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))

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:

((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.

((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)
(1 2 3 4 5 6 7 8)
(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))
                     (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))
(EVERY NUMBERP '(1 2 A 4 5))

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)

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

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

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))

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))

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

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

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))

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)
  (penup) (home) (forward 40)
  (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 (( (car point) (rac point) '(60 -100 80 -60))
         (apply adjust.x point))
        (( (car point) (rac point) '(60 -40 80 0))
         (apply adjust.y point))
        (( (car point) (rac point) '(60 20 80 60))
         (apply adjust.z point))
        (( (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 (( x y (car xboxes))
         (invertrect (car xboxes))
         (setq xx (- xx 2))
         (invertrect (car xboxes)))
          (invertrect (rac xboxes))
          (setq xx (+ xx 2))
          (invertrect (rac xboxes)))))

(defun adjust.z (x y)
  (cond (( x y (car zboxes))
         (invertrect (car zboxes))
         (setq zz (- zz 2))
         (invertrect (car zboxes)))
          (invertrect (rac zboxes))
          (setq zz (+ zz 2))
          (invertrect (rac zboxes)))))

(defun adjust.y (x y)
  (cond (( x y (car yboxes))
         (invertrect (car yboxes))
         (setq yy (- yy 2))
         (invertrect (car yboxes)))
          (invertrect (rac yboxes))
          (setq yy (+ yy 2))
          (invertrect (rac yboxes)))))

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

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

Tweetbot 2.1 - Popular Twitter client. (...
Tweetbot is a full-featured OS X Twitter client with a lot of personality. Whether it's the meticulously-crafted interface, sounds and animation, or features like multiple timelines and column views... Read more
MacPilot 8.0 - Enable over 1,200 hidden...
MacPilot gives you the power of UNIX and the simplicity of Macintosh, which means a phenomenal amount of untapped power in your hands! Use MacPilot to unlock over 1,200 features, and access them all... Read more
Typinator 6.7 - Speedy and reliable text...
Typinator turbo-charges your typing productivity. Type a little. Typinator does the rest. We've all faced projects that require repetitive typing tasks. With Typinator, you can store commonly used... Read more
Adobe Lightroom 6.2 - Import, develop, a...
Adobe Lightroom is available as part of Adobe Creative Cloud for as little as $9.99/month bundled with Photoshop CC as part of the photography package. Lightroom 6 is also available for purchase as a... Read more
ForeverSave 2.1.4 - Universal auto-save...
ForeverSave auto-saves all documents you're working on while simultaneously doing backup versioning in the background. Lost data can be quickly restored at any time. Losing data, caused by... Read more
VueScan 9.5.27 - Scanner software with a...
VueScan is a scanning program that works with most high-quality flatbed and film scanners to produce scans that have excellent color fidelity and color balance. VueScan is easy to use, and has... Read more
AirPort Utility 6.3.6 - Set up and manag...
Note: Most recent release available only within OS X 10.11 El Capitan update. Use AirPort Utility to set up and manage your Wi-Fi network and AirPort base stations, including AirPort Express, AirPort... Read more
Quicksilver 1.3.1 - Application launcher...
Quicksilver is a light, fast and free Mac application that gives you the power to control your Mac with keystrokes alone. Quicksilver allows you to find what you need quickly and easily, then act... Read more
Tidy Up (Five Users) 4.1.5 - Find duplic...
Tidy Up is a complete duplicate finder and disk-tidiness utility. With Tidy Up you can search for duplicate files and packages by the owner application, content, type, creator, extension, time... Read more
Mellel 3.4.3 - The word processor of cho...
Mellel is the leading word processor for OS X and has been widely considered the industry standard since its inception. Mellel focuses on writers and scholars for technical writing and multilingual... Read more

Royal Bounty HD (Games)
Royal Bounty HD 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: New World Computing Approved "Hi Guys! looks good so far! keep up the good work. I worked on HoMM 3 and 4 creating all of the... | Read more »
Swords & Crossbones: An Epic Pirate...
Swords & Crossbones: An Epic Pirate Story 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: | Read more »
Camel Up (Games)
Camel Up 1.0.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0.0 (iTunes) Description: | Read more »
The Martian: Bring Him Home (Games)
The Martian: Bring Him Home 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: Based on the best selling novel and critically acclaimed film, THE MARTIAN tells the story of Astronaut Mark... | Read more »
This Week at 148Apps: September 21-30, 2...
Leap Into Fall With 148Apps How do you know what apps are worth your time and money? Just look to the review team at 148Apps. We sort through the chaos and find the apps you're looking for. The ones we love become Editor’s Choice, standing out above... | Read more »
Tweetbot 4 for Twitter (Social Networki...
Tweetbot 4 for Twitter 4.0 Device: iOS Universal Category: Social Networking Price: $4.99, Version: 4.0 (iTunes) Description: *** 50% off for a limited time. *** | Read more »
Mori (Games)
Mori 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: Stop, rewind and unwind with Mori. Time is always running, take a moment to take control. Mori is an action puzzle game about infinitely... | Read more »
100 Years' War (Games)
100 Years' War 1.0 Device: iOS Universal Category: Games Price: $3.99, Version: 1.0 (iTunes) Description: | Read more »
Tower in the Sky (Games)
Tower in the Sky 0.0.60 Device: iOS Universal Category: Games Price: $1.99, Version: 0.0.60 (iTunes) Description: | Read more »
hocus. (Games)
hocus. 1.0.0 Device: iOS Universal Category: Games Price: $.99, Version: 1.0.0 (iTunes) Description: New, polished, mind-bending, minimal puzzle game with dozens of levels and extra-ordinary design Features:- Beautifully crafted... | Read more »

Price Scanner via

Is The iPad Pro Really A Serious Laptop Repla...
Probably not, at least for productive professionals and other power users. Steve Jobs declared that we’d entered the “post-PC Era” with the advent of the original iPad in 2010, a phrase we don’t hear... Read more
Wednesday Deal: 13-inch Retina MacBook Pros f...
Adorama has 13″ Retina MacBook Pros on sale for up to $130 off MSRP. Shipping is free, and Adorama charges sales tax for NY & NJ residents only: - 13″ 2.7GHz/128GB Retina MacBook Pro: $1199.99 $... Read more
uBar 3.0 for Mac OS X – Custom Dock Replaceme...
Brawer Software has announced the release of uBar 3.0, an important update to their popular app and window manager for Mac OS X. uBar allows users to position it whichever side of the screen they... Read more
13-inch 2.5GHz MacBook Pro (refurbished) avai...
Apple has Certified Refurbished 13″ 2.5GHz MacBook Pros available for $829, or $270 off the cost of new models. Apple’s one-year warranty is standard, and shipping is free: - 13″ 2.5GHz MacBook Pros... Read more
27-inch 3.2GHz iMac on sale for $1689, save $...
Adorama has the 27″ 3.2GHz iMac on sale for $1689 including free shipping plus NY & NJ sales tax only. Their price is $110 off MSRP. Read more
12-inch Retina MacBooks on sale for up to $12...
B&H Photo has 12″ Retina MacBooks in stock today and on sale for up to $120 off MSRP. B&H will include free shipping, and there is NY sales tax only: - 12″ 1.1GHz Gray Retina MacBook: $1224 $... Read more
Tablets Shaping Up for Growth in 2016 – Strat...
Observing that Apple, Samsung, and Microsoft have refocused what tablet computers can do, market analysis firm Strategy Analytics believes there is immense opportunity for new and replacement sales... Read more
Apple Interbrand’s Number One Most Valuable G...
Apple and Google hold aced #1 and #2 spots respectively in Interbrand’s 2015 Best Global Brands Report, leading all tech brands that now comprise more than a third of the entire rankings value.... Read more
Apple offering refurbished 2015 13-inch Retin...
Apple is offering Certified Refurbished 2015 13″ Retina MacBook Pros for up to $270 (15%) off the cost of new models. An Apple one-year warranty is included with each model, and shipping is free: -... Read more
Apple refurbished 2015 MacBook Airs available...
Apple has Certified Refurbished 2015 11″ and 13″ MacBook Airs (the latest models), available for up to $180 off the cost of new models. An Apple one-year warranty is included with each MacBook, and... Read more

Jobs Board

Touch Validation Design (EE) - *Apple* Watc...
**Job Summary** Help launch next-generation Touch Technologies in Apple products. The Touch Technology team develops cutting-edge Touch solutions and technologies that Read more
WW Sales Strategy & Program Manager, *Ap...
**Job Summary** Imagine what you could do here. At Apple , great ideas have a way of becoming great products, services, and customer experiences very quickly. Bring Read more
*Apple* TV Product Design Internship (Spring...
…the mechanical design effort associated with creating world-class products with the Apple TV PD Group. Responsibilities will include working closely with manufacturing, Read more
Product Design Engineer - *Apple* Watch - A...
**Job Summary** Product Design Engineer - WATCH ( Apple Watch) Be an integral part of a small and visible team of world-class Mechanical Engineers making Apple 's Read more
Senior Software System App Engineer, *Apple*...
**Job Summary** The Apple Watch system application team is looking for great software engineers who are comfortable working across all levels of the software stack. From Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.