Welcome to mpost-wrapper.

Version: 5.1.1

Welcome to mpost-wrapper.

Many examples are listed as below. In order to run these examples, we need first require the snip module to show figures.

Example:

> (require (planet wcy/mpost-wrapper/snip))

1 ex-1

1.1 source code in ex-1.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (draw
   (call-with-values A-B-C
     op--)))

1.2 the result of ex-1

Examples:
> (require "examples/ex-1.rkt")
> (make-figure "ex-1" main)

2 ex-2

2.1 source code in ex-2.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (draw
   (call-with-values A-B-C
     (lambda (A B C)
       (op-- A B C 'cycle)))))

2.2 the result of ex-2

Examples:
> (require "examples/ex-2.rkt")
> (make-figure "ex-2" main)

3 ex-3

3.1 source code in ex-3.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (op-- A B C D 'cycle))
      (draw (op-- A C))
      (draw (op-- B D)))))

3.2 the result of ex-3

Examples:
> (require "examples/ex-3.rkt")
> (make-figure "ex-3" main)

4 ex-4

4.1 source code in ex-4.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
(draw (point 0 0)
#:withpen (scale '4bp 'pencircle)))

4.2 the result of ex-4

Examples:
> (require "examples/ex-4.rkt")
> (make-figure "ex-4" main)

5 ex-5

5.1 source code in ex-5.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (draw (op-- A B C 'cycle))
      (for ((p (in-list (list A B C))))
           (draw p #:withpen (scale '4bp 'pencircle)))
      )))

5.2 the result of ex-5

Examples:
> (require "examples/ex-5.rkt")
> (make-figure "ex-5" main)

6 ex-6

6.1 source code in ex-6.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (op-- A B C D 'cycle))
      (draw (op-- A C))
      (draw (op-- B D))
      (for ((p (in-list (list A B C D))))
           (draw p #:withpen (scale '4bp 'pencircle))))))

6.2 the result of ex-6

Examples:
> (require "examples/ex-6.rkt")
> (make-figure "ex-6" main)

7 ex-7

7.1 source code in ex-7.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (draw (op-- A B  C 'cycle))
      (draw (op-- (mediation '.5 B C) A))
      (draw (op-- (mediation '.5 A C) B))
      (draw (op-- (mediation '.5 B A) C))
      )))

7.2 the result of ex-7

Examples:
> (require "examples/ex-7.rkt")
> (make-figure "ex-7" main)

8 ex-8

8.1 source code in ex-8.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (draw (op-- A  B  C 'cycle))
      (draw (op-- (mediation 0.5 B C) A))
      (draw (op-- (mediation 0.5 A C) B))
      (draw (op-- (mediation 0.5 B A) C))
      (draw (op* 1/3  (op+ A B C))
            #:withpen (scale '4bp 'pencircle))
      )))

8.2 the result of ex-8

Examples:
> (require "examples/ex-8.rkt")
> (make-figure "ex-8" main)

9 ex-9

9.1 source code in ex-9.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (draw (op-- A B C 'cycle))
      (draw (op-- A B) #:withpen (scale '4bp 'pencircle))
      )))

9.2 the result of ex-9

Examples:
> (require "examples/ex-9.rkt")
> (make-figure "ex-9" main)

10 ex-10

10.1 source code in ex-10.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (draw (op-- A B C 'cycle))
      (draw (op-- A B)
            #:withcolor (op+ 'green 'red))
      )))

10.2 the result of ex-10

Examples:
> (require "examples/ex-10.rkt")
> (make-figure "ex-10" main)

11 ex-11

11.1 source code in ex-11.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (draw (op-- A B))
      (draw (op-- B C) #:dashed 'evenly)
      (draw (op-- C A) #:dashed 'withdots)
      )))

11.2 the result of ex-11

Examples:
> (require "examples/ex-11.rkt")
> (make-figure "ex-11" main)

12 ex-12

12.1 source code in ex-12.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (for ((p (in-list (list (op-- A B)
                              (op-- B C)
                              (op-- C A)
                              )))
            (color (in-list (list 0.8 0.6 0.4))))
           (draw p
                 #:withpen (scale '2bp 'pencircle)
                 #:withcolor (op* color 'white)))
      )))

12.2 the result of ex-12

Examples:
> (require "examples/ex-12.rkt")
> (make-figure "ex-12" main)

13 ex-13

13.1 source code in ex-13.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (op-- A  B  C 'cycle))
      (draw (op-- (mediation '.5 B C) A) #:dashed 'evenly)
      (draw (op-- (mediation '.5 A C) B) #:dashed 'evenly)
      (draw (op-- (mediation '.5 B A) C) #:dashed 'evenly)
      (draw (op* 1/3
                 (op+ A B C)) #:withpen (scale '4bp 'pencircle)
                 #:withcolor 'red)
      )))

13.2 the result of ex-13

Examples:
> (require "examples/ex-13.rkt")
> (make-figure "ex-13" main)

14 ex-14

14.1 source code in ex-14.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
(draw (op-- (point 0 0)
(point '3cm 0)) #:dashed (scale 2 'evenly)))

14.2 the result of ex-14

Examples:
> (require "examples/ex-14.rkt")
> (make-figure "ex-14" main)

15 ex-15

15.1 source code in ex-15.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (draw (op-- (point 0 0)
              (point '3cm 0))
        #:dashed (dashpattern "on 2bp off 3bp")))

15.2 the result of ex-15

Examples:
> (require "examples/ex-15.rkt")
> (make-figure "ex-15" main)

16 ex-16

16.1 source code in ex-16.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (draw (op-- (point 0 0)
              (point '3cm 0))
        #:dashed (dashpattern "on 1bp off 2bp on 10bp off 2bp")))

16.2 the result of ex-16

Examples:
> (require "examples/ex-16.rkt")
> (make-figure "ex-16" main)

17 ex-17

17.1 source code in ex-17.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (drawarrow (op-- C B A))
      (drawarrow (op-- A C) #:withpen (scale '2bp 'pencircle)))))

17.2 the result of ex-17

Examples:
> (require "examples/ex-17.rkt")
> (make-figure "ex-17" main)

18 ex-18

18.1 source code in ex-18.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (drawdblarrow (op-- C B A 'cycle))
      (drawdblarrow (op-- A C) #:withpen (scale '2bp 'pencircle)))))

18.2 the result of ex-18

Examples:
> (require "examples/ex-18.rkt")
> (make-figure "ex-18" main)

19 ex-19

19.1 source code in ex-19.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (draw (op--
         (point '-1.5cm 0)
         (point '1.5cm 0))))

19.2 the result of ex-19

Examples:
> (require "examples/ex-19.rkt")
> (make-figure "ex-19" main)

20 ex-20

20.1 source code in ex-20.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (fill (op-- A B C 'cycle) #:withcolor (op* 0.8 'white)))))

20.2 the result of ex-20

Examples:
> (require "examples/ex-20.rkt")
> (make-figure "ex-20" main)

21 ex-21

21.1 source code in ex-21.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (fill (op-- A B C 'cycle) #:withcolor (op* 0.8 'white))
      (draw (op-- A B C 'cycle)))))

21.2 the result of ex-21

Examples:
> (require "examples/ex-21.rkt")
> (make-figure "ex-21" main)

22 ex-22

22.1 source code in ex-22.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (fill (op-- A B C 'cycle) #:withcolor (op* 0.8 'white))
      (draw (op-- A B C 'cycle) #:withpen (scale '2bp 'pencircle)))))

22.2 the result of ex-22

Examples:
> (require "examples/ex-22.rkt")
> (make-figure "ex-22" main)

23 ex-23

23.1 source code in ex-23.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (draw (op-- A B C 'cycle) #:withpen (scale '2bp 'pencircle))
      (fill (op-- A B C 'cycle) #:withcolor (op* 0.8 'white)))))

23.2 the result of ex-23

Examples:
> (require "examples/ex-23.rkt")
> (make-figure "ex-23" main)

24 ex-24

24.1 source code in ex-24.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (fill (op--  A C B D 'cycle) #:withcolor (op* 0.8 'white)))))

24.2 the result of ex-24

Examples:
> (require "examples/ex-24.rkt")
> (make-figure "ex-24" main)

25 ex-25

25.1 source code in ex-25.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (let ((p (op--  A C B D 'cycle)))
        (fill p #:withcolor (op* 0.8 'white))
        (draw p)))))

25.2 the result of ex-25

Examples:
> (require "examples/ex-25.rkt")
> (make-figure "ex-25" main)

26 ex-26

26.1 source code in ex-26.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((A (point '-1.5cm '-1.5cm))
        (B (point '1.5cm '-1.5cm))
        (C (point '1.5cm '1.5cm))
        (D (point '-1.5cm '1.5cm)))
    (fill (op-- A C B D  'cycle) #:withcolor (op* 0.8 'white))
    (draw (op-- (point '-1.5cm 0) (point '1.5cm '0)))
    (draw (op-- (point 0 '-1.5cm) (point 0 '1.5cm)))
    (drawarrow (op-- (point 0 0) (point '1cm 0))
               #:withpen (scale '2bp 'pencircle))
    (drawarrow (op-- (point 0 0) (point 0 '1cm))
               #:withpen (scale '2bp 'pencircle))))

26.2 the result of ex-26

Examples:
> (require "examples/ex-26.rkt")
> (make-figure "ex-26" main)

27 ex-27

27.1 source code in ex-27.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(require (planet wcy/mpost-wrapper/label))
(provide main)

(define (main)
  (let ((A (point 0 0)))
    (draw A #:withpen (scale '4bp 'pencircle))
    (label-top (btex "Au dessus") A)
    (label-bot  (btex "En dessous") A)
    (label-rt (btex "^^c0 droite") A)
    (label-lft  (btex "^^c0 gauche") A)))

27.2 the result of ex-27

Examples:
> (require "examples/ex-27.rkt")
> (make-figure "ex-27" main)

28 ex-28

28.1 source code in ex-28.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(require (planet wcy/mpost-wrapper/label))
(provide main)

(define (main)
  (let ((A (point 0 0)))
    (draw A #:withpen (scale '4bp 'pencircle))
    (label-ulft (btex "En haut ^^e0 gauche") A)
    (label-urt  (btex "En haut ^^e0 droite") A)
    (label-llft (btex "En bas ^^e0 gauche") A)
    (label-lrt  (btex "En bas ^^e0 droite") A)))

28.2 the result of ex-28

Examples:
> (require "examples/ex-28.rkt")
> (make-figure "ex-28" main)

29 ex-29

29.1 source code in ex-29.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(require (planet wcy/mpost-wrapper/label))
(provide main)

(define (main)
(dot-label-urt (btex "$A$") (point 0 0)))

29.2 the result of ex-29

Examples:
> (require "examples/ex-29.rkt")
> (make-figure "ex-29" main)

30 ex-30

30.1 source code in ex-30.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(require (planet wcy/mpost-wrapper/label))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (draw (op-- A B C 'cycle))
      (dot-label-llft (btex "$A$") A)
      (dot-label-lrt (btex "$B$") B)
      (dot-label-top (btex "$C$") C))))

30.2 the result of ex-30

Examples:
> (require "examples/ex-30.rkt")
> (make-figure "ex-30" main)

31 ex-31

31.1 source code in ex-31.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(require (planet wcy/mpost-wrapper/label))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (draw (op-- A B C 'cycle))
      (label-bot (btex "$1$") (mediation  0.5 A B))
      (label-lft (btex "$1$") (mediation  1/2 A C))
      (label-urt (btex "$\\sqrt 2$") (mediation 1/2 B C)))))

31.2 the result of ex-31

Examples:
> (require "examples/ex-31.rkt")
> (make-figure "ex-31" main)

32 ex-32

32.1 source code in ex-32.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(require (planet wcy/mpost-wrapper/label))
(provide main)

(define (ex-32-points y xs)
  (map(lambda (x) (point x y)) xs))
(define (main)
  (let* ((u '1cm)
         (xs (list  (op* -1 u) 0 u))
         (u-points (ex-32-points u xs))
         (l-points (ex-32-points 0 xs)))
    (for* ((a (in-list l-points))
           (b (in-list u-points)))
          (draw  (op--  a b)))
    (for ((ut (in-list (list "$a$" "$b$" "$c$")))
          (a  (in-list u-points))
          (lt (in-list (list "$a'$" "$b'$" "$c'$")))
          (b  (in-list l-points)))
         (dot-label-top (btex ut) a)
         (dot-label-bot (btex lt) b))))

32.2 the result of ex-32

Examples:
> (require "examples/ex-32.rkt")
> (make-figure "ex-32" main)

33 ex-33

33.1 source code in ex-33.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
(draw (fullcircle)))

33.2 the result of ex-33

Examples:
> (require "examples/ex-33.rkt")
> (make-figure "ex-33" main)

34 ex-34

34.1 source code in ex-34.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
(draw (point 0 0 ) #:withpen (scale '4bp 'pencircle)))

34.2 the result of ex-34

Examples:
> (require "examples/ex-34.rkt")
> (make-figure "ex-34" main)

35 ex-35

35.1 source code in ex-35.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
(draw (point 0 0 ) #:withpen (scale '4bp 'pencircle)))

35.2 the result of ex-35

Examples:
> (require "examples/ex-35.rkt")
> (make-figure "ex-35" main)

36 ex-36

36.1 source code in ex-36.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C)
  (values (point 0 0)
          (point '1cm 0)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C
    (lambda (A B C)
      (draw (op-- A B C 'cycle))
      (for ((a-point (in-list (list A B C))))
           (fill (fullcircle  '4bp a-point) #:withcolor 'white))
      (for ((a-point (in-list (list A B C))))
           (draw  (fullcircle  '4bp a-point))))))

36.2 the result of ex-36

Examples:
> (require "examples/ex-36.rkt")
> (make-figure "ex-36" main)

37 ex-37

37.1 source code in ex-37.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (op.. A D B C))
      (for ((A (in-list (list A B C D))))
           (draw A #:withpen (scale '4bp 'pencircle))))))

37.2 the result of ex-37

Examples:
> (require "examples/ex-37.rkt")
> (make-figure "ex-37" main)

38 ex-38

38.1 source code in ex-38.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (path A '-- D '..  B '.. C))
      )))

38.2 the result of ex-38

Examples:
> (require "examples/ex-38.rkt")
> (make-figure "ex-38" main)

39 ex-39

39.1 source code in ex-39.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (path A '--- D '..  B '.. C))
      )))

39.2 the result of ex-39

Examples:
> (require "examples/ex-39.rkt")
> (make-figure "ex-39" main)

40 ex-40

40.1 source code in ex-40.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (path A '..  D '.. B '.. C))
      )))

40.2 the result of ex-40

Examples:
> (require "examples/ex-40.rkt")
> (make-figure "ex-40" main)

41 ex-41

41.1 source code in ex-41.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (op.. A B C D 'cycle)
            ))))

41.2 the result of ex-41

Examples:
> (require "examples/ex-41.rkt")
> (make-figure "ex-41" main)

42 ex-42

42.1 source code in ex-42.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (op.. A  C  'cycle)
            ))))

42.2 the result of ex-42

Examples:
> (require "examples/ex-42.rkt")
> (make-figure "ex-42" main)

43 ex-43

43.1 source code in ex-43.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
(draw (path (point 0 0) (dir-spec (point 0 1)) ".."
(point '2cm 0) (dir-spec (point 1 0)))))

43.2 the result of ex-43

Examples:
> (require "examples/ex-43.rkt")
> (make-figure "ex-43" main)

44 ex-44

44.1 source code in ex-44.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
(draw (path (point 0 0) (dir-spec (dir 90)) ".."
(point '2cm 0) (dir-spec (dir 0)))))

44.2 the result of ex-44

Examples:
> (require "examples/ex-44.rkt")
> (make-figure "ex-44" main)

45 ex-45

45.1 source code in ex-45.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
(draw (path (point 0 0) (dir-spec 'up) ".."
(point '2cm 0) (dir-spec 'right))))

45.2 the result of ex-45

Examples:
> (require "examples/ex-45.rkt")
> (make-figure "ex-45" main)

46 ex-46

46.1 source code in ex-46.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
(draw (path (point 0 0) (dir-spec 'up) ".."
(point '2cm 0) (dir-spec 'up))))

46.2 the result of ex-46

Examples:
> (require "examples/ex-46.rkt")
> (make-figure "ex-46" main)

47 ex-47

47.1 source code in ex-47.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (draw (path (point 0    0) (dir-spec 'up)  ".."
              (point '2cm 0) (dir-spec 'up)  ".."
              'cycle)))

47.2 the result of ex-47

Examples:
> (require "examples/ex-47.rkt")
> (make-figure "ex-47" main)

48 ex-48

48.1 source code in ex-48.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (arc O A B rou)
  (let ((alpha (op-angle (op- A O)))
        (beta  (op-angle (op- B O))))
    (path (op+ O (polar rou alpha)) (dir-spec (dir (op+ alpha 90))) ".."
          (op+ O (polar rou beta )) (dir-spec (dir (op+ beta  90))))))
(define (main)
  (let* ((O (point 0 0))
         (alpha 30)
         (A (polar '2cm 0))
         (B (polar '2cm alpha)))
    (draw (path O ".." A))
    (draw (path O ".." B))
    (draw (arc O A B '1cm))))

48.2 the result of ex-48

Examples:
> (require "examples/ex-48.rkt")
> (make-figure "ex-48" main)

49 ex-49

49.1 source code in ex-49.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (arc O A B rou)
  (let ((alpha (op-angle (op- A O)))
        (beta  (op-angle (op- B O))))
    (path (op+ O (polar rou alpha)) (dir-spec (dir (op+ alpha 90))) ".."
          (op+ O (polar rou beta )) (dir-spec (dir (op+ beta  90))))))
(define (main)
  (let* ((O (point 0 0))
         (alpha 30)
         (A (polar '2cm 0))
         (B (polar '2cm alpha)))
    (draw (path O ".." A))
    (draw (path O ".." B))
    (draw (arc O A B '1cm))
    (draw (arc O A B '1.1cm))))

49.2 the result of ex-49

Examples:
> (require "examples/ex-49.rkt")
> (make-figure "ex-49" main)

50 ex-50

50.1 source code in ex-50.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (arc O A B rou)
  (let ((alpha (op-angle (op- A O)))
        (beta  (op-angle (op- B O))))
    (path (op+ O (polar rou alpha)) (dir-spec (dir (op+ alpha 90))) ".."
          (op+ O (polar rou beta )) (dir-spec (dir (op+ beta  90))))))
(define (draw-angle A B C n)
  (let ((rou '4.5mm))
    (if (> n 0)
        (begin
          (draw (arc A B C (op+ rou (op* n '0.5mm))))
          (draw-angle  A B C (- n 1)))
        (void))))
(define (main)
  (let ((A (point 0 0))
        (B (point '3cm 0))
        (C (point '1cm '2cm)))
    (draw (op-- A B C 'cycle))
    (draw-angle A B C 1)
    (draw-angle B C A 2)
    (draw-angle C A B 3)))

50.2 the result of ex-50

Examples:
> (require "examples/ex-50.rkt")
> (make-figure "ex-50" main)

51 ex-51

51.1 source code in ex-51.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (p (path (point u 0) (dir-spec 'up)  ".."
                  (point (op* -1 u) 0) (dir-spec 'down) "--"
                  'cycle)))
    (fill p #:withcolor (op* 0.8 'white))
    (draw p #:withpen (scale '1bp 'pencircle))
    ))

51.2 the result of ex-51

Examples:
> (require "examples/ex-51.rkt")
> (make-figure "ex-51" main)

52 ex-52

52.1 source code in ex-52.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (p (path (point u 0)            (dir-spec 'up) ".."
                  (point (op* -1   u) 0) (dir-spec 'down) "--"
                  (point (op* -0.2 u) 0) (dir-spec 'up) ".."
                  (point (op*  0.2 u) 0) (dir-spec 'down) "--"
                  'cycle)))
    (fill p #:withcolor (op* 0.8 'white))
    (draw p #:withpen (scale '1bp 'pencircle))
    ))

52.2 the result of ex-52

Examples:
> (require "examples/ex-52.rkt")
> (make-figure "ex-52" main)

53 ex-53

53.1 source code in ex-53.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (A  (point (op*  0.2 u) (op*  0.05 u)))
         (AA (point (op*  0.2 u) (op* -0.05 u)))
         (B  (point (op*  1.0 u) (op*  0.05 u)))
         (BB (point (op*  1.0 u) (op* -0.05 u)))
         (C  (point (op* -0.2 u) (op*  0    0)))
         (D  (point (op* -1.0 u) (op*  0    0)))
         (p (path B  (dir-spec 'up) ".."
                  D  (dir-spec 'down) ".."
                  BB (dir-spec 'up) "--"
                  AA (dir-spec 'down) ".."
                  C  (dir-spec 'up) ".."
                  A  (dir-spec 'down) "--"
                  'cycle)))
    (fill p #:withcolor (op* 0.8 'white))
    (draw p #:withpen (scale '1bp 'pencircle))
    ))

53.2 the result of ex-53

Examples:
> (require "examples/ex-53.rkt")
> (make-figure "ex-53" main)

54 ex-54

54.1 source code in ex-54.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (A (point 0 0))
         (B (polar u  60))
         (C (polar u -60))
         (D (point (op* 2 u) 0)))
    (for ((x (in-list (list A B C D))))
         (draw x #:withpen (scale '4bp 'pencircle)))
    (draw (op-- A D B D C))
    (for ((x (in-list (list (path A (dir-spec 'up) ".." B)
                            (path A (dir-spec 'down) ".." C)
                            (path A (dir-spec (dir  30)) ".." B)
                            (path A (dir-spec (dir -30)) ".." C)))))
         (draw x)
         )))

54.2 the result of ex-54

Examples:
> (require "examples/ex-54.rkt")
> (make-figure "ex-54" main)

55 ex-55

55.1 source code in ex-55.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
(draw (op.. (point 0 0) (point '1cm '1cm) (point '2cm 0))))

55.2 the result of ex-55

Examples:
> (require "examples/ex-55.rkt")
> (make-figure "ex-55" main)

56 ex-56

56.1 source code in ex-56.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (draw (path (point 0 0) '..
              "tension 2" '..
              (point '1cm '1cm) '..
              (point '2cm 0))))

56.2 the result of ex-56

Examples:
> (require "examples/ex-56.rkt")
> (make-figure "ex-56" main)

57 ex-57

57.1 source code in ex-57.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((u '1cm))
    (draw (path (polar u  90) (dir-spec (dir 0))    '..
                (polar u  -150) (dir-spec (dir 120))  '..
                (polar u  -30 ) (dir-spec (dir -120))  '..
                'cycle))))

57.2 the result of ex-57

Examples:
> (require "examples/ex-57.rkt")
> (make-figure "ex-57" main)

58 ex-58

58.1 source code in ex-58.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((u '1cm)
        (tension " tension 2 "))
    (draw (path (polar u  90) (dir-spec (dir 0))    '.. tension '..
                (polar u  -150 ) (dir-spec (dir 120))  '.. tension '..
                (polar u  -30 ) (dir-spec (dir -120))  '.. tension '..
                'cycle))))

58.2 the result of ex-58

Examples:
> (require "examples/ex-58.rkt")
> (make-figure "ex-58" main)

59 ex-59

59.1 source code in ex-59.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((u '1cm)
        (tension " tension 4 "))
    (draw (path (polar u  90) (dir-spec (dir 0))    '.. tension '..
                (polar u  -150 ) (dir-spec (dir 120))  '.. tension '..
                (polar u  -30 ) (dir-spec (dir -120))  '.. tension '..
                'cycle))))

59.2 the result of ex-59

Examples:
> (require "examples/ex-59.rkt")
> (make-figure "ex-59" main)

60 ex-60

60.1 source code in ex-60.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '0.5cm)
         (A (point 0 0))
         (B (point (op* -1 u) (op* 2 u)))
         (C (point (op* 4  u) (op* 3 u)))
         (D (point (op* 3  u) 0)))
    (draw (path
           A ".." " controls " B " and " C ".." D)
          #:withpen (scale '2pt 'pencircle))
    (draw (op-- B C) #:dashed 'evenly)
    (drawarrow (op-- A B))
    (drawarrow (op-- D C))))

60.2 the result of ex-60

Examples:
> (require "examples/ex-60.rkt")
> (make-figure "ex-60" main)

61 ex-61

61.1 source code in ex-61.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)

(define (main)
  (define (f z1 zn)
    (if (null? zn)
        z1
        (let ((x (f2 z1 zn)))
          (f (car x) (cdr x)))))
  (define (f2 z1 zn)
    (if (null? (cdr zn))
        (list (mediation 1/2 z1 (car zn)))
        (cons (mediation 1/2 z1 (car zn))
              (f2 (car zn) (cdr zn)))))
  (let* ((u '1cm)
         (A (point 0 0))
         (B (point (op* -1 u) (op* 2 u)))
         (C (point (op* 3  u) (op* 3 u)))
         (D (point (op* 2  u) 0)))
    (for ((A (in-list (list A B C D))))
         (draw A #:withpen (scale '4bp 'pencircle)))
    (draw (path A ".." " controls " B " and " C ".." D))
    (draw (f A (list B C D))
          #:withpen (scale '4bp 'pencircle))))

61.2 the result of ex-61

Examples:
> (require "examples/ex-61.rkt")
> (make-figure "ex-61" main)

62 ex-62

62.1 source code in ex-62.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (define  (bezier n A B C D)
    (let* ((a1 A)
           (a2 B)
           (a3 C)
           (a4 D)
           (a12 (mediation 1/2 a1   a2))
           (a23 (mediation 1/2 a2   a3))
           (a34 (mediation 1/2 a3   a4))
           (a123 (mediation 1/2  a12  a23))
           (a234 (mediation 1/2  a23  a34))
           (a1234(mediation 1/2  a123 a234)))
      (if (> n 0)
          (begin
            (bezier (- n 1) a1 a12 a123 a1234)
            (bezier (- n 1) a1234 a234 a34 a4))
          (draw a1234 #:withpen (scale '2bp 'pencircle)))))
  (let* ((u '1cm)
         (A (point 0 0))
         (B (point (op* -1 u) (op* 2 u)))
         (C (point (op* 3  u) (op* 3 u)))
         (D (point (op* 2  u) 0)))
    (for ((A (in-list (list A B C D))))
         (draw A #:withpen (scale '4bp 'pencircle)))
    ;; (draw (path A ".." " controls " B " and " C ".." D))
    (bezier 5 A B C D)))

62.2 the result of ex-62

Examples:
> (require "examples/ex-62.rkt")
> (make-figure "ex-62" main)

63 ex-63

63.1 source code in ex-63.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (draw (path (point 0 0) (dir-spec 'up) '..
              (point '1cm '1mm) ".."
              (point '2cm 0) (dir-spec 'down))))

63.2 the result of ex-63

Examples:
> (require "examples/ex-63.rkt")
> (make-figure "ex-63" main)

64 ex-64

64.1 source code in ex-64.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (draw (path (point 0 0) (dir-spec 'up) '...
              (point '1cm '1mm) "..."
              (point '2cm 0) (dir-spec 'down))))

64.2 the result of ex-64

Examples:
> (require "examples/ex-64.rkt")
> (make-figure "ex-64" main)

65 ex-65

65.1 source code in ex-65.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (path A " {curl 0} " ".."
                  D ".."
                  B ".."
                  C )))))

65.2 the result of ex-65

Examples:
> (require "examples/ex-65.rkt")
> (make-figure "ex-65" main)

66 ex-66

66.1 source code in ex-66.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (path A " {curl 1} " ".."
                  D ".."
                  B ".."
                  C )))))

66.2 the result of ex-66

Examples:
> (require "examples/ex-66.rkt")
> (make-figure "ex-66" main)

67 ex-67

67.1 source code in ex-67.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (A-B-C-D)
  (values (point 0 0)
          (point '1cm 0)
          (point '1cm '1cm)
          (point 0 '1cm)))
(define (main)
  (call-with-values A-B-C-D
    (lambda (A B C D)
      (draw (path A " {curl 2} " ".."
                  D ".."
                  B ".."
                  C )))))

67.2 the result of ex-67

Examples:
> (require "examples/ex-67.rkt")
> (make-figure "ex-67" main)

68 ex-68

68.1 source code in ex-68.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((A (unknown-point))
        (B (unknown-point))
        (C (unknown-point))
        (D (unknown-point)))
    (eqn= (xpart A) (ypart A) (ypart B) (xpart C) 0)
    (eqn= (xpart B) (ypart C) (xpart D) (ypart D) '2cm)
    (draw (op-- A B C D 'cycle)
          #:withpen (scale '2bp 'pencircle))))

68.2 the result of ex-68

Examples:
> (require "examples/ex-68.rkt")
> (make-figure "ex-68" main)

69 ex-69

69.1 source code in ex-69.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point 0 0))
         (B (point '2cm '3cm))
         (C (point '1cm 0))
         (D (point '-1cm '2cm))
         (M (unknown-point))
         (lambda1 (unknown-numeric))
         (mu (unknown-numeric)))
    (eqn= M  (mediation lambda1  A B)
          (mediation mu C D))
    (draw (op-- A B))
    (draw (op-- C D))
    (draw M #:withpen (scale '4bp 'pencircle))))

69.2 the result of ex-69

Examples:
> (require "examples/ex-69.rkt")
> (make-figure "ex-69" main)

70 ex-70

70.1 source code in ex-70.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point 0 0))
         (B (point '2cm '3cm))
         (C (point '1cm 0))
         (D (point '-1cm '2cm))
         (M (unknown-point)))
    (eqn= M  (mediation (whatever)  A B)
          (mediation (whatever) C D))
    (draw (op-- A B))
    (draw (op-- C D))
    (draw M #:withpen (scale '4bp 'pencircle))))

70.2 the result of ex-70

Examples:
> (require "examples/ex-70.rkt")
> (make-figure "ex-70" main)

71 ex-71

71.1 source code in ex-71.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point 0 0))
         (B (point '3cm 0))
         (C (point '1cm '2cm))
         (AA (mediation 0.5 B C))
         (BB (mediation 0.5 A C))
         (CC (mediation 0.5 A B))
         (G (unknown-point)))
    (eqn= G
          (mediation (whatever) A AA)
          (mediation (whatever) B BB))
    (draw (op-- A B C 'cycle))
    (for ((a (list A B C))
          (b (list AA BB CC)))
         (draw  (op-- a b) #:dashed  'withdots))
    (draw G #:withpen (scale '4bp 'pencircle))))

71.2 the result of ex-71

Examples:
> (require "examples/ex-71.rkt")
> (make-figure "ex-71" main)

72 ex-72

72.1 source code in ex-72.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((p  (fullcircle '5mm))
        (x (point '1mm '2mm)))
    (for ((n (in-range 5)))
         (draw (shift  (op* n x) p )))))

72.2 the result of ex-72

Examples:
> (require "examples/ex-72.rkt")
> (make-figure "ex-72" main)

73 ex-73

73.1 source code in ex-73.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((p (path (point '5mm '-5mm) (dir-spec 'right) '..
                 (point '2cm 0))))
    (for ((n (in-range 10)))
         (draw (rotate (* 10 n) p)))))

73.2 the result of ex-73

Examples:
> (require "examples/ex-73.rkt")
> (make-figure "ex-73" main)

74 ex-74

74.1 source code in ex-74.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((p  (fullcircle '5mm))
        (x (point '1mm '2mm)))
    (for ((n (in-range 1 5)))
         (draw (xscale n p)))))

74.2 the result of ex-74

Examples:
> (require "examples/ex-74.rkt")
> (make-figure "ex-74" main)

75 ex-75

75.1 source code in ex-75.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point '1cm 0))
         (B (rotate 72 A))
         (C (rotate 72 B))
         (D (rotate 72 C))
         (E (rotate 72 D)))
    (draw (op-- A B C D E 'cycle))))

75.2 the result of ex-75

Examples:
> (require "examples/ex-75.rkt")
> (make-figure "ex-75" main)

76 ex-76

76.1 source code in ex-76.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point '1cm 0))
         (B (rotate 72 A))
         (C (rotate 72 B))
         (D (rotate 72 C))
         (E (rotate 72 D)))
    (draw (op-- A C  E B D 'cycle))))

76.2 the result of ex-76

Examples:
> (require "examples/ex-76.rkt")
> (make-figure "ex-76" main)

77 ex-77

77.1 source code in ex-77.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point '1cm 0))
         (B (rotate 72 A))
         (C (rotate 72 B))
         (D (rotate 72 C))
         (E (rotate 72 D))
         (AA (unknown-point))
         (BB (unknown-point))
         (CC (unknown-point))
         (DD (unknown-point))
         (EE (unknown-point)))
    (eqn= AA (mediation (whatever) A C))
    (eqn= AA (mediation (whatever) B D))
    (eqn= BB (mediation (whatever) B D))
    (eqn= BB (mediation (whatever) C E))
    (eqn= CC (mediation (whatever) C E))
    (eqn= CC (mediation (whatever) D A))
    (eqn= DD (mediation (whatever) D A))
    (eqn= DD (mediation (whatever) E B))
    (eqn= EE (mediation (whatever) E B))
    (eqn= EE (mediation (whatever) A C))
    (fill (op-- A C  E B D 'cycle) #:withcolor (op* 0.8 'white))
    (fill (op-- AA  BB  CC  DD  EE  'cycle) #:withcolor 'white)
    (draw (op-- A  C  E  B  D  'cycle))))

77.2 the result of ex-77

Examples:
> (require "examples/ex-77.rkt")
> (make-figure "ex-77" main)

78 ex-78

78.1 source code in ex-78.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((p (path (op--
                  (point 0 0)
                  (point '1cm 0)))))
    (drawarrow p #:withpen (scale '2bp 'pencircle))
    (drawarrow (zscale (point 1 2) p))))

78.2 the result of ex-78

Examples:
> (require "examples/ex-78.rkt")
> (make-figure "ex-78" main)

79 ex-79

79.1 source code in ex-79.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (p (path (op-- (point 0 0)
                        (point u 0))))
         (A (point u (op* -1 u)))
         (alpha 90))
    (drawarrow p #:withpen (scale '1bp 'pencircle))
    (drawarrow ((rotate-around A alpha) p))
    (drawarrow
     (shift A (rotate alpha (shift (op* -1 A) p)))
     #:withpen (scale '1bp 'pencircle) #:dashed 'withdots)))

79.2 the result of ex-79

Examples:
> (require "examples/ex-79.rkt")
> (make-figure "ex-79" main)

80 ex-80

80.1 source code in ex-80.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(require (planet wcy/mpost-wrapper/label))
(provide main)

(define (main)
  (let* ((p (path
             (point 0 0) '--
             (point '1cm 0)))
         (A (point '1cm '-1cm))
         (alpha 90))
    (drawarrow p #:withpen (scale '1bp 'pencircle))
    (draw A #:withpen (scale '4bp 'pencircle))
    (label-ulft (btex "$A$") A)
    (draw (point 0 0) #:withpen (scale '4bp 'pencircle))
    (label-bot (btex "$O$") (point 0 0))
    (let loop ((i 0))
      (if (< i 10)
          (begin
            (drawarrow (shift  (op* -1 (op/ (op* i A) 10)) p) #:withcolor 'red)
            (drawarrow (rotate (op/ (op* i alpha) 10) (shift (op* -1 A) p)) #:withcolor 'green)
            (drawarrow (shift  (op/ (op* i A) 10) (rotate alpha (shift (op* -1 A) p)))
                       #:withcolor 'blue)
            (loop (+ 1 i)))
          (void)))))

80.2 the result of ex-80

Examples:
> (require "examples/ex-80.rkt")
> (make-figure "ex-80" main)

81 ex-81

81.1 source code in ex-81.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (define (f AA A B C)
    (eqn= (op- AA A)
          (rotate  90 (op* (unknown-numeric)
                           (op- B C))))
    (eqn= AA (mediation (whatever) B C)))
  (let* ((A (point 0 0))
         (B (point '3cm 0))
         (C (point '1cm '2cm))
         (AA (unknown-point))
         (BB (unknown-point))
         (CC (unknown-point))
         (H (unknown-point)))
    (f AA A B C)
    (f BB B A C)
    (f CC C B A)
    (eqn= H (mediation (whatever) A AA))
    (eqn= H (mediation (whatever) B BB)) ;
    (for ((x (in-list (list
                       (op-- A B C 'cycle)
                       (op-- A AA)
                       (op-- B BB)
                       (op-- C CC)))))
         (draw x))
    (draw H #:withpen (scale '4bp 'pencircle))
    ))

81.2 the result of ex-81

Examples:
> (require "examples/ex-81.rkt")
> (make-figure "ex-81" main)

82 ex-82

82.1 source code in ex-82.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((A (point 0 0))
        (B (point '3cm 0))
        (C (point '1cm '2cm))
        (H (unknown-point)))
    (eqn= (op- H A)
          (rotate 90 (op* (whatever)
                          (op- B C))))
    (eqn= (op- H B)
          (rotate 90 (op* (whatever)
                          (op- A C))))
    (draw (op-- A  B  C  'cycle))
    (draw H #:withpen (scale '4bp 'pencircle))
    ))

82.2 the result of ex-82

Examples:
> (require "examples/ex-82.rkt")
> (make-figure "ex-82" main)

83 ex-83

83.1 source code in ex-83.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((A (point 0 0))
        (B (point '3cm 0))
        (C (point '1cm '2cm))
        (O (unknown-point)))
    (define (f B C)
      (eqn= (op- O
                 (mediation 1/2 B C))
            (op* (whatever)
                 (rotate 90 (op- B C)))))
    (f B C)
    (f A B)
    (draw (op-- A  B  C  'cycle))
    (draw O #:withpen (scale '4bp 'pencircle))
    (draw (fullcircle (op* 2 (op-abs (op- O A))) O))))

83.2 the result of ex-83

Examples:
> (require "examples/ex-83.rkt")
> (make-figure "ex-83" main)

84 ex-84

84.1 source code in ex-84.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '2cm)
         (A (point 0 0))
         (B (point u 0))
         (C (point u u))
         (D (point 0 u))
         (T (unknown-transform))
         (p  (op-- A  B  C  D  'cycle))
         )
    (eqn= (transform T A)
          (mediation 1/5 A B))
    (eqn= (transform T B)
          (mediation 1/5 B C))
    (eqn= (transform T C)
          (mediation 1/5 C D))
    (draw p)
    (draw (transform T p))))

84.2 the result of ex-84

Examples:
> (require "examples/ex-84.rkt")
> (make-figure "ex-84" main)

85 ex-85

85.1 source code in ex-85.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '2cm)
         (A (point 0 0))
         (B (point u 0))
         (C (point u u))
         (D (point 0 u))
         (Tx (unknown-transform))
         (p  (op-- A  B  C  D  'cycle))
         )
    (eqn= (transform Tx A)
          (mediation 1/5 A B))
    (eqn= (transform Tx B)
          (mediation 1/5 B C))
    (eqn= (transform Tx C)
          (mediation 1/5 C D))
    (for/fold
        ((p p))
        ((i (in-range 0 100)))
      (draw p)
      (transform Tx p))
    ))

85.2 the result of ex-85

Examples:
> (require "examples/ex-85.rkt")
> (make-figure "ex-85" main)

86 ex-86

86.1 source code in ex-86.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point '1cm 0))
         (B (rotate 72 A))
         (C (rotate 72 B))
         (D (rotate 72 C))
         (E (rotate 72 D))
         (p (op-- A B C D E 'cycle))
         (T (unknown-transform)))
    (eqn= (transform T A)
          (mediation 1/5 A B))
    (eqn= (transform T B)
          (mediation 1/5 B C))
    (eqn= (transform T C)
          (mediation 1/5 C D))
    (for/fold
        ((p p))
        ((i (in-range 0 3)))
      (draw p)
      (transform T p))))

86.2 the result of ex-86

Examples:
> (require "examples/ex-86.rkt")
> (make-figure "ex-86" main)

87 ex-87

87.1 source code in ex-87.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '3mm)
         (p (fullcircle (op* 2 u)))
         (p2 (scale 0.5 p)))
    (for ((x (in-list (list p
                            (shift (op* u (dir 30)) p2)
                            (shift (op* u (dir 150)) p2)
                            ))))
         (fill x #:withcolor (op* 0.8 'white)))))

87.2 the result of ex-87

Examples:
> (require "examples/ex-87.rkt")
> (make-figure "ex-87" main)

88 ex-88

88.1 source code in ex-88.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '3mm)
         (p (fullcircle (op* 2 u)))
         (p2 (scale 0.5 p))
         (T (unknown-transform)))
    (eqn= (transform T (point 0 0)) (point 0 0))
    (eqn= (transform T (point 1 0)) (point 1 1))
    (eqn= (transform T (point 0 1)) (point 1 0))
    (for ((p (in-list (list p
                            (shift (op* u (dir 30)) p2)
                            (shift (op* u (dir 150)) p2)
                            ))))
         (fill (transform T p) #:withcolor (op* 0.8 'white)))))

88.2 the result of ex-88

Examples:
> (require "examples/ex-88.rkt")
> (make-figure "ex-88" main)

89 ex-89

89.1 source code in ex-89.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '3mm)
         (p (fullcircle (op* 2 u)))
         (p2 (scale 0.5 p))
         (T (unknown-transform)))
    (eqn= (xpart T) (ypart T)  0)
    (eqn= (xxpart T) 1)
    (eqn= (yxpart T) 2)
    (eqn= (xypart T) 3)
    (eqn= (yypart T) 4)
    (for ((p (in-list (list p
                            (shift (op* u (dir 30)) p2)
                            (shift (op* u (dir 150)) p2)
                            ))))
         (fill (transform T p) #:withcolor (op* 0.8 'white)))))

89.2 the result of ex-89

Examples:
> (require "examples/ex-89.rkt")
> (make-figure "ex-89" main)

90 ex-90

90.1 source code in ex-90.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((pic-1 (new-picture
                (lambda ()
                  (let ((p1 (fullcircle '1cm))
                        (p2 (fullcircle '5mm)))
                    (draw p1)
                    (draw (shift (polar '1cm 45) p2))
                    (draw (shift (polar '1cm 135) p2)))))))
    (for ((a (in-list (list (point 0 0)
                            (point '1mm '1mm)
                            (point '2mm '2mm)))))
         (draw (shift a pic-1)))))

90.2 the result of ex-90

Examples:
> (require "examples/ex-90.rkt")
> (make-figure "ex-90" main)

91 ex-91

91.1 source code in ex-91.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((pic (unknown-picture)))
    (addto pic 'contour (fullcircle '1cm)
           #:withcolor (op* 0.8 'white))
    (addto pic 'doublepath (fullcircle '1cm)
           #:withpen (scale '0.5bp 'pencircle))
    (addto pic 'also (shift (point '1mm '1mm) pic))
    (draw pic)))

91.2 the result of ex-91

Examples:
> (require "examples/ex-91.rkt")
> (make-figure "ex-91" main)

92 ex-92

92.1 source code in ex-92.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((u '3mm)
        (mickey (unknown-picture)))
    (addto mickey 'contour (fullcircle (op* 2 u))
           #:withcolor (op* 0.8 'white))
    (addto mickey 'contour (fullcircle u (polar u 150))
           #:withcolor (op* 0.8 'white))
    (addto mickey 'contour (fullcircle u (polar u 30))
           #:withcolor (op* 0.8 'white))
    (draw mickey)))

92.2 the result of ex-92

Examples:
> (require "examples/ex-92.rkt")
> (make-figure "ex-92" main)

93 ex-93

93.1 source code in ex-93.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((u '3mm)
        (mickey (unknown-picture))
        (T (unknown-transform)))
    (addto mickey 'contour (fullcircle (op* 2 u))
           #:withcolor (op* 0.8 'white))
    (addto mickey 'contour (fullcircle u (polar u 150))
           #:withcolor (op* 0.8 'white))
    (addto mickey 'contour  (fullcircle u (polar u 30))
           #:withcolor (op* 0.8 'white))
    (eqn= (transform T (point 0 0 )) (point 0 0))
    (eqn= (transform T (point 1 0 )) (point 1 1))
    (eqn= (transform T (point 0 1 )) (point 1 0))
    (draw (transform T mickey))))

93.2 the result of ex-93

Examples:
> (require "examples/ex-93.rkt")
> (make-figure "ex-93" main)

94 ex-94

94.1 source code in ex-94.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((mickey (new-picture
                 (lambda ()
                   (let ((u '3mm))
                     (for ((p (in-list
                               (list (fullcircle (op* 2 u))
                                     (fullcircle u (polar u 150))
                                     (fullcircle u (polar u 30))))))
                          (fill p #:withcolor (op* 0.8 'white)))))))
        (T (unknown-transform)))
    (for ((v1 (in-list (list (point 0 0)
                             (point 1 0)
                             (point 0 1))))
          (v2 (in-list (list (point 0 0)
                             (point 1 1)
                             (point 1 0)))))
         (eqn= (transform T v1) v2))
    (draw (transform T mickey))))

94.2 the result of ex-94

Examples:
> (require "examples/ex-94.rkt")
> (make-figure "ex-94" main)

95 ex-95

95.1 source code in ex-95.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point 0 '1cm))
         (B (rotate 120 A))
         (p (path A (dir-spec (dir 0)) '..
                  'tension 2 '..
                  B (dir-spec (dir 120)))))
    (for ((p (in-list (list p (rotate 120 p) (rotate -120 p)))))
         (draw p))
    ))

95.2 the result of ex-95

Examples:
> (require "examples/ex-95.rkt")
> (make-figure "ex-95" main)

96 ex-96

96.1 source code in ex-96.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((n 5)
         (alpha (/ (* 2 360) n))
         (A (point 0 '1cm))
         (B (rotate alpha A))
         (p (path A (dir-spec (dir 180)) '..
                  'tension 4 '..
                  B (dir-spec (dir (+ 180 alpha))))))
    (draw p #:withcolor 'red)
    (for ((i (in-range 1 5)))
         (draw (rotate (* i (/ 360 n)) p)))
    ))

96.2 the result of ex-96

Examples:
> (require "examples/ex-96.rkt")
> (make-figure "ex-96" main)

97 ex-97

97.1 source code in ex-97.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((c0 (fullcircle '1cm (point 0 '1cm) 1 0.5))
         (c1 (rotate 120 c0))
         (c2 (rotate 120 c1))
         (A (point '-0.5cm '1cm))
         (l0 (path A (dir-spec 'down) '..
                   (rotate 120 (xscale -1 A)) (dir-spec (rotate 120 (op* -1 'down)))))
         (l1 (rotate 120 l0))
         (l2 (rotate 120 l1)))
    (for ((x (in-list (list c0 c1 c2  l0 l1 l2
                            ))))
         (draw x)
         )))

97.2 the result of ex-97

Examples:
> (require "examples/ex-97.rkt")
> (make-figure "ex-97" main)

98 ex-98

98.1 source code in ex-98.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((c0 (fullcircle '1cm (point 0 '1cm) 1 0.5))
         (c1 (rotate 90 c0))
         (c2 (rotate 90 c1))
         (c3 (rotate 90 c2))
         (A (point '-0.5cm '1cm))
         (l0 (path A (dir-spec 'down) '..
                   (rotate 90 (xscale -1 A)) (dir-spec (rotate 90 (op* -1 'down)))))
         (l1 (rotate 90 l0))
         (l2 (rotate 90 l1))
         (l3 (rotate 90 l2)))
    (for ((x (in-list (list c0 c1 c2 c3 l0 l1 l2 l3
                            ))))
         (draw x)
         )))

98.2 the result of ex-98

Examples:
> (require "examples/ex-98.rkt")
> (make-figure "ex-98" main)

99 ex-99

99.1 source code in ex-99.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point 0  0))
         (B (point '2cm '1cm))
         (p (fullcircle (op-abs (op- B A))
                        (mediation 0.5 A B))))
    (for ((x (in-list (list A B))))
         (draw x #:withpen (scale '4bp 'pencircle)))
    (draw p)))

99.2 the result of ex-99

Examples:
> (require "examples/ex-99.rkt")
> (make-figure "ex-99" main)

100 ex-100

100.1 source code in ex-100.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((origin (point 0 0))
         (A (point '2cm '2cm)))
    (for ((i (in-range 4)))
         (drawarrow (rotate (op* (* i -1/3) (op-angle A))
                            (op-- origin A))))))

100.2 the result of ex-100

Examples:
> (require "examples/ex-100.rkt")
> (make-figure "ex-100" main)

101 ex-101

101.1 source code in ex-101.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((origin (point 0 0))
         (A (point '1cm '2cm))
         (B (point '2cm '1cm))
         (alpha (op- (op-angle A)
                     (op-angle B))))
    (drawarrow (op-- origin A))
    (drawarrow (op-- origin B))
    (for ((i (in-range 3)))
         (drawarrow (rotate (op* (* i -1/3) alpha)
                            (op-- origin A))))
    ))

101.2 the result of ex-101

Examples:
> (require "examples/ex-101.rkt")
> (make-figure "ex-101" main)

102 ex-102

102.1 source code in ex-102.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(require (planet wcy/mpost-wrapper/label))
(provide main)
(define (main)
  (let* ((A (point 0 0))
         (B (point '3cm 0))
         (C (point '1cm '2cm)))
    (draw (op-- A B C 'cycle))
    (label-llft (TEX (decimal (op- (op-angle (op- C A))
                                   (op-angle (op- B A))))) A)
    (label-lrt (TEX (decimal (op- (op-angle (op- A B))
                                  (op-angle (op- C B))))) B)
    (label-urt (TEX (decimal (op- (op-angle (op- B C))
                                  (op-angle (op- A C))))) C)
    ))

102.2 the result of ex-102

Examples:
> (require "examples/ex-102.rkt")
> (make-figure "ex-102" main)

103 ex-103

103.1 source code in ex-103.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point 0 0))
         (B (point '3cm 0))
         (C (point '1cm '2cm))
         (AA (mediation 0.5 B C))
         (BB (mediation 0.5 A C))
         (CC (mediation 0.5 A B))
         (O (unknown-point))
         (polar (unknown-numeric)))
    (eqn= (op- O (mediation 0.5 BB CC))
          (op* (whatever) (rotate 90 (op- BB CC))))
    (eqn= (op- O (mediation 0.5 AA BB))
          (op* (whatever) (rotate 90 (op- AA BB))))
    (draw (op-- A B C 'cycle))
    (for ((x (in-list (list AA BB CC))))
         (draw x #:withpen (scale '4bp 'pencircle )))
    (draw (fullcircle (op* 2 (op-abs (op- O AA)))
                      O))
    (let ((AA (unknown-point))
          (BB (unknown-point))
          (CC (unknown-point))
          (H  (unknown-point)))
      (for ((vAA (in-list (list AA BB CC)))
            (vA (in-list (list A B C)))
            (vB (in-list (list B C A)))
            (vC (in-list (list C A B))))
           (eqn= (op- vAA vA)
                 (op* (whatever) (rotate  90 (op- vB vC))))
           (eqn= vAA (mediation (whatever) vB vC)))
      (for ((vA (in-list (list A B C)))
            (vAA (in-list (list AA BB CC))))
           (draw (op-- vA vAA)))
      (for ((x (in-list (list AA BB CC))))
           (draw x #:withpen (scale '4bp 'pencircle )))
      (eqn= H (mediation (whatever) A AA))
      (eqn= H (mediation (whatever) B BB))
      (for ((x (in-list (list A B C))))
           (draw (mediation 0.5 x H) #:withpen (scale '4bp 'pencircle)))
      )))

103.2 the result of ex-103

Examples:
> (require "examples/ex-103.rkt")
> (make-figure "ex-103" main)

104 ex-104

104.1 source code in ex-104.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '2cm)
         (A (point 0 0))
         (B (point (op* 2 u) (op* -0.5 u)))
         (C (point u u))
         (M (unknown-point))
         (h (unknown-point)))
    (draw (op-- A B C 'cycle))
    (eqn= (op- M A)
          (op* (whatever)
               (rotate (op* 0.5
                            (op-
                             (op-angle (op- B A))
                             (op-angle (op- C A))))
                       (op- A C))))
    (eqn= (op- M B)
          (op* (whatever)
               (rotate (op* 0.5
                            (op-
                             (op-angle (op- C B))
                             (op-angle (op- A B))))
                       (op- B A))))
    (for ((x (in-list (list A B C))))
         (draw (op-- M x)))
    (eqn= (op- M h)
          (op* (whatever) (rotate 90 (op- B C))))
    (eqn= h (mediation (whatever) B C) )
    (draw (fullcircle (op* 2 (op-abs (op- M h)))
                      M))))

104.2 the result of ex-104

Examples:
> (require "examples/ex-104.rkt")
> (make-figure "ex-104" main)

105 ex-105

105.1 source code in ex-105.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((p (path (point 0 0) (dir-spec 'up) '..
                  (point '2cm 0) (dir-spec 'down))))
    (draw p)
    (for ((i (in-list (list 0 0.5 1))))
         (draw (point-of i p) #:withpen (scale '4bp 'pencircle)))
    ))

105.2 the result of ex-105

Examples:
> (require "examples/ex-105.rkt")
> (make-figure "ex-105" main)

106 ex-106

106.1 source code in ex-106.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((p (path (point 0 0) (dir-spec 'up) '..
                  (point '2cm 0) (dir-spec 'down)))
         (A (point-of 0 p)))
    (draw p)
    (for ((i (in-list (list 0 0.5 1))))
         (let* ((A (point-of i p))
                (B (op+ A (polar '1cm (op-angle (direction-of i p))))))
           (drawarrow (op-- A B) #:withpen (scale '1bp 'pencircle))))))

106.2 the result of ex-106

Examples:
> (require "examples/ex-106.rkt")
> (make-figure "ex-106" main)

107 ex-107

107.1 source code in ex-107.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '5mm)
         (p (path (point 0 0) (dir-spec '(curl 0)) '..
                  (point u (op* 2 u)) '..
                  (point (op* 2 u) (op* 1.5 u)) '..
                  (point (op* 3 u) (op* 2   u)) '..
                  (dir-spec '(curl 0)) (point (op* 4 u) 0))))
    (draw (subpath-of 0 1 p) #:withcolor 'red)
    (draw (subpath-of 1 2 p) #:withcolor 'green)
    (draw (subpath-of 2 3 p) #:withcolor 'blue)
    (draw (subpath-of 3 3.5 p) #:dashed 'evenly)
    (draw (subpath-of 3.5 4 p) #:dashed 'withdots)))

107.2 the result of ex-107

Examples:
> (require "examples/ex-107.rkt")
> (make-figure "ex-107" main)

108 ex-108

108.1 source code in ex-108.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (p (path (point 0 0) (dir-spec 'up) '..
                  (point u (op* 2 u)) (dir-spec 'up)))
         (q (path (point u 0) (dir-spec 'up) '..
                  (point 0 (op* 2 u)) (dir-spec 'up))))
    (draw p)
    (draw (subpath-of 0 0.4 q) #:withpen (scale '1bp 'pencircle))
    (draw (subpath-of 0.6 1 q) #:withpen (scale '1bp 'pencircle))))

108.2 the result of ex-108

Examples:
> (require "examples/ex-108.rkt")
> (make-figure "ex-108" main)

109 ex-109

109.1 source code in ex-109.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (a (path (point (op* -1 u) (op* -0.2 u)) '..
                  'tension 1.2 '..
                  (point u (op* -0.2 u)) (dir-spec 'down)))
         (b (rotate 90 a))
         (c (rotate 90 b))
         (d (rotate 90 c)))
    (fill (buildcycle a b c d) #:withcolor (op* 0.8 'white))
    (map draw (list a b c d))))

109.2 the result of ex-109

Examples:
> (require "examples/ex-109.rkt")
> (make-figure "ex-109" main)

110 ex-110

110.1 source code in ex-110.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (c1 (fullcircle u))
         (c2 (fullcircle u (point 0 (op* 0.5 u)))))
    (draw c1 #:dashed 'evenly)
    (draw c2 #:dashed 'evenly)
    (draw (buildcycle c1 c2) #:withpen (scale '1bp 'pencircle))))

110.2 the result of ex-110

Examples:
> (require "examples/ex-110.rkt")
> (make-figure "ex-110" main)

111 ex-111

111.1 source code in ex-111.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (a (fullcircle (op* 2 u) (point (op* 0.5 u) 0)))
         (b (rotate (/ 360 3) a))
         (c (rotate (/ 360 3) b)))
    (fill a #:withcolor 'red)
    (fill b #:withcolor 'green)
    (fill c #:withcolor 'blue)
    (fill (buildcycle a b) #:withcolor (op+ 'red   'green))
    (fill (buildcycle b c) #:withcolor (op+ 'green 'blue))
    (fill (buildcycle c a) #:withcolor (op+ 'blue  'red))
    (fill (buildcycle a b c) #:withcolor 'white)
    (draw a) (draw b) (draw c)
    ))

111.2 the result of ex-111

Examples:
> (require "examples/ex-111.rkt")
> (make-figure "ex-111" main)

112 ex-112

112.1 source code in ex-112.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (define (compute_curve f xmin xmax xinc)
    (apply op.. (for/list ((x (in-range xmin xmax xinc)))
                          (point x (f x)))))
  (define (f x)
    (op+ 1 (op** x 2)))
  (define (g x)
    (op- 2 (op** (op- x 1) 2)))
  (let* ((p (scale '1cm (compute_curve f -1 1.5 0.1)))
         (q (scale '1cm (compute_curve g -0.5 2 0.1))))
    (fill (buildcycle p (op-reverse q)) #:withcolor (op+ 'red 'green))
    (draw p #:withpen (scale '1bp 'pencircle))
    (draw q #:withpen (scale '1bp 'pencircle))
    (draw (op-- (point '-1cm 0)  (point '2cm 0)))
    (draw (op-- (point 0 (op* (g -0.5) '1cm))
                (point 0 (op* (f  1.5) '1cm))))
    ))

112.2 the result of ex-112

Examples:
> (require "examples/ex-112.rkt")
> (make-figure "ex-112" main)

113 ex-113

113.1 source code in ex-113.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((p (path (point 0 0) (dir-spec 'up) '..
                  (point '2cm 0) (dir-spec 'up)))
         (q (path (point 0 '1cm) (dir-spec (dir -60)) '..
                  (point '1cm '-1cm) '..
                  (dir-spec (dir 60)) (point '2cm '1cm))))
    (draw p)
    (draw q)
    (draw (intersectionpoint p q) #:withpen (scale '4bp 'pencircle))))

113.2 the result of ex-113

Examples:
> (require "examples/ex-113.rkt")
> (make-figure "ex-113" main)

114 ex-114

114.1 source code in ex-114.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((p (path (point 0 0) (dir-spec 'up) '..
                  (point '2cm 0) (dir-spec 'up)))
         (q (path (point 0 '1cm) (dir-spec (dir -60)) '..
                  (point '1cm '-1cm) '..
                  (dir-spec (dir 60)) (point '2cm '1cm)))
         (a (unknown-numeric))
         (b (unknown-numeric)))
    (draw p)
    (draw q)
    (eqn= (point a (whatever))
          (intersectiontimes p q))
    (draw (point-of a p) #:withpen (scale '4bp 'pencircle))))

114.2 the result of ex-114

Examples:
> (require "examples/ex-114.rkt")
> (make-figure "ex-114" main)

115 ex-115

115.1 source code in ex-115.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((A (point 0 '1cm))
         (B (rotate 120 A))
         (p (path A (dir-spec (dir 0)) '..
                  'tension 2 '..
                  B (dir-spec (dir 120))))
         (a (unknown-numeric)))
    (eqn= (point a (whatever))
          (intersectiontimes p (rotate 120 p)))
    (draw (subpath-of 0 (op- a 0.02) p))
    (draw (subpath-of (op+ a 0.02) 1 p))
    (draw (subpath-of 0 (op- a 0.02) (rotate 120 p)))
    (draw (subpath-of (op+ a 0.02) 1 (rotate 120 p)))
    (draw (subpath-of 0 (op- a 0.02) (rotate -120 p)))
    (draw (subpath-of (op+ a 0.02) 1 (rotate -120 p)))))

115.2 the result of ex-115

Examples:
> (require "examples/ex-115.rkt")
> (make-figure "ex-115" main)

116 ex-116

116.1 source code in ex-116.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (draw-extra n p op-x)
  (let ((pn (point-of n p)))
    (draw (op-- pn (op-x pn (op* '4mm (unitvector (direction-of n p))))))))

(define (main)
  (let* ((u '2cm)
         (A0 (op* u 'up))
         (A (reverse (for/fold ((r (list A0)))
                         ((i (in-range 1 11)))
                       (cons (rotate 72 (car r)) r))))
         (B*  (for/list ((A_i (in-list A))
                         (A_i+1 (in-list (cdr A)))
                         (i (in-range 0 10)))
                        (mediation 0.5 A_i A_i+1)))
         (B (for/list ((b_i (in-range 0 10)))
                      (list-ref B* (if (= b_i 5) 0 b_i))))
         (C (for/list ((b_i (in-list B)))
                      (op* 0.8 b_i))))
    (for ((A_i (in-list A))
          (A_i+1 (in-list (cdr A))))
         (let* ((p_i (op-- A_i A_i+1)))
           (draw p_i)
           (draw-extra 1 p_i op+)
           (draw-extra 0 p_i op-)))
    (let ((p (for/list ((i (in-range 0 5)))
                       (let* ((p_i (path (list-ref B i) '---
                                         (list-ref C i) '..
                                         (list-ref C (+ 2 i))  (dir-spec (dir  (* 72 i)))
                                         )))
                         (draw p_i)
                         (draw-extra 2 p_i op+ )
                         (draw-extra 0 p_i op- ) p_i))))
      (for ((p_i (in-list p)))
           (draw (subpath-of 1 1.4 p_i) #:withpen (scale '4bp 'pencircle) #:withcolor 'white)
           (draw (subpath-of 0 1.5 p_i) ))
      (for ((A_i (in-list A))
            (B_i (in-list B))
            (C_i (in-list C)))
           (for ((x (in-list (list A_i B_i C_i))))
                (draw x #:withpen (scale '4bp 'pencircle)))))))

116.2 the result of ex-116

Examples:
> (require "examples/ex-116.rkt")
> (make-figure "ex-116" main)

117 ex-117

117.1 source code in ex-117.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '2cm)
         (A (op* u 'up))
         (B (mediation 0.5 A (rotate 72 A)))
         (C (op* 0.8 B))
         (p (op-- (mediation  -0.2 A (rotate 72 A))
                  (mediation  1.2 A (rotate 72 A)))))
    (for ((i (in-range 6)))
         (draw (rotate (* i 72) p)))
    (let* ((p* (path B '--- C '.. (rotate (* 2 72) C) (dir-spec 'right)))
           (p  (op& (path (op- (point-of 0 p*)
                               (op* '4mm (unitvector (direction-of 0 p*))))
                          '--
                          (point-of 0 p*))
                    p*
                    (path (point-of 2 p*)
                          '--
                          (op+ (point-of 2 p*)
                               (op* '4mm (unitvector (direction-of 2 p*)))))))
           (E (intersectionpoint p (rotate 72 p)))
           (q (cutbefore p (fullcircle  '-2mm E)))
           (r (cutafter p (fullcircle '2mm E))))
      (for ((i (in-range 6)))
           (let ((rotate-it (lambda (x) (rotate (* 72 i) x))))
             (for ((x (in-list (list q r A))))
                  (draw (rotate-it x)))
             (for ((x (in-list (list A B C))))
                  (draw (rotate-it x) #:withpen (scale '4bp 'pencircle))))))))

117.2 the result of ex-117

Examples:
> (require "examples/ex-117.rkt")
> (make-figure "ex-117" main)

118 ex-118

118.1 source code in ex-118.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (for ((i (in-range 4)))
       (draw (rotate (* i 90) (op* '1cm 'right))
             #:withpen (scale '4bp 'pencircle))))

118.2 the result of ex-118

Examples:
> (require "examples/ex-118.rkt")
> (make-figure "ex-118" main)

119 ex-119

119.1 source code in ex-119.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (draw (apply op--
               `(,@(for/list ((i (in-range 4)))
                             (rotate (* i 90) (op* '1cm 'right)))
                 cycle))))

119.2 the result of ex-119

Examples:
> (require "examples/ex-119.rkt")
> (make-figure "ex-119" main)

120 ex-120

120.1 source code in ex-120.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((n 5))
    (draw (apply op--
                 `(,@(for/list ((i (in-range n)))
                               (rotate (/ (* i 360) n) (op* '1cm 'up)))
                   cycle)))))

120.2 the result of ex-120

Examples:
> (require "examples/ex-120.rkt")
> (make-figure "ex-120" main)

121 ex-121

121.1 source code in ex-121.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let ((n 7))
    (draw (apply op--
                 `(,@(for/list ((i (in-range n)))
                               (rotate (/ (* i 360) n) (op* '1cm 'up)))
                   cycle)))))

121.2 the result of ex-121

Examples:
> (require "examples/ex-121.rkt")
> (make-figure "ex-121" main)

122 ex-122

122.1 source code in ex-122.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((p (op.. (point 0 0)
                  (point '-1cm '2cm)
                  (point '2cm '1cm)
                  (point '1cm 0)))
         (n 10)
         (length-p (length p)))
    (draw p)
    (for ((i (in-range (+ 1 n))))
         (draw (point-of (op* (/ i n)
                              length-p)
                         p)
               #:withpen (scale '4bp 'pencircle)))))

122.2 the result of ex-122

Examples:
> (require "examples/ex-122.rkt")
> (make-figure "ex-122" main)

123 ex-123

123.1 source code in ex-123.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((p (op.. (point 0 0)
                  (point '-1cm '2cm)
                  (point '2cm '1cm)
                  (point '1cm 0)))
         (n 10)
         (length-p (length p)))
    (draw p)
    (for ((i (in-range 0 1 (/ 1 n))))
         (let ((pi (point-of (op* i length-p) p)))
           (drawarrow (op-- pi
                            (shift pi (op* '1cm (unitvector (direction-of (op* i length-p) p))))))))))

123.2 the result of ex-123

Examples:
> (require "examples/ex-123.rkt")
> (make-figure "ex-123" main)

124 ex-124

124.1 source code in ex-124.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm))
    (draw (op-- (point (op* -2 u) 0)
                (point (op*  2 u) 0)))
    (draw (op-- (point 0 (op* -2 u))
                (point 0 (op*  2 u))))
    (for ((i (in-range -2 3 1)))
         (draw (op-- (point (op* i u) (op/ u  20))
                     (point (op* i u) (op/ u -20))))
         (draw (op-- (point (op/ u  20) (op* i u))
                     (point (op/ u -20) (op* i u)))))))

124.2 the result of ex-124

Examples:
> (require "examples/ex-124.rkt")
> (make-figure "ex-124" main)

125 ex-125

125.1 source code in ex-125.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm))
    (draw (op-- (point (op* -2 u) 0)
                (point (op*  2 u) 0)))
    (draw (op-- (point 0 (op* -2 u))
                (point 0 (op*  2 u))))
    (for ((i (in-range -2 3 1)))
         (draw (op-- (point (op* i u) (op/ u 10))
                     (point (op* i u) (op/ u -10))))
         (draw (op-- (point (op/ u  10) (op* i u))
                     (point (op/ u -10) (op* i u)))))
    (for ((i (in-range -2 2.01 0.2)))
         (draw (op-- (point (op* i u) (op/ u  20))
                     (point (op* i u) (op/ u -20))))
         (draw (op-- (point (op/ u  20) (op* i u))
                     (point (op/ u -20) (op* i u)))))))

125.2 the result of ex-125

Examples:
> (require "examples/ex-125.rkt")
> (make-figure "ex-125" main)

126 ex-126

126.1 source code in ex-126.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm))
    (draw (op-- (point (op* -2 u) 0)
                (point (op*  2 u) 0)))
    (draw (op-- (point 0 (op* -2 u))
                (point 0 (op*  2 u))))
    (for ((i (in-range -2 2.01 1)))
         (draw (op-- (point (op* i u) (op* u  2))
                     (point (op* i u) (op* u -2))))
         (draw (op-- (point (op* u  2) (op* i u))
                     (point (op* u -2) (op* i u))))
         )))

126.2 the result of ex-126

Examples:
> (require "examples/ex-126.rkt")
> (make-figure "ex-126" main)

127 ex-127

127.1 source code in ex-127.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm))
    (draw (op-- (point (op* -2 u) 0)
                (point (op*  2 u) 0)))
    (draw (op-- (point 0 (op* -2 u))
                (point 0 (op*  2 u))))
    (for ((i (in-range -2 2.01 1)))
         (draw (op-- (point (op* i u) (op* u  2))
                     (point (op* i u) (op* u -2))))
         (draw (op-- (point (op* u  2) (op* i u))
                     (point (op* u -2) (op* i u))))
         )
    (for ((i (in-range -2 2.01 0.2)))
         (draw (op-- (point (op* i u) (op* u  2))
                     (point (op* i u) (op* u -2)))
               #:withpen (scale '0.2bp 'pencircle))
         (draw (op-- (point (op* u  2) (op* i u))
                     (point (op* u -2) (op* i u)))
               #:withpen (scale '0.2bp 'pencircle))
         )))

127.2 the result of ex-127

Examples:
> (require "examples/ex-127.rkt")
> (make-figure "ex-127" main)

128 ex-128

128.1 source code in ex-128.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '5mm))
    (define (f x)
      (op- (op** x 2 ) 0.1))
    (define (my-draw x)
      (draw (scale u x)))
    (define (f-x x)
      (point x (f x)))
    (define (axes xmin xmax ymin ymax)
      (my-draw  (op-- (point xmin 0) (point xmax 0)))
      (my-draw  (op-- (point 0 ymin) (point 0 ymax))))
    (define (courbe f xmin xmax M)
      (let ((x-range (in-range xmin xmax (/ (- xmax xmin) M))))
        (my-draw (apply op-- (map f-x (stream->list x-range))))))
    (define (newton f y h M)
      (define (diff-f x)
        (op/ (op- (f (op+ x h)) (f x)) h))
      (define (newton-helper x)
        (op- x (op/ (f x) (diff-f x))))
      (for/fold ((x y)
                 (t (newton-helper y)))
          ((i (in-range M)))
        (my-draw (op-- (f-x x) (point t 0) (f-x t)))
        (values t (newton-helper x))))
    (axes -0.5 2 -0.5 4)
    (courbe f -0.5 2 100)
    (newton f 2 0.01 10)))

128.2 the result of ex-128

Examples:
> (require "examples/ex-128.rkt")
> (make-figure "ex-128" main)

129 ex-128-b

129.1 source code in ex-128-b.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '5mm))
    (define (f x)
      (op- (op** x 2 ) 0.1))
    (define (my-draw x)
      (draw (scale u x)))
    (define (f-x x)
      (point x (f x)))
    (define (axes xmin xmax ymin ymax)
      (my-draw  (op-- (point xmin 0) (point xmax 0)))
      (my-draw  (op-- (point 0 ymin) (point 0 ymax))))
    (define (courbe f xmin xmax M)
      (let ((x-range (in-range xmin xmax (/ (- xmax xmin) M))))
        (my-draw (apply op-- (map f-x (stream->list x-range))))))
    (define (newton f y h M)
      (define (diff-f x)
        (op/ (op- (f (op+ x h)) (f x)) h))
      (define (newton-helper x)
        (op- x (op/ (f x) (diff-f x))))
      (for/fold ((x y)
                 (t (newton-helper y)))
          ((i (in-range M)))
        (my-draw (op-- (f-x x) (point t 0) (f-x t)))
        (values t (newton-helper x))))
    (axes -0.5 2 -0.5 4)
    (courbe f -0.5 2 100)
    (newton f 2 0.01 10)))

129.2 the result of ex-128-b

Examples:
> (require "examples/ex-128-b.rkt")
> (make-figure "ex-128-b" main)

130 ex-129

130.1 source code in ex-129.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((T (unknown-transform))
         (u '1cm)
         (z0 (point 0 0))
         (z1 (point (op* 2 u) 0))
         (z3 (rotate 90 z1))
         (z2 (op+ z1 z3))
         (p (op-- z0 z1 z2 z3 'cycle)))
    (for ((a (in-list (list z0 z1 z2)))
          (b (in-list (list z1 z2 z3))))
         (eqn= (transform T a) (mediation 0.1 a b)))
    (fill p #:withcolor (op* 0.8 'white))
    (fill (transform T p) #:withcolor 'white)
    ))

130.2 the result of ex-129

Examples:
> (require "examples/ex-129.rkt")
> (make-figure "ex-129" main)

131 ex-130

131.1 source code in ex-130.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((T (unknown-transform))
         (u '1cm)
         (z0 (point 0 0))
         (z1 (point (op* 2 u) 0))
         (z3 (rotate 90 z1))
         (z2 (op+ z1 z3))
         (p (op-- z0 z1 z2 z3 'cycle)))
    (for ((a (in-list (list z0 z1 z2)))
          (b (in-list (list z1 z2 z3))))
         (eqn= (transform T a) (mediation 0.1 a b)))
    (for/fold ((p p))
        ((i (in-range 201)))
      (fill p #:withcolor (if (= (modulo i 2) 0)
                              (op* 0.8 'white)
                              'white))
      (transform T p))))

131.2 the result of ex-130

Examples:
> (require "examples/ex-130.rkt")
> (make-figure "ex-130" main)

132 ex-131

132.1 source code in ex-131.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((T (unknown-transform))
         (u '1cm)
         (z (point 0 (op* 2 u)))
         (n 5)
         (zn (map (lambda (i) (rotate (/ (* 360 i) n)
                                      z))
                  (stream->list (in-range n))))
         (p (apply op--  `(,@zn cycle))))
    (for ((i (in-range 1 4)))
         (eqn= (transform T (list-ref zn i))
               (mediation 0.1
                          (list-ref zn i)
                          (list-ref zn (+ 1 i)))))
    (for/fold ((p p))
        ((i (in-range 201)))
      (fill p #:withcolor (if (= (modulo i 2) 0)
                              (op* 0.8 'white)
                              'white))
      (transform T p))))

132.2 the result of ex-131

Examples:
> (require "examples/ex-131.rkt")
> (make-figure "ex-131" main)

133 ex-132

133.1 source code in ex-132.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (n 7)
         (A0 (point u 0))
         (An (map (lambda (i) (rotate (/ (* 360 i) n)
                                      A0))
                  (stream->list (in-range n)))))
    (for ((Ai (in-list An)))
         (draw Ai #:withpen (scale '4bp 'pencircle)))
    (for* ((i (in-range n))
           (j (in-range n)))
          (when (not (= i j))
            (draw (op-- (list-ref An i)
                        (list-ref An j)))))))

133.2 the result of ex-132

Examples:
> (require "examples/ex-132.rkt")
> (make-figure "ex-132" main)

134 ex-133

134.1 source code in ex-133.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (define (funcall f) (f))
  (let* ((u '2cm)
         (n 4)
         (m 5)
         (An (map funcall (make-list n unknown-point)))
         (Bn (map funcall (make-list m unknown-point))))
    (for ((Xn (in-list (list An Bn))))
         (for ((Xi (in-list Xn))
               (Xi+1 (in-list (cdr Xn))))
              (eqn= (op- Xi+1 Xi)
                    (point 0 (op* 0.2 u)))))
    (eqn= (apply op+ An) (point 0 0))
    (eqn= (apply op+ Bn) (point (op* 4 u) 0))
    (define (draw-point x) (draw x #:withpen (scale '4bp 'pencircle)))
    (map draw-point An)
    (map draw-point Bn)
    (for* ((Ai (in-list An))
           (Bi (in-list Bn)))
          (draw (op-- Ai Bi)))))

134.2 the result of ex-133

Examples:
> (require "examples/ex-133.rkt")
> (make-figure "ex-133" main)

135 ex-134

135.1 source code in ex-134.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (define (funcall f) (f))
  (let* ((u '1cm)
         (n 3)
         (m 3)
         (An (map funcall (make-list n unknown-point)))
         (Bn (map funcall (make-list m unknown-point))))
    (for ((Xn (in-list (list An Bn))))
         (for ((Xi (in-list Xn))
               (Xi+1 (in-list (cdr Xn))))
              (eqn= (op- Xi+1 Xi)
                    (point (op* 0.5 u) 0))))
    (eqn= (apply op+ An) (point 0 0))
    (eqn= (apply op+ Bn) (point 0 (op* 4 u)))
    (define (draw-point x) (draw x #:withpen (scale '4bp 'pencircle)))
    (map draw-point An)
    (map draw-point Bn)
    (for* ((Ai (in-list An))
           (Bi (in-list Bn)))
          (draw (op-- Ai Bi)))))

135.2 the result of ex-134

Examples:
> (require "examples/ex-134.rkt")
> (make-figure "ex-134" main)

136 ex-135

136.1 source code in ex-135.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((n 6)
         (P (lambda (d)
              (for/list ((i (in-range (+ 1 n))))
                        (rotate (/ (* i 360) n)
                                (op* d 'right)))))
         (An (P '1cm))
         (Bn (P '2cm)))
    (define (draw-point x) (draw x #:withpen (scale '4bp 'pencircle)))
    (map draw-point An)
    (map draw-point Bn)
    (for ((Ai (in-list An))
          (Ai+1 (in-list (cdr An)))
          (Bi (in-list Bn))
          (Bi+1 (in-list (cdr Bn))))
         (draw (op-- Ai Ai+1 Bi+1 Bi)))))

136.2 the result of ex-135

Examples:
> (require "examples/ex-135.rkt")
> (make-figure "ex-135" main)

137 ex-136

137.1 source code in ex-136.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((n 5)
         (O (point 0 0))
         (A (op* '1cm 'up))
         (B ((rotate-around A 30 )
             (op* '2cm 'up)))
         (C (op* '2cm 'up))
         (D ((rotate-around A -30)
             (op* '2cm 'up))))
    (define (draw-point x) (draw x #:withpen (scale '4bp 'pencircle)))
    (define ((rotate-draw i f) obj) (f (rotate (/ (* i 360) n) obj)))
    (for ((i (in-range n)))
         ((rotate-draw i draw) (op-- O A C))
         ((rotate-draw i draw) (op-- B A D))
         (map (rotate-draw i draw-point) (list A B C D)))))

137.2 the result of ex-136

Examples:
> (require "examples/ex-136.rkt")
> (make-figure "ex-136" main)

138 ex-137

138.1 source code in ex-137.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '1cm)
         (p (yscale (op* 3 u) (xscale (op* -1 u) 'fullcircle))))
    (draw p)
    (define (draw-point x) (draw x #:withpen (scale '4bp 'pencircle)))
    (for ((i (in-range 2 6.1 0.5)))
         (draw (path (point-of 2 p) (dir-spec 'down)
                     '..
                     (point-of i p))))))

138.2 the result of ex-137

Examples:
> (require "examples/ex-137.rkt")
> (make-figure "ex-137" main)

139 ex-138

139.1 source code in ex-138.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (define (i-of-360 i n) (/ (* 360 i ) n))
  (let* ((u '0.5cm)
         (P* (for/list ((i (in-range 5)))
                       (rotate (i-of-360 i 5)
                               (op* u 'down))))
         (P `(,@P* ,(car P*)))
         (Q* (for/list ((Pi (in-list P))
                        (Pi+1 (in-list (cdr P))))
                       (op* 3 (mediation 0.5 Pi Pi+1))))
         (Q `(,@Q* ,(car Q*)))
         (R* (for/list ((Qi (in-list Q))
                        (Qi+1 (in-list (cdr Q)))
                        (Pi+1 (in-list (cdr P))))
                       (op* 1/3 (op+ Qi Qi+1 Pi+1))))
         (R `(,@R* ,(car R*)))
         (S (map (curry op* 1.5) Q)))
    (for ((Pi (in-list P))
          (Pi+1 (in-list (cdr P)))
          (Qi (in-list Q))
          (Qi+1 (in-list (cdr Q)))
          (Ri (in-list R))
          (Si (in-list S))
          (Si+1 (in-list (cdr S))))
         (draw (op-- Pi Pi+1))
         (draw (op-- Pi+1 Ri))
         (draw (op-- Qi Ri))
         (draw (op-- Ri Qi+1))
         (draw (op-- Qi Si))
         (draw (op-- Si Si+1))
         )))

139.2 the result of ex-138

Examples:
> (require "examples/ex-138.rkt")
> (make-figure "ex-138" main)

140 ex-139

140.1 source code in ex-139.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (define (i-of-360 i n) (/ (* 360 i ) n))
  (let* ((u '0.5cm)
         (P* (for/list ((i (in-range 5)))
                       (rotate (i-of-360 i 5)
                               (op* u 'down))))
         (P `(,@P* ,(car P*)))
         (Q* (for/list ((Pi (in-list P))
                        (Pi+1 (in-list (cdr P))))
                       (op* 3 (mediation 0.5 Pi Pi+1))))
         (Q `(,@Q* ,(car Q*)))
         (R* (for/list ((Qi (in-list Q))
                        (Qi+1 (in-list (cdr Q)))
                        (Pi+1 (in-list (cdr P))))
                       (op* 1/3 (op+ Qi Qi+1 Pi+1))))
         (R `(,@R* ,(car R*)))
         (S (map (curry op* 1.5) Q)))
    (for ((Pi (in-list P))
          (Pi+1 (in-list (cdr P)))
          (Qi (in-list Q))
          (Qi+1 (in-list (cdr Q)))
          (Ri (in-list R))
          (Si (in-list S))
          (Si+1 (in-list (cdr S))))
         (draw (op-- Pi Pi+1))
         (draw (op-- Pi+1 Ri))
         (draw (op-- Qi Ri))
         (draw (op-- Ri Qi+1))
         (draw (op-- Qi Si))
         (draw (op-- Si Si+1)))
    (draw (op-- (list-ref P 2)  (list-ref P 3)  (list-ref P 4)  (list-ref P 0)  (list-ref P 1)
                (list-ref R 0)  (list-ref Q 0)  (list-ref R 4)  (list-ref Q 4)  (list-ref R 3)
                (list-ref Q 3)  (list-ref R 2)  (list-ref Q 2)
                (list-ref S 2)  (list-ref S 3)  (list-ref S 4)  (list-ref S 0)  (list-ref S 1)
                (list-ref Q 1)  (list-ref R 1)  'cycle)
          #:withpen (scale '2bp 'pencircle))))

140.2 the result of ex-139

Examples:
> (require "examples/ex-139.rkt")
> (make-figure "ex-139" main)

141 ex-140

141.1 source code in ex-140.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (for ((i (in-range 1.0 0.0 -0.01 )))
       (fill (fullcircle (op* i '2cm))
             #:withcolor (op* i 'white)))
  (draw (fullcircle '2cm)
        #:withpen (scale '2bp 'pencircle)))

141.2 the result of ex-140

Examples:
> (require "examples/ex-140.rkt")
> (make-figure "ex-140" main)

142 ex-141

142.1 source code in ex-141.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((u '5mm)
         (p (shift (point -1 0)
                   (op.. (point 0 0)
                         (point -1 1)
                         (point 2 0)
                         (point 0 -3)
                         'cycle))))
    (for ((i (in-range 1.0 0.0 -0.01 )))
         (fill (scale  (op* i u) p)
             #:withcolor (op* i 'white)))
    (draw (scale u p)
        #:withpen (scale '2bp 'pencircle))))

142.2 the result of ex-141

Examples:
> (require "examples/ex-141.rkt")
> (make-figure "ex-141" main)

143 ex-142

143.1 source code in ex-142.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((z0 (point 50 50))
         (z1 (rotate 90 z0))
         (z2 (rotate 90 z1))
         (z3 (rotate 90 z2))
         (carre (op-- z0 z1 z2 z3 'cycle))
         (s 0.01)
         (z4 (mediation s z2 z3))
         (z5 (mediation s z1 z0))
         (rect (op-- z1 z2 z3 z4 z5 'cycle)))
    (for ((i (in-range 0.0 1.0 s )))
         (fill (shift (op* i (op- z0 z1)) rect)
               #:withcolor (op* i 'white)))
    (draw carre
          #:withpen (scale '2bp 'pencircle))))

143.2 the result of ex-142

Examples:
> (require "examples/ex-142.rkt")
> (make-figure "ex-142" main)

144 ex-143

144.1 source code in ex-143.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (let* ((z0 (point 50 50))
         (z1 (rotate 90 z0))
         (z2 (rotate 90 z1))
         (z3 (rotate 90 z2))
         (carre (op-- z0 z1 z2 z3 'cycle))
         (s 0.01))
    (for ((i (in-range 1  s (- s) )))
         (fill (scale i carre)
               #:withcolor (op* i 'white)))))

144.2 the result of ex-143

Examples:
> (require "examples/ex-143.rkt")
> (make-figure "ex-143" main)

145 ex-144

145.1 source code in ex-144.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (define (degrade q p M N)
    (let ((a (length p))
          (b (length q)))
      (for ((i (in-range 0 (+ 1 M))))
           (draw (apply op..
                        `(,(mediation (/ i M) (point-of 0 p) (point-of 0 q))
                          ,@(for/list ((j (in-range 0 (+ 1 N))))
                                      (mediation (/ i M )
                                                 (point-of (op* a (/ j N)) p)
                                                 (point-of (op* b (/ j N)) q)))))))))
  (let* ((u '1cm))
    (degrade (op.. (point (op* -0.1 u)
                          (op* -0.1 u))
                   (point (op* 0.1 u)
                          (op* 0.1 u))
                   'cycle)
             (op-- (point (op* -1 u)
                          (op* -1 u))
                   (point (op*  1 u)
                          (op* -1 u))
                   (point (op*  1 u)
                          (op*  1 u))
                   (point (op* -1 u)
                          (op*  1 u))
                   'cycle) 10 100)))

145.2 the result of ex-144

Examples:
> (require "examples/ex-144.rkt")
> (make-figure "ex-144" main)

146 ex-145

146.1 source code in ex-145.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (define (couleur c) (op* (- 1.0 c) 'white))
  (define (degrade q p M N)
    (let ((a (length p))
          (b (length q)))
      (for ((i (in-range 0 (+ 1 M))))
           (draw (apply op..
                        `(,(mediation (/ i M) (point-of 0 p) (point-of 0 q))
                          ,@(for/list ((j (in-range 0 (+ 1 N))))
                                      (mediation (/ i M )
                                                 (point-of (op* a (/ j N)) p)
                                                 (point-of (op* b (/ j N)) q)))))
                 #:withcolor (couleur (/ i M))))))

  (let* ((u '1cm))
    (degrade (op.. (point (op* -0.5 u)
                          (op* -0.5 u))
                   (point (op* 0.5 u)
                          (op* 0.5 u))
                   'cycle)
             (op-- (point (op* -1 u)
                          (op* -1 u))
                   (point (op*  1 u)
                          (op* -1 u))
                   (point (op*  1 u)
                          (op*  1 u))
                   (point (op* -1 u)
                          (op*  1 u))
                   'cycle) 70 100)))

146.2 the result of ex-145

Examples:
> (require "examples/ex-145.rkt")
> (make-figure "ex-145" main)

147 ex-146

147.1 source code in ex-146.rkt

#lang racket
(require (planet wcy/mpost-wrapper))
(provide main)
(define (main)
  (define (couleur c) (op* (- 1.0 c) 'white))
  (define (d-s-j-n c j M n p)
    (direction-of c
                  (subpath-of
                   (op/ (op* (- j 1) n) M)
                   (op/ (op* j n) M) p)))
  (define (degrade q p N)
    (let* ((n (length p))
           (m (length q))
           (M (*  8 4);; (op* m n)
              ))
      (for ((i (in-range 0 (+ 1 N))))
           (draw (apply path
                        `(,(mediation (/ i N) (point-of 0 p) (point-of 0 q))
                          ,(dir-spec (mediation (/ i N)
                                                (direction-of 0 p)
                                                (direction-of 0 q)))
                          ,@(flatten
                             (for/list ((j (in-range 1 M)))
                                       `(..
                                         ,(dir-spec
                                           (mediation
                                            (/ i N)
                                            (d-s-j-n 1 j M n p)
                                            (d-s-j-n 1 j M m q)))
                                         ,(mediation (/ i N)
                                                     (point-of (op/ (op* j n) M) p)
                                                     (point-of (op/ (op* j m) M) q))
                                         ,(dir-spec
                                           (mediation
                                            (/ i N)
                                            (d-s-j-n 1 (+ j 1) M n p)
                                            (d-s-j-n 1 (+ j 1) M m q))))))
                          ..
                          ,(dir-spec
                            (mediation (/ i N)
                                       (direction-of n p)
                                       (direction-of m q)))
                          ,(mediation (/ i N)
                                      (point-of n p)
                                      (point-of m q))))))))
  (let* ((u '2cm)
         (p (fullcircle u))
         (q (op-- (point (op* -1 u)
                         (op* -1 u))
                  (point (op*  1 u)
                         (op* -1 u))
                  (point (op*  1 u)
                         (op*  1 u))
                  (point (op* -1 u)
                         (op*  1 u))
                  'cycle)))
    (degrade p q 10)))

147.2 the result of ex-146

Examples:
> (require "examples/ex-146.rkt")
> (make-figure "ex-146" main)

1	ex-1
2	ex-2
3	ex-3
4	ex-4
5	ex-5
6	ex-6
7	ex-7
8	ex-8
9	ex-9
10	ex-10
11	ex-11
12	ex-12
13	ex-13
14	ex-14
15	ex-15
16	ex-16
17	ex-17
18	ex-18
19	ex-19
20	ex-20
21	ex-21
22	ex-22
23	ex-23
24	ex-24
25	ex-25
26	ex-26
27	ex-27
28	ex-28
29	ex-29
30	ex-30
31	ex-31
32	ex-32
33	ex-33
34	ex-34
35	ex-35
36	ex-36
37	ex-37
38	ex-38
39	ex-39
40	ex-40
41	ex-41
42	ex-42
43	ex-43
44	ex-44
45	ex-45
46	ex-46
47	ex-47
48	ex-48
49	ex-49
50	ex-50
51	ex-51
52	ex-52
53	ex-53
54	ex-54
55	ex-55
56	ex-56
57	ex-57
58	ex-58
59	ex-59
60	ex-60
61	ex-61
62	ex-62
63	ex-63
64	ex-64
65	ex-65
66	ex-66
67	ex-67
68	ex-68
69	ex-69
70	ex-70
71	ex-71
72	ex-72
73	ex-73
74	ex-74
75	ex-75
76	ex-76
77	ex-77
78	ex-78
79	ex-79
80	ex-80
81	ex-81
82	ex-82
83	ex-83
84	ex-84
85	ex-85
86	ex-86
87	ex-87
88	ex-88
89	ex-89
90	ex-90
91	ex-91
92	ex-92
93	ex-93
94	ex-94
95	ex-95
96	ex-96
97	ex-97
98	ex-98
99	ex-99
100	ex-100
101	ex-101
102	ex-102
103	ex-103
104	ex-104
105	ex-105
106	ex-106
107	ex-107
108	ex-108
109	ex-109
110	ex-110
111	ex-111
112	ex-112
113	ex-113
114	ex-114
115	ex-115
116	ex-116
117	ex-117
118	ex-118
119	ex-119
120	ex-120
121	ex-121
122	ex-122
123	ex-123
124	ex-124
125	ex-125
126	ex-126
127	ex-127
128	ex-128
129	ex-128-b
130	ex-129
131	ex-130
132	ex-131
133	ex-132
134	ex-133
135	ex-134
136	ex-135
137	ex-136
138	ex-137
139	ex-138
140	ex-139
141	ex-140
142	ex-141
143	ex-142
144	ex-143
145	ex-144
146	ex-145
147	ex-146