Rectangle vertexes

Maybe this is been already solved:

given a list of four couples of vertexes that represents
a rectangle or a square (also rotated):

((
(40.0 20.0 0.0) ; P1
(88.5071 32.1268 0.0) ; P2
)
(
(88.5071 32.1268 0.0) ; P2
(81.2311 61.2311 0.0) ; P3
)
(
(81.2311 61.2311 0.0) ; P3
(32.7239 49.1043 0.0) ; P4
)
(
(32.7239 49.1043 0.0) ; P4
(40.0 20.0 0.0) ; P1
))


the couples in the list can be in every sequence
as the vertexes inside the couple

(as in a rectangle formed by 4 lines drawed in
various directions)


Given a direction, for example (ang P2 P3),
I need to find:

Px = center of the rectangle (or square)
H = length on given angle
L = length on (given angle +- 90)

P4-----------------P3
| |
| |
| Px? | H?
| |
| |
P1-----------------P2
L?

 

Thanks Herman.

Cheers.

Marco

 

I don't know if this is any help or not
it's part of what i use to test for 'rectangleness'
;;; given a list of four points
;;; returns list of three distances, shortest, middle, longest
;;; between any one point and 3 other points in list
;;; if the list is the same measured from any two of the points in the list
;;; or nil if the points don't form a rectangle (within fuzz)
;;; thus for a rectangle the shortest is height, middle is length, and
longest is diagonal
;;; from this you can easily get center pt etc
;;; or at least that's what it's supposed to do...no guarantees
;;; i think i seemed to work in limited testing but it's been a while since
i've looked at it
;;; cleaned up a bit to post here so hope i didn't screw it up.
(defun GetRectDistList (lst / DistList lastDistList Result idx fuzz)
(setq idx 0 Fuzz 0.00000001)
(repeat 2
(setq distlist (get-list-of-Distances lst idx))
(if LastDistList ; if this isn't the first time
;check this list of distances against last list
(if (equal DistList LastDistList fuzz)
(setq result DistList);return list of distances
;else
(setq result NIL)
) ;_ endif
;progn
;else its the first time
(progn
;so save the last list of distances to compare to the next one
(setq LastDistList DistList)
;reset counter
(setq idx (1+ idx))
) ;progn
) ;if
) ;repeat
result ;return list or nil
)
(defun get-list-of-distances (ptlst idx / distlist)
(setq I idx J -1)
(repeat (length ptlst)
(setq j(1+ j))
(if(not(= i j));don't read the same point twice
(setq Distlist
(cons
(distance
(nth I ptlst)
(nth J ptlst)
) ;distance
Distlist
)
) ;setq
);end if
);repeat
(setq distlist (sort-distlist distlist));sort from short to long or
however..
;return distlist
);end defun
;;;;;;-------------------------------------------
(defun sort-distlist (lst)
(vl-sort
lst
'<
)
);end

hth
Mark

 

Here's a start (solves for px):

(setq p1 '(40.0 20.0 0.0)
p2 '(88.5071 32.1268 0.0)
p3 '(81.2311 61.2311 0.0)
p4 '(32.7239 49.1043 0.0)
)

(defun ctr (p1 p2 p3 p4 / ex nx px)
(setq ex (/ (+ (car p1) (car p2) (car p3) (car p4)) 4.0)
nx (/ (+ (cadr p1)(cadr p2)(cadr p3)(cadr p4)) 4.0)
zx (/ (+ (caddr p1)(caddr p2)(caddr p3)(caddr p4)) 4.0)
; or just set zx to 0.0 for 2d
px (list ex nx zx)
)
)



; Command: (ctr p1 p2 p3 p4)
; (60.6155 40.6155 0.0)

 

; Makes no sense in 3d anyway, so use 0.0:

(defun rect-ctr (p1 p2 p3 p4 / ex nx px)
(setq ex (/ (+ (car p1) (car p2) (car p3) (car p4)) 4.0)
nx (/ (+ (cadr p1)(cadr p2)(cadr p3)(cadr p4)) 4.0)
px (list ex nx 0.0)
)
)

 

Marco,
Try this for the centroid:

(setq rect '((
(40.0 20.0 0.0) ; P1
(88.5071 32.1268 0.0) ; P2
)
(
(88.5071 32.1268 0.0) ; P2
(81.2311 61.2311 0.0) ; P3
)
(
(81.2311 61.2311 0.0) ; P3
(32.7239 49.1043 0.0) ; P4
)
(
(32.7239 49.1043 0.0) ; P4
(40.0 20.0 0.0) ; P1
)))

(defun cntroid (rect) ;D.C.B-2004
(mapcar '(lambda (x) (/ x 8.0))
(apply 'mapcar
(cons '+ (apply 'append rect)))))

 

Thanks Doug and all.