[plt-scheme] Image identity hackery

Although this is a little bit more tricky in 2htdp, since I added not
just 0x0 sized images, but also 0xN and Nx0 sized images. Sometimes
they can evaporate and sometimes they can't depending on if they
"stick out" or not and change the bounding box.

Robby

On Thu, Dec 3, 2009 at 7:56 PM, Matthias Felleisen <matthias at ccs.neu.edu> wrote:
>
> Just to clarify, you can also do this:
>
>  (require 2htdp/universe)
>
>  (define id-image (color-list->image empty 0 0 0 0))
>  (define id-image2 (circle 0 'solid 'white))
>  (define id-image3 (circle 0 'solid 'red))
>  (define id-image4 (rectangle 0 0 'solid 'red))
>
>  (image=? id-image id-image2)
>  (image=? id-image2 id-image3)
>  (image=? id-image3 id-image4)
>
> i.e., your image is a 0-sized image. Several of us
> begged Robby until he added this -- precisely because
> it is the identity element of the image "algebra".
> (I don't know how to get inverses for all images,
> so images + overlay really just a monoid -- but
> I wouldn't mind being convinced otherwise.)
>
> And once you have that, it is trivial to define
> your function as
>
>  ;; make-swatches : loc number number -> image
>  ;; creates a rectangle showing the colors in the list from left to
>  ;; right, each as rectangle with width w and height h.
>  (define (make-swatches l w h)
>    (foldr (lambda (f r) (overlay/xy (nw:rectangle w h 'solid f) w 0 r)) ID l))
>
> Keep in mind that fold{l|r} needs the identity element
> to do this elegantly.
>
> -- Matthias
>
>
>
>
>
> On Dec 3, 2009, at 8:21 PM, Jordan Johnson wrote:
>
>>
>> Hi all,
>>
>> Last year I had a student ask me:  Hey, if
>>
>>    (sum empty)
>>
>> is 0, and
>>
>>    (product empty)
>>
>> is 1, what can we use for some function that makes an image?
>>
>> This led to a neat little discussion of inverses with respect to a given
>> operation, and we didn't pursue the image question much beyond musing
>> that there's no obvious image I such that
>>
>>    (overlay X I) = X
>> or
>>    (overlay I X) = X
>>
>> for all x (in the sense of image=?).
>>
>> Today I gave the students an assignment involving color-lists, and one
>> student observed that
>>
>>    (image->color-list (color-list->image empty 0 0 0 0))
>>
>> produces the empty list.  We experimented, and found that the image
>> given by
>>
>>    (color-list->image empty 0 0 0 0)
>>
>> satisfies the overlay equations given above.  For that matter, it also
>> satisfies
>>
>>    (overlay/xy I 0 0 X) = X
>> and (overlay/xy X m n I) = X
>>
>> for all m in [0, (image-width X)] and n in [0, (image-height X)].
>>
>> I get the impression the HtDP image code wasn't intentionally written to
>> handle this as an "identity image" -- it breaks rather gracelessly when
>> used as a background scene for place-image, for example -- but it still
>> afforded me a neat conversation with the student and some interesting
>> coding after class (see below).
>>
>> Has anybody else played with this at all?
>>
>> Best,
>> jmj
>>
>> ;; ----- sample code -----
>>
>> ;; loc = listof[color]
>>
>> (define id-image (color-list->image empty 0 0 0 0))
>>
>> ;; make-swatches : loc number number -> image
>> ;; creates a rectangle showing the colors in the list from left to
>> ;; right, each as rectangle with width w and height h.
>> (define (make-swatches aloc w h)
>>  (cond
>>    [(empty? aloc) id-image]
>>    [(cons? aloc)
>>     (overlay/xy (nw:rectangle w h 'solid (first aloc))
>>                 w 0
>>                 (make-swatches (rest aloc) w h))]))
>>
>> (check-expect (make-swatches (list 'red 'blue 'green) 20 30)
>>              (overlay/xy (nw:rectangle 20 30 'solid 'red)
>>                          20 0
>>                          (overlay/xy (nw:rectangle 20 30 'solid 'blue)
>>                                      20 0
>>                                      (nw:rectangle 20 30 'solid 'green))))
>> _________________________________________________
>> For list-related administrative tasks:
>> http://list.cs.brown.edu/mailman/listinfo/plt-scheme
>
> _________________________________________________
>  For list-related administrative tasks:
>  http://list.cs.brown.edu/mailman/listinfo/plt-scheme
>