Lee Mac - Geometry function explined

hi

learning Lee's geometry functions , starting with Perpendicular-p()

what is vxv and and what is the decimal 1e-8 mean?

;; Perpendicular-p  -  Lee Mac
;; Returns T if vectors v1,v2 are perpendicular

(defun LM:Perpendicular-p ( v1 v2 )
   (equal 0.0 ([b][color="red"]vxv[/color][/b] v1 v2) [color="red"][b]1e-8[/b][/color])
)

That function stands for a dot product of 2 vectors (as opposed to a cross product). From Lee's collection:

;; Vector Dot Product  -  Lee Mac
;; Args: u,v - vectors in R^n

(defun vxv ( u v )
   (apply '+ (mapcar '* u v))
)

The 1e-8 is the scientific notation for 10 raised at -8, used to simplify writing of such numbers; its equivalent with:

(expt 10.0 -

Lee Mac nice coding style simple but works!!

still long way to achieve his level

Here just to share another method

my version 3-lines cosine

(defun per-p (a b c fuzz)
(equal ( / pi 2)
 ('((d )
    (if
      (equal (abs d) 1. 1e-16)
     0.
     (+ (* 2. (atan 1.)) (atan (/ d (sqrt (- 1. (* d d ))))) ); (* 2. (atan 1.))= (/ pi 2)
     )
    )
   (/ (+ (* a a) (* b b) (-(* c c)))(* 2. a b))
   )
fuzz)
) ;_ end of defun

(per-p 3. 4. 5. 1e-16); T

*EDIT comment removed

hi

i always treat entites by points, in this function , the expected areguments are vectors, how can i use it? can someonr please post an example?

Thanks

S

Apply in math

Area Formula:

| x1 x2 x3 x4 xn.. |

| \/ \/ \/ \/ \/ |

|. /\ /\ /\ /\ /\ |

| y1 y2 y3 y4 yn.. | .1/2

;hanhphuc 07/07/2014
(defun 2d-area (l)
 (abs
   (/ (apply '-
      (mapcar '(lambda (x y)
   (vxv  ; sub function by LEE MAC
     (mapcar '(eval x) l)
     (mapcar '(eval y)
      (append (cdr l) (list (car l)))
     )
   ) ;_ vxv
        ) ;_ end of lambda
       '(car cadr)
       '(cadr car)
      ) ;_ end of mapcar
      ) ;_ end of apply
      2.
   ) ;_ end of /
   
 );_ end of abs
 
) ;_ end of defun

;Test:

(2d-area '((0.0 0.0 ) (4.0 0.0 ) (4.0 3.0 )) )

;6.0

Apply in math

Area Formula:

| x1 x2 x3 x4 xn.. |

| \/ \/ \/ \/ \/ |

|. /\ /\ /\ /\ /\ |

| y1 y2 y3 y4 yn.. | .1/2

 

;hanhphuc 07/07/2014
(defun 2d-area (l)
 (abs
   (/ (apply '-
      (mapcar '(lambda (x y)
   (vxv  ; sub function by LEE MAC
     (mapcar '(eval x) l)
     (mapcar '(eval y)
      (append (cdr l) (list (car l)))
     )
   ) ;_ vxv
        ) ;_ end of lambda
       '(car cadr)
       '(cadr car)
      ) ;_ end of mapcar
      ) ;_ end of apply
      2.
   ) ;_ end of /
   
 );_ end of abs
 
) ;_ end of defun

 

;Test:

(2d-area '((0.0 0.0 ) (4.0 0.0 ) (4.0 3.0 )) )

;6.0

sorry i still dont understand...could it be simpler?

sorry i still dont understand...could it be simpler?

hi hope this helps?

pls advise if i get you wrong direction, thanx

1e-8 is used to improve comparison of two values where one has more decimal places in its value not returning true

V1 = 123.123

v2 = 123.12300003

v1 is not equal to v2 but taking into acount tolerance it is.

hi hope this helps?

 

 

pls advise if i get you wrong direction, thanx

THANK YOU for the visual explanation,

vxv() compares the x.y of the 3 given coordinates and multiply and divide their components in order the get the area, that cool!

but how its related to passing vectors to a function?

Thanks

Shay

anyone please? just need to know how to pass 2 vectors to Mac Lee's function

;; Perpendicular-p  -  Lee Mac
;; Returns T if vectors v1,v2 are perpendicular

(defun LM:Perpendicular-p ( v1 v2 )
   (equal 0.0 (vxv v1 v2) 1e-
)

As MSasu explained: vxv is dot product

(vxv '(P Q) '(R S)) = P*R + Q*S

If a Line A (x1,y1) to B (x2,y2) ,the vector only 2 directions:

(x1-x2 , y1-y2) or (x2-x1 , y2-y1)

Example:

assume A to B, delta = '(-3.0 -4.0 )

C to D, delta = '(-4.0 3.0 )

meaning : (vxv A-B C-D )

(vxv '(-3.0 -4.0 ) '(-4.0 3.0 ))
; -3*-4 + -4*3 = 12 + -12 = 0.0

if we change the C to D direction ,ie= D to C, so delta = '(4.0 -3.0 )

(vxv '(-3.0 -4.0 ) '(4.0 -3.0 ))
; -3*4 + -4*-3 = -12 + 12 = 0.0

still zerop, T

p/s: sorry previous picture, the sum label which before AREA result should be indicated as sum1-2 instead of sum, spread sheet explains.

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