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

Trend Micro 11.0.2062 - An essential sec...
Trend Micro Antivirus provides essential security for macOS with real-time malware detection and mitigation in an affordable solution with a simple, intuitive interface. However, be aware that more... Read more
Backblaze 7.0.2.490 - Online backup serv...
Backblaze is an online backup service designed from the ground-up for the Mac. With unlimited storage available for $6 per month, as well as a free 15-day trial, peace of mind is within reach with... Read more
Pro Video Formats 2.2.1 - Updates for pr...
Pro Video Formats includes support for the following professional video codecs: Apple Intermediate Codec Apple ProRes AVC-Intra 50 / 100 / 200 / 4:4:4 / LT AVC-LongG XAVC XF-AVC DVCPRO HD HDV XDCAM... Read more
Boom 3D 1.3.11 - $19.99
Boom 3D is a revolutionary app with 3D Surround Sound and phenomenally rich and intense audio that is realistic and works on any headphones. Features 3D surround sound Built-in audio player... Read more
Final Cut Pro 10.5.2 - Professional vide...
Redesigned from the ground up, Final Cut Pro combines revolutionary video editing with a powerful media organization and incredible performance to let you create at the speed of thought.... Read more
Chromium 89.0.4389.72 - Fast and stable...
Chromium is an open-source browser project that aims to build a safer, faster, and more stable way for all Internet users to experience the web. Version 89.0.4389.72: Complete list of changes can... Read more
iMovie 10.2.3 - Edit personal videos and...
With a streamlined design and intuitive editing features, iMovie lets you create Hollywood-style trailers and beautiful movies like never before. Browse your video library, share favorite moments,... Read more
OmniPlan 4.2.5 - Professional-grade proj...
With OmniPlan, you can create logical, manageable project plans with Gantt charts, schedules, summaries, milestones, and critical paths. Break down the tasks needed to make your project a success,... Read more
Compressor 4.5.2 - Adds power and flexib...
Compressor adds power and flexibility to Final Cut Pro X export. Customize output settings, work faster with distributed encoding, and tap into a comprehensive set of delivery features. Features:... Read more
Motion 5.5.1 - Create and customize Fina...
Motion is designed for video editors, Motion 5 lets you customize Final Cut Pro titles, transitions, and effects. Or create your own dazzling animations in 2D or 3D space, with real-time feedback as... Read more

Latest Forum Discussions

See All

Frogger in Toy Town's latest update...
Konami Digital Entertainment has announced today that their Apple Arcade title Frogger in Toy Town has been updated to introduce a new ranked Endurance Mode. This new game variant's arrival is also accompanied by a few other changes. [Read more] | Read more »
Mitoza is surreal adventure toy you can...
The folks behind the Rusty Lake games have just put a new title onto the App Store. Second Maze, Rusty Lake's collaborative publishing brand, has just brought this 10 year old adventure game from Gal Mamalya to mobile. The best part about all of... | Read more »
Pocket Gamer Awards 2021: You have five...
Three weeks ago our sister site, Pocket Gamer, entered the voting stage for the upcoming Pocket Gamer Awards 2021 and is now in the final stretch. You only have a few hours left to vote for the games you’ve enjoyed on mobile in the past year, as... | Read more »
Patty Stack is a casual arcade game, ava...
Patty Stack is a casual arcade title that's available now for iOS and Android. It's the debut game from developer Feeka Games tasks players with making an increasingly giant burger tower. Think of it as Tower Bloxx but more edible. [Read more] | 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 »
Genshin Impact Guide - Gacha Strategy: W...
This is part 2 of our Genshin Impact gacha strategy guides. See part 1 here. You can check out more guides for Genshin Impact here. | Read more »
Slashy Camp is a new endless runner insp...
Blue Wizard Digital has released Slashy Camp onto iOS and Android after it spent a short amount of time in early access. [Read more] | Read more »
Kinder World is a relaxing game about lo...
Lumi Interactive is releasing a game called Kinder World later this year on iOS and Android, which is all about looking after houseplants. [Read more] | Read more »
Steam Link Spotlight - Fights in Tight S...
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 on Hades. Read about how it plays using Steam Link over here. | Read more »
Lyxo, the light-based puzzler for mobile...
Vienna-based independent game studio Emoak has just released its unique light-based puzzler for iOS and Android. Founded in 2014 by Tobias Sturn, the company is also the creative force behind the infinite climbing game Paper Climb, as well as the... | Read more »

Price Scanner via MacPrices.net

Weekend Sale: $100 off Apple iPad Magic Keybo...
Amazon has Apple iPad Magic Keyboards on sale for $100 off MSRP for a limited time. Amazon’s prices are the lowest available for iPad Magic Keyboard from any Apple reseller this weekend: – Magic... Read more
Gazelle now offering a full line of refurbish...
Gazelle is now offering a full range of discounted, refurbished, unlocked Apple iPhone 12 models starting at $649. iPhones are offered in Fair, Good, and Excellent conditions, and multiple colors are... Read more
These are the latest discounted iPhones Apple...
Apple has a range of Certified Refurbished iPhones available right now starting at only $339. Apple includes a standard one-year warranty, new outer shell, and shipping is free. According to Apple, “... Read more
Save up to $64 on new M1 MacBook Airs at Expe...
Apple reseller Expercom has 2020 13″ M1 MacBook Airs on sale for $51-$64 off Apple’s MSRP with prices starting at $947.96. In addition to their MacBook Air sale prices, take $50 off AppleCare+ when... Read more
Discounts available on 16″ MacBook Pros with...
Upgrade a 16″ 6-Core or 8-Core MacBook Pro from 16GB of standard RAM to 32GB at Adorama, and save $100-$210 over Apple’s price for this custom option: – 16″ 6-Core MacBook Pro/32GB RAM: $2699, save $... Read more
10.9″ iPad Airs on sale for $50-$70 off Apple...
Amazon has new 2020 10.9″ Apple WiFi iPad Airs in stock and on sale today for up to $70 off MSRP with prices starting at $549. Note that Amazon’s sale price might be restricted to certain colors (see... Read more
Apple restocks 2020 27″ 5K iMacs for up to $3...
After an initial offering in January, Apple has restocked a full line of Certified Refurbished 2020 27″ 5K iMacs starting at $1529 and up to $350 off original MSRP. Apple’s one-year warranty is... Read more
Sale! 16″ 8-Core MacBook Pro for $2449, $350...
Apple reseller Adorama has the 16″ 2.3GHz 8-Core Space Gray MacBook Pro in stock and on sale today for $2449 including free shipping. Their price is $350 off Apple’s MSRP for this model, and it’s the... Read more
Roundup of 13″ Multi-Core Intel MacBook Pro s...
Apple resellers are offering significant sales & deals this week on 2020 13″ MacBook Pros with 10th generation Intel CPUs. Take up to $250 off Apple’s MSRP, get free fast shipping, and/or pay no... Read more
64GB iPhone 8 Plus available for $379 at Appl...
Apple has the 64GB iPhone 8 Plus in Space Gray & Gold colors available for $379 today, Certified Refurbished. Each phone is unlocked and comes with Apple’s standard 1-year warranty and free... Read more

Jobs Board

Geek Squad Advanced Repair *Apple* Professi...
**795178BR** **Job Title:** Geek Squad Advanced Repair Apple Professional **Job Category:** Store Associates **Store Number or Department:** 001406-Allen Park-Store Read more
Geek Squad *Apple* Consultation Professiona...
**796549BR** **Job Title:** Geek Squad Apple Consultation Professional **Job Category:** Store Associates **Store Number or Department:** 001800-Hot Springs-Store Read more
*Apple* Mobility Specialist - Best Buy (Unit...
**796014BR** **Job Title:** Apple Mobility Specialist **Job Category:** Store Associates **Store Number or Department:** 001776-Woodmore Towne Centre-Store **Job Read more
Systems Architect, *Apple* Production Engin...
…package beginning on your first day? If so, we hope you'll keep reading! The Apple Sales Engineering and account team is looking for a stellar presales engineer with Read more
Systems Engineer, Webscale, *Apple* Retail,...
…beginning on your first day? If so, we hope you'll keep reading! The Apple Sales Engineering team is looking for a pre-sales engineer with Enterprise engineering Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.