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

How to become the ultimate robot warrior...
Chrono Strike is a delightfully immersive beat ‘em up with a sense of humor (any game with a good Sims reference gets points in my book). [Read more] | Read more »
Tips and tricks to get a higher score in...
Snow Roll is a devilish endless runner very much in the vein of Flappy Bird. It revels in its dastardly level of difficulty, and doesn’t really care how angry you get at it as it knows you’ll keep coming back for more. [Read more] | Read more »
How to win big in Slots Deluxe
Cheating while gambling is illegal and morally wrong, and in some parts of the world it leads to men with names like Vinnie "Six Knuckles" Manchenzo beating you to a pulp in a dark alley. [Read more] | Read more »
How to take over the world in Dictator 2
Running a country isn't easy - especially when you're a dictator who wants to take over the world and crush everyone in your path while you do it. [Read more] | Read more »
Tips and tricks to get a higher score in...
Tank.iois - you guessed it! - another multiplayer arena battler and It does differentiate itself by putting you in a tiny tank though, so it's not exactly the same. To help you get that all-important high score, we've got a... | Read more »
How to unlock characters in One Tap Tenn...
As the title suggests, One Tap Tennis requires only a single tap to play its particular brand of tennis, and rewards you with a ton of unlockable characters if you perform well. Fortunately for you, we at 148Apps have got a few tips and tricks to... | Read more »
Grab it now: Game Craft’s Legend of War...
The real time strategy game is now available for you to sink your teeth into, through the App Store and Google Play. Combining elements of skill, strategy and empire building, Legend of War is a real gamers’ game. [Read more] | Read more »
Skateboard Party 3 ft. Greg Lutzka (Gam...
Skateboard Party 3 ft. Greg Lutzka 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: Skateboard Party is back! This third edition of the popular sports franchise features professional skater... | Read more »
Cubious (Games)
Cubious 1.0 Device: iOS Universal Category: Games Price: $.99, Version: 1.0 (iTunes) Description: Cubious – How smart are you? How high is your IQube? Solve the impossible puzzles to find out, and help a lost little cube find his... | Read more »
Goat Simulator Waste of Space (Games)
Goat Simulator Waste of Space 1.1 Device: iOS Universal Category: Games Price: $4.99, Version: 1.1 (iTunes) Description: ** IMPORTANT - SUPPORTED DEVICESiPhone 4S, iPad 2, iPod Touch 5 or better.** | Read more »

Price Scanner via

Enterprise Workers Pick Technology Over Perks...
New Adobe study shows surprising attitudes about office jobs and where the future of work is heading. Adobe has released survey findings revealing that a surprising 70 percent of U.S. office workers... Read more
Memorial Day Weekend Sale: $50-$100 off 11-in...
B&H Photo has 13″ and 11″ MacBook Airs with 256GB SSDs on sale for $50-$100 off MSRP. Shipping is free, and B&H charges NY sales tax only: - 11″ 1.6GHz/256GB MacBook Air: $999 $100 off MSRP... Read more
Memorial Day Weekend Sales: Apple MacBook Pro...
B&H Photo has 13″ and 15″ Retina MacBook Pros on sale for up to $210 off MSRP. Shipping is free, and B&H charges NY tax only: - 15″ 2.2GHz Retina MacBook Pro: $1799 $200 off MSRP - 15″ 2.5GHz... Read more
Memorial Day Weekend Sales: Apple iMacs and M...
Take up to $150 off the price of a new iMac or Mac mini at the following Apple resellers this Memorial Day weekend: iMacs: B&H Photo has 21″ and 27″ iMacs on sale for up to $150 off MSRP... Read more
Apple refurbished Retina MacBook Pros availab...
Apple has Certified Refurbished 2015 13″ and 15″ Retina MacBook Pros available for up to $380 off the cost of new models. An Apple one-year warranty is included with each model, and shipping is free... Read more
Apple refurbished 11-inch MacBook Airs availa...
Apple has Certified Refurbished 11″ MacBook Airs (the latest models), available for up to $170 off the cost of new models. An Apple one-year warranty is included with each MacBook, and shipping is... Read more
Goal Zero and OtterBox Partner to Expand iPh...
Goal Zero, specialists in portable power, have announced a partnership with OtterBox, brand smartphone case protection, to offer the Slide and Slide Plus Batteries as modules compatible with the new... Read more
15-inch Retina MacBook Pros on sale for up to...
B&H Photo has 15″ Retina MacBook Pros on sale for up to $210 off MSRP. Shipping is free, and B&H charges NY tax only: - 15″ 2.2GHz Retina MacBook Pro: $1799 $200 off MSRP - 15″ 2.5GHz Retina... Read more
Clearance 2015 13-inch MacBook Airs available...
B&H Photo has clearance 2015 13″ MacBook Airs available for $250 off original MSRP. Shipping is free, and B&H charges NY sales tax only: - 13″ 1.6GHz/4GB/128GB MacBook Air (MJVE2LL/A): $799... Read more
Apple refurbished Apple TVs available for up...
Apple has Certified Refurbished 32GB and 64GB Apple TVs available for up to $30 off the cost of new models. Apple’s standard one-year warranty is included with each model, and shipping is free: -... Read more

Jobs Board

*Apple* Solutions Consultant - APPLE (United...
Job Summary As an Apple Solutions Consultant, you'll be the link between our future customers and our products. You'll showcase your entrepreneurial spirit as you Read more
*Apple* Project Engineer - Smart Source Inc...
SmartSource is in need of an Apple Project Engineer for a 12 month contract opportunity in Pittsburg, PA. Role: Apple Project Engineer Location: Pittsburg, PA Read more
Automotive Sales Consultant - Apple Ford Linc...
…you. The best candidates are smart, technologically savvy and are customer focused. Apple Ford Lincoln Apple Valley is different, because: $30,000 annual salary Read more
Service Assistant - *Apple* Chevrolet *App...
Apple Automotive is one of the fastest growing dealer...and it shows. Consider making the switch to the Apple Automotive Group today! At Apple Automotive, we Read more
Editor, *Apple* News - APPLE (United States...
Job Summary The Apple News team is looking for a passionate and knowledgeable editor with experience covering entertainment/pop culture and experience running social Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.