (distance-to-0 (make-posn 0 7)) "should be" 7 (distance-to-0 (make-posn 10 10)) "should be" 141.4…

13. Example 3: distance-to-0 ; Purpose: To determine how far a point is from the origin. ; Contract: posn -> number ; Skeleton: ; (define (distance-to-0 a-posn) ; …a-posn…) "Examples of distance-to-0” (distance-to-0 (make-posn 3 4)) "should be" 5 (distance-to-0 (make-posn 0 7)) "should be" 7 (distance-to-0 (make-posn 10 10)) "should be" 141.4…

14. Example 3: distance-to-0 ; Purpose: To determine how far a point is from the origin. ; Contract: posn -> number ; Template: ; (define (distance-to-0 a-posn) ; …a-posn… ; a posn ; … (posn-x a-posn)… ; a number ; … (posn-y a-posn)…) ; a number "Examples of distance-to-0” (distance-to-0 (make-posn 3 4)) "should be" 5 (distance-to-0 (make-posn 0 7)) "should be" 7 (distance-to-0 (make-posn 10 10)) "should be" 141.4…

15. Example 3: distance-to-0 ; Purpose: To determine how far a point is from the origin. ; Contract: posn -> number (define (distance-to-0 a-posn) (sqrt (+ (sqr (posn-x a-posn)) (sqr (posn-y a-posn)) ))) "Examples of distance-to-0” (distance-to-0 (make-posn 3 4)) "should be" 5 (distance-to-0 (make-posn 0 7)) "should be" 7 (distance-to-0 (make-posn 10 10)) "should be" 141.4…

16. Example 4: distance Takes two points and finds the distance between them. Hint: the formula is (sqrt((x 1 -x 2 ) 2 + (y 1 -y 2 ) 2 ))

17. Example 4: distance ; Purpose: To find the distance between two points. ; Contract: distance : posn posn -> number ; (define (distance here there) ; … here … a posn ; … there … a posn ;) "Examples of distance:" (distance (make-posn 4 5) (make-posn 4 5)) "should be 0" (distance (make-posn 4 5) (make-posn 1 5)) "should be 3" (distance (make-posn 4 5) (make-posn 4 17)) "should be 12" (distance (make-posn 4 5) (make-posn 7 9)) "should be 5"

18. Example 4: distance ; Purpose: To find the distance between two points. ; Contract: distance : posn posn -> number (define (distance here there) ; … here … a posn ; … there … a posn ; … (posn-x here) … a number ; … (posn-x there) … a number ; … (posn-y here) … a number ; … (posn-y there) … a number ) "Examples of distance:" (distance (make-posn 4 5) (make-posn 4 5)) "should be 0" (distance (make-posn 4 5) (make-posn 1 5)) "should be 3" (distance (make-posn 4 5) (make-posn 4 17)) "should be 12" (distance (make-posn 4 5) (make-posn 7 9)) "should be 5"

19. Example 4: distance ; Purpose: To find the distance between two points. ; Contract: distance : posn posn -> number (define (distance here there) (sqrt (+ (sqr (- (posn-x here) (posn-x there))) (sqr (- (posn-y here) (posn-y there))))) ) "Examples of distance:" (distance (make-posn 4 5) (make-posn 4 5)) "should be 0" (distance (make-posn 4 5) (make-posn 1 5)) "should be 3" (distance (make-posn 4 5) (make-posn 4 17)) "should be 12" (distance (make-posn 4 5) (make-posn 7 9)) "should be 5"

20. Example 5: Function re-use Define a function that takes in two points and returns their distance plus 2.

21. Example 5: Function re-use Define a function that takes in two points and returns their distance plus 2. Solution: (define (add2-to-distance here there) (+ 2 (distance here there) )

22. Example 6: Function re-use Define a function that takes in two points and returns their distance plus a variable “n”.

23. Example 6: Function re-use Define a function that takes in two points and returns their distance plus 2. Solution: (define (addn-to-distance here there n) (+ n (distance here there) )

24. In summary… You have seen how to work with a structure that is defined. It is possible to define your own structures, but we will skip this due to time constraints. Next time… Summary of Computer Programming and Scheme