TweetFollow Us on Twitter

3-D Rotation
Volume Number:1
Issue Number:13
Column Tag:Lisp Listener

3-D Rotations

By Andy Cohen, Engineer, MacTutor Contributing Editor

Mapping Functions

Applicative operators are functions which use other functions as inputs. One of the most typical across Lisp dialects is MAPCAR. MAPCAR can perform an operation on each member of one given list, sequentially. It is therefore another form of iteration. MAPCAR operates in the same manner APPLY works in the following:

(apply + '(2 3 4 5))
14

MAPCAR, however, provides the capability to perform a given function for each atom within a given list. It can be seen as an "APPLY_TO_ALL". For example, suppose one wanted the square root of each value in a list of five values and create a corresponding list of these square roots. One way to do this is to remove the values from the list with nested CARS. Then, after applying the SQRT function to each value, a new list would need to be produced with a CONS. This method might get needlessly tedious. MAPCAR makes it possible to get this list in a much more convenient fashion.

(MAPCAR (lambda (x) (SQRT x)) '(2 3 4 5))
(1.41421356 1.73205080 2. 2.23606797)

LAMBDA is a special word that tells Lisp that what is following is to be treated as a function similar to DEFUN. LAMBDA acts like a one time only DEFUN. The (x) is the passed value and the list with the square root primitive is the expression to be carried out. MAPCAR takes the first value from the list (2 3 4 5) sequentially (that is why it is MAPCAR) and places it into x. It then puts each computed value into a list. How about another sample:

(setq x '(2 5)) (setq y '(5 7))
(mapcar (lambda (n) (* .5 n)) (append x y)))
(2  5 )
(5  7 )
(1.  2.5  2.5  3.5 )

APPEND puts the values represented by the symbols x and y into a list. MAPCAR takes one atom at a time from the new list and multiplies it by .5.

MAPLIST is another form of mapping or sequencing function. However, instead of sequencing through a list one atom at a time MAPLIST performs a function on two entire lists. For example:

(MAPLIST APPEND '(A B C) '(D E F))
((A B C D E F)(B C E F)(C F))

MAPLIST removes the first atom of both lists and performs the function on the two new lists. It then removes the next two atoms and performs the function on the two lists with the remaining atoms. This continues until there are no more atoms in one of the two lists. The lists do not have to contain the same number of atoms.

(MAPLIST APPEND '(A B C) '(D E F G H))
((A B C D E F G H)(B C E F G H)
 (C F G H))

MAPCAN and MAPCON are just like MAPCAR and MAPLIST, respectively except that they do not return lists that are made using LIST. MAPCAN and MAPCON use NCONC. NCONC takes the values from two lists and places all of them into the first, thereby destroying the original list. For example:

(SETQ x '(1 2 3 4) y '(5 6 7 8))
(NCONC x y)
(5 6 7 8)
(1 2 3 4 5 6 7 8)
x
(1 2 3 4 5 6 7 8)
y
(5 6 7 8)

NCONC put all eight values into "x" while it left "y" alone. Since it changed "x" it is considered destructive.An example using MAPCAN follows:

(MAPCAN (LAMBDA (x) (AND (NUMBERP x)              (SETQ y (SQRT x)) (LIST 
y)))'(2 3 4 5 A))
(1.41421356 1.73205080 2. 2.23606797)

The AND and the NUMBERP functions in the above, give indication as to when the numbers in the list end by having NUMBERP return nil from the letter "A". AND then stops evaluation. Otherwise the SETQ assigns the square root of each atom to "y" then places it within a list with LIST. Since MAPCAN was used each of the returned values were NCONCed into "y". If one used MAPCAR each value would be placed into a list represented by "y" which would then be placed into the resulting list. The SETQ changes "y" for each value and the resulting list is quite different.

(MAPCAR (LAMBDA (x) (AND (NUMBERP x)              (SETQ y (SQRT x)) (LIST 
y)))'(2 3 4 5 A))
((1.41421356)(1.73205080)(2.)
                     (2.23606797 ) nil)

MAPC and MAPL are also related to MAPCAR and MAPLIST, respectively. These functions are supposed to return the original input list of values instead of a list of resultant values. They are typically used for their side effect such as assigning a new value to a global variable. Unfortunately they don't seem to return results in this manner. Instead of returning the original input list, they both return nil.

EVERY is a totally different type of sequencing function. EVERY applies a predicate to each atom in a list.If the predicate returns "t" for each atom EVERY returns "t". If the predicate returns nil at least once so does EVERY.

(EVERY NUMBERP '(1 2 3 4 5))
t 
(EVERY NUMBERP '(1 2 A 4 5))
nil

One interesting feature about EVERY is that one may specify how EVERY will sequence through the list. Without specifying the sequence EVERY defaults to CDR as a step. For example, if we take the second EVERY example above and step through the list with a CDDDR, it returns "t" since the CDDDR makes the evaluation of the predicate skip the letter "A".

(EVERY NUMBERP '(1 2 A 4 5) cdddr)
t

FIND-IF applies a predicate function to each atom in a list until the predicate returns "t". FIND-IF returns the atom which satisfies the predicate then ends the evaluation.

(FIND-IF EVENP '(3 5 7 8 10))
8
(FIND-IF (lambda (x) (> x 5)) '(2 3 4 5 6 7 8))
6

FIND-IF-NOT does the exact opposite of FIND-IF. It returns the first atom of a list which does not satisfy the predicate.

(FIND-IF EVENP '(2 3 5 7 8))
3
(FIND-IF-NOT  (lambda (x) (> x 5)) '(2 3 4 5 6))
2

REDUCE performs a function that requires two inputs. It performs the function on the first two atoms of a list, starting from left to right, then performs the function upon the result of the first two with the very next atom. It then performs the same function with the second result with the next atom. It returns the result when no more atoms are available. For example the following multiplies a sequence of numeric values:

(REDUCE  * '(7 6 13 76))
41496

If one places a T before the last closing parenthesis REDUCE performs the same function on the list from right to left.

(REDUCE - '(7 6 13 76))
-88

The above is equal to (-(-(-7 6)13)76).

 (REDUCE - '(7 6 13 76) T) 
-62

The above is now equal to (- 7 (- 6 (- 13 76))).

NOTANY is the equivalent of (NOT (EVERY.... It returns "t" if none of the atoms of a list satisfy the given predicate.

NOTEVERY is the same as FIND-IF-NOT. However, instead of returning the value that did not satisfy the predicate NOTEVERY returns "t" as follows:

(NOTEVERY  (lambda (x) (> x 5)) '(2 3 4 5 6))
t

Besides MAPC and MAPL there is one more mapping function which not only doesnt work as the literature (Common Lisp by Guy Steele) describes it, but just doesnt seem to work in ExperLisp version 1.04. This function is called SOME. SOME is supposed to look successively to the elements of a list and stop when it finds an element which satisfies a predicate function. The following should return the number five:

(defun try (x)
  (oddp x))

(SOME try '(2 4 5))

Instead of returning "5" after the defined function name, "unbound variable f" is returned along with a dump of what seems to be the heap.We will be talking to ExperTelligence about the status of these functions.

Last month I mentioned that we would be starting a tutorial on ExperOps5 in this month's issue. Unfortunately, the author of that segment did not make the deadline. We hope to start the tutorial as soon as we can, if it is possible, in coming Mactutor issues. Instead, we are again treated to a nifty program by Dean Ritz of ExperTelligence. The following functions build a small pyramid-like object in three dimensions. Three controls are also produced as seen in Figure 1. These controls rotate the object along three different planes and at varying speeds. After compiling, type (Tetrahedron) into the Listener window and enjoy!

By the way, Happy Holidays!

;••••••••••••••••••••••••••••••••
;TETRAHEDRON animates a tetrahedron rotating in ;3-Dimensional space. 
 
;It allows a person to adjust the rate of rotation
;through the use of mouse sensative controls.
;Produced by Dean Ritz of ExperTelligence
(defun tetrahedron (&aux (curbun (new3dbun)))
  (setq xx 0
        yy 0
        zz 0
        xboxes '((60  -100  80  -80) (60  -80  80  -60))
        yboxes '((60  -40  80  -20) (60  -20  80  0))
        zboxes '((60  20  80  40) (60  40  80  60))
        quit '(60  80  80  120)
        std_graf (newgrafwindow '(45 5 310 500)))
  (std_graf 'setwtitle "ExperTetrahedron")
  (std_graf 'showwindow)
  (std_graf 'selectwindow)
  (textface 0) (pendown)
  (draw.controls)
  (penup) (home) (forward 40)
  (pendown)
  (catch 'flag (doit 1))
  (disposhandle (coercetype $68 curbun))
  (std_graf 'closewindow))

(defmacro rac (l)
  `(car (last ,l)))

;Hitting a key represent
(defun doit (tt &aux speed)
  (cond ((keyp) 
         (setq speed (read-char))
         (if (numberp speed) (setq tt speed))))
  (if (button) (adjust.controls))
  (roll yy)
  (pitch xx)
  (yaw zz)
  (fillrect '(-130 -100 50 100) white)
  (dotimes  (i tt) (tetra 70))
  (doit tt))

;* * * * * * * * * * * * * * * * *
;DRAW.CONTROLS draws the mouse sensative controls.

(defun draw.controls ()
  (moveto -100 75)
  (drawstring "  -   +")
  (framerect (car xboxes))
  (framerect (rac xboxes))
  (moveto -40 75)
  (drawstring "  -   +")
  (framerect (car yboxes))
  (framerect (rac yboxes))
  (moveto 20 75)
  (drawstring "  -   +")
  (framerect (car zboxes))
  (framerect (rac zboxes))
  (moveto 80 75)
  (drawstring "  Quit")
  (framerect quit)
  (moveto -100 100)
  (drawstring " Roll         Pitch        Yaw"))

;* * * * * * * * * * * * * * * * *
;ADJUST.CONTROLS is only called if the mouse button is ;depressed.
;It is responsible for calling the commands which adjust the
;rotation of the tetrahedron.  It also sets the QUIT flag if
;the mouse is clicked in the "Quit" box.
(defun adjust.controls (&aux (point (getmouse)))
  (cond ((pt.in.rect (car point) (rac point) '(60 -100 80 -60))
         (apply adjust.x point))
        ((pt.in.rect (car point) (rac point) '(60 -40 80 0))
         (apply adjust.y point))
        ((pt.in.rect (car point) (rac point) '(60 20 80 60))
         (apply adjust.z point))
        ((pt.in.rect (car point) (rac point) quit)
         (invertrect quit)
         (wait) (invertrect quit)
         (throw 'flag))))

;* * * * * * * * * * * * * * * * * 
;The three commands ADJUST.X, ADJUST.Z, and ADJUST.Y ;are only
;called if the mouse is clicked while on one of the controls.
;It inverts the proper button (box), increments a global
;variable for moving the bunny, waits for the mouse button to
;be released, and then re-inverts the button.
(defun adjust.x (x y)
  (cond ((pt.in.rect x y (car xboxes))
         (invertrect (car xboxes))
         (setq xx (- xx 2))
         (wait)
         (invertrect (car xboxes)))
        (t 
          (invertrect (rac xboxes))
          (setq xx (+ xx 2))
          (wait)
          (invertrect (rac xboxes)))))

(defun adjust.z (x y)
  (cond ((pt.in.rect x y (car zboxes))
         (invertrect (car zboxes))
         (setq zz (- zz 2))
         (wait)
         (invertrect (car zboxes)))
        (t
          (invertrect (rac zboxes))
          (setq zz (+ zz 2))
          (wait)
          (invertrect (rac zboxes)))))

(defun adjust.y (x y)
  (cond ((pt.in.rect x y (car yboxes))
         (invertrect (car yboxes))
         (setq yy (- yy 2))
         (wait)
         (invertrect (car yboxes)))
        (t
          (invertrect (rac yboxes))
          (setq yy (+ yy 2))
          (wait)
          (invertrect (rac yboxes)))))

;* * * * * * * * * * * * * * * * * 

;WAIT waits until the mouse button
; is depressed.Then it returns control
; to the calling function.
(defun wait ()
  (prog ()
        top
        (if (button) 
            (go top))))

;* * * * * * * * * * * * * * * * * 
;TETRA and PART draw a tetrahedron 
 ;using 3-D bunny graphics.
(defun tetra (s)
 (dotimes (i 3) 
          (part s) (roll 90) 
          (lt -45) (fd s) 
          (bk s) (lt 45) (roll -90)))

(defun part (s)
 (lt 45) (fd s) (rt 45)
 (pitch 90)
 (rt 45) (fd s) (bk s) (lt 45)
 (roll -90))

;* * * * * * * * * * * * * * * * * 

;PT.IN.RECT tests to see whether an specific X and Y ;coordiate
;lies within a given boundary rectangle :RECT.
;RECT whould be a list of [TOP LEFT BOTTOM RIGHT] ;coordinates.
(defun pt.in.rect (x y rect)
  (and (< x (nth 3 rect))
       (  x (nth 1 rect))
       (¾ y (nth 2 rect))
       (  y (nth 0 rect))
       t))  ;returns T if true, NIL otherwise
 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Tidy Up 5.3.7 - Find duplicate files and...
Tidy Up is a full-featured duplicate finder and disk-tidiness utility. Features: Supports Lightroom: it is now possible to search and collect duplicates directly in the Lightroom library. Multiple... Read more
Pinegrow 5.97 - Mockup and design web pa...
Pinegrow (was Pinegrow Web Designer) is desktop app that lets you mockup and design webpages faster with multi-page editing, CSS and LESS styling, and smart components for Bootstrap, Foundation,... Read more
BlueStacks 4.210.0 - Run Android applica...
BlueStacks App Player lets you run your Android apps fast and fullscreen on your Mac. Feature comparison chart How to install Bluestacks on your Mac Go to MacUpdate and click the green "Download"... Read more
WhatsApp 2.2027.10 - Desktop client for...
WhatsApp is the desktop client for WhatsApp Messenger, a cross-platform mobile messaging app which allows you to exchange messages without having to pay for SMS. WhatsApp Messenger is available for... Read more
Art Text 4.0.1 - $29.99
Art Text is graphic design software specifically tuned for lettering, typography, text mockups and various artistic text effects. Supplied with a great variety of ready to use styles and materials,... Read more
Adobe Dreamweaver CC 2020 20.2 - Build w...
Dreamweaver CC 2020 is available as part of Adobe Creative Cloud for as little as $20.99/month (or $9.99/month if you're a previous Dreamweaver customer). Adobe Dreamweaver CC 2020 allows you to... Read more
Adobe Acrobat DC 20.009.20074 - Powerful...
Acrobat DC is available only as a part of Adobe Creative Cloud, and can only be installed and/or updated through Adobe's Creative Cloud app. Adobe Acrobat DC with Adobe Document Cloud services is... Read more
beaTunes 5.2.10 - Organize your music co...
beaTunes is a full-featured music player and organizational tool for music collections. How well organized is your music library? Are your artists always spelled the same way? Any R.E.M. vs REM?... Read more
DiskCatalogMaker 8.1.5 - Catalog your di...
DiskCatalogMaker is a simple disk management tool which catalogs disks. Simple, light-weight, and fast Finder-like intuitive look and feel Super-fast search algorithm Can compress catalog data for... Read more
Meteorologist 3.4.1 - Popular weather ap...
Meteorologist is a simple interface to weather provided by weather.com. It provides the ability to show the weather in the main menu bar, displaying more detail in a pop-up menu, whose contents are... Read more

Latest Forum Discussions

See All

Steam Link Spotlight - Disco Elysium
Steam Link Spotlight is a feature where we look at PC games that play exceptionally well using the Steam Link app. Our last entry was Signs of the Sojourner Read about how it plays using Steam Link over here. | Read more »
Distract Yourself With These Great Mobil...
There’s a lot going on right now, and I don’t really feel like trying to write some kind of pithy intro for it. All I’ll say is lots of people have been coming together and helping each other in small ways, and I’m choosing to focus on that as I... | Read more »
Pokemon Go's July Community Day wil...
Pokemon Go developers have announced the details concerning the upcoming Gastly Community Day. This particular event was selected by the players of the game after the Gas Pokemon came in second place after a poll that decided which Pokemon would... | Read more »
Clash Royale: The Road to Legendary Aren...
Supercell recently celebrated its 10th anniversary and their best title, Clash Royale, is as good as it's ever been. Even for lapsed players, returning to the game is as easy as can be. If you want to join us in picking the game back up, we've put... | Read more »
Detective Di is a point-and-click murder...
Detective Di is a point-and-click murder mystery set in Tang Dynasty-era China. You'll take on the role of China's best-known investigator, Di Renjie, as he solves a series of grisly murders that will ultimately lead him on a collision course with... | Read more »
Dissidia Final Fantasy Opera Omnia is se...
Dissidia Final Fantasy Opera Omnia, one of Square Enix's many popular mobile RPGs, has announced a plethora of in-game events that are set to take place over the summer. This will include several rewards, Free Multi Draws and more. [Read more] | Read more »
Sphaze is a neat-looking puzzler where y...
Sphaze is a neat-looking puzzler where you'll work to guide robots through increasingly elaborate mazes. It's set in a visually distinct world that's equal parts fantasy and sci-fi, and it's finally launched today for iOS and Android devices. [... | Read more »
Apple Arcade is in trouble
Yesterday, Bloomberg reported that Apple is disappointed in the performance of Apple Arcade and will be shifting their approach to the service by focusing on games that can retain subscribers and canceling other upcoming releases that don't fit... | Read more »
Pixel Petz, an inventive platform for de...
Pixel Petz has built up a sizeable player base thanks to its layered, easy-to-understand creative tools and friendly social experience. It revolves around designing, trading, and playing with a unique collection of pixel art pets, and it's out now... | Read more »
The King of Fighters Allstar's late...
The King of Fighters ALLSTAR, Netmarble's popular action RPG, has once again been updated with a plethora of new content. This includes battle cards, events and 21 new fighters, which increases the already sizeable roster even more. [Read more] | Read more »

Price Scanner via MacPrices.net

Clearance 2019 13″ 2.4GHz/256GB MacBook Pro o...
B&H Photo has dropped their price on the clearance 2019 13″ 2.4GHz/256GB Quad-Core Silver MacBook Pro by $500 off Apple’s original MSRP to a new low of only $1299. Expedited shipping is free to... Read more
$219 Apple AirPods Pro are back at Verizon, s...
Verizon has Apple AirPods Pro on sale again for a limited time for $219.99 on their online store. Their price is $30 off Apple’s MSRP, and it’s the lowest price we’ve seen for AirPods Pro. Available... Read more
Apple’s $779 13″ MacBook Air deal returns to...
Apple has clearance, Certified Refurbished, 2019 13″ MacBook Airs available again starting at $779. Each MacBook features a new outer case, comes with a standard Apple one-year warranty, and is... Read more
$200 13″ MacBook Pro discounts are back at Am...
Amazon has 2020 13″ 2.0GHz MacBook Pros on sale again today for $150-$200 off Apple’s MSRP. Shipping is free. Be sure to purchase the MacBook Pro from Amazon, rather than a third-party seller, and... Read more
Deal Alert! Apple AirPods with Wireless Charg...
Sams Club has Apple AirPods with Wireless Charging Case on sale on their online store for only $149.98 from July 6, 2020 to July 9, 2020. Their price is $50 off Apple’s MSRP, and it’s the lowest... Read more
Xfinity Mobile promo: Apple iPhone XS models...
Take $300 off the purchase of any Apple iPhone XS model at Xfinity Mobile while supplies last. Service plan required: – 64GB iPhone XS: $599.99 save $300 – 256GB iPhone XS: $749.99 save $300 – 512GB... Read more
New July 2020 promo at US Cellular: Switch an...
US Cellular has introduced a new July 2020 deal offering free 64GB Apple iPhone 11 smartphones to customers opening a new line of service. No trade-in required, and discounts are applied via monthly... Read more
Apple offers up to $400 Education discount on...
Apple has launched their Back to School promotion for 2020. They will include one free pair Apple AirPods (with charging case) with the purchase of a MacBook Air, MacBook Pro, iMac, or iMac Pro (Mac... Read more
July 4th Sale: Woot offers wide range of Macs...
Amazon-owned Woot is blowing out a wide range of Apple Macs and iPads for July 4th staring at $279 and ranging up to just over $1000. Models vary from older iPads and 11″ MacBook Airs to some newer... Read more
Apple Pro Display XDR with Nano-Texture Glass...
Abt Electronics has Apple’s new 32″ Pro Display XDR model with the nano-texture glass in stock and on sale today for up to $144 off MSRP. Shipping is free: – Pro Display XDR (nano-texture glass): $... Read more

Jobs Board

Physical Therapist Assistant - *Apple* Hill...
Physical Therapist Assistant - Apple Hill Rehab - Full Time Tracking Code 62519 Job Description General Summary: Under the direct supervision of a licensed Physical Read more
Operating Room Assistant, *Apple* Hill Surg...
Operating Room Assistant, Apple Hill Surgical Center - Full Time, Day Shift, Monday - Saturday availability required Tracking Code 62363 Job Description Operating Read more
Perioperative RN - ( *Apple* Hill Surgical C...
Perioperative RN - ( Apple Hill Surgical Center) Tracking Code 60593 Job Description Monday - Friday - Full Time Days Possible Saturdays General Summary: Under the Read more
Product Manager, *Apple* Commercial Sales -...
Product Manager, Apple Commercial Sales Austin, TX, US Requisition Number:77652 As an Apple Product Manager for the Commercial Sales team at Insight, you Read more
*Apple* Mac Product Engineer - Barclays (Uni...
Apple Mac EngineerWhippany, NJ Support the development and delivery of solutions, products, and capabilities into the Barclays environment working across technical Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.