Circle (lisp) routine in autocad

[Toulinash]

Hey guys,

I'm looking for a circle routine that computes a circle through several points.
Here's the twist though: I need the circle to have a certain diameter/radius.
Preferably I'd like the routine to compute the circle, and give me an deviation towards the radius per point.

Kind regards,

CK

[Oatfedgoat]

I know it's not quite what you are looking for, but it is not uncommon in the rail industry (I'm assuming tunneling as well) to require a circularity check on a profile of a tunnel.
We wrote an internal macro for Excel to do this based upon data exported from our mobile scanning systems.

I wouldnt be suprised if a similar macro is not available to download somewhere online.

[gareth10]

Not sure I fully understand. Am I right that you want to input a radius or diameter of a circle, then pick a number of points on the screen (or inputed) and then get a best fit for a drawn circle?

Cadplan

[Toulinash]

Correct,
Right now I use the attached routine.
But for example with flanges, they are machined, so the radius is quite precise.
Therefore I want to eliminate the deviation, created either by the surveyor or total station, by telling Autocad what radius it should be.

Cheers!

[gareth10]

I think I see what you are trying to achieve and a routine can be made to pick all the points and to draw a circle of a certain radius/diameter. The difficulty it seems to me might be how to position the circle to create the best fit with the points.

[Phill]

CK

See attached. BTW least squares really messes with my brain. Please dont ask for this in 3d, I have no idea how those Cyclone gurus do a fit to cloud cyclinder. I have attached the pdf I based the calcs on and my answer matches the example data. I have got the lisp to calc the center of a nominal circle to fit the points but made the text differences from the user inputed radius (the calced best fit radius is printed as Nominal radius on the command prompt). I am assuming that the center of a best fit circle would be the same as if it were fitting a given radius to the points.

Hope this is what you were looking for. If it's useful you owe me a beer or two. If you edit it to make it better, repost so others can use it as well.

Cheers

Phill

[Toulinash]

Hey Phill, thanks!
I'm in the field right now so I can't check it out.

I think by now I owe you a crate already.

Cheers!

CK

[FritjofS]

If you get your hands on the old Leica program calles AXYZ, you can calculate circles with a given radius. I always use this program when measuring spools and flanges. This program also include many other types of geometry calculation.

[Andrew]

Thanks Phil. This is very useful. I had a similar least squares routine that I somehow lost.

I've tweaked it slightly to draw the best-fit circle using the design radius and also output to 4dp, as that suits how I work. As it may be of use to others, here it is:

Code: Select all

(PRINC "\nFit circle to points Version 1.0, type FC2P to run")

(DEFUN C:FC2P ( /  )
  
 
(SETQ aws (SSGET  '((0 . "POINT"))))

  (SETQ POINTLIST NIL)
  (SETQ COUNT 0)
  ;CREATE POINT LIST
(REPEAT (SSLENGTH aws)
(SETQ P1 (CDR(ASSOC 10 (ENTGET (SSNAME aws COUNT)))))
  (SETQ P1 (TRANS P1 1 0))
(SETQ POINTLIST (APPEND POINTLIST P1))
(SETQ COUNT (+ COUNT 1))
); ende repeat

  ;GET SUM AND AVERAGE FOR U,V VALUES
(SETQ SUMX 0)
  (SETQ SUMY 0)
  (SETQ COUNT 0)
  (SETQ N (/ (LENGTH POINTLIST) 3))
  (REPEAT N

  (SETQ X (NTH COUNT POINTLIST))
  (SETQ COUNT (+ COUNT 1))
  (SETQ Y (NTH COUNT POINTLIST))
  (SETQ COUNT (+ COUNT 1))
  (SETQ COUNT (+ COUNT 1))
  (SETQ SUMX (+ SUMX X))
  (SETQ SUMY (+ SUMY Y))
 )

  (SETQ AVGX (/ SUMX N))
  (SETQ AVGY (/ SUMY N))

  ;CREATE UVLIST WITH MULTIPLES AND SUMS
  (SETQ UVLIST NIL)
  (SETQ SUU 0
	SVV 0
	SUV 0
	SUUU 0
	SVVV 0
	SUVV 0
	SVUU 0
	)
  

  (SETQ COUNT 0)
  (REPEAT N
    (SETQ U (- (NTH  COUNT POINTLIST) AVGX))
    (SETQ COUNT (+ COUNT 1))
    (SETQ V (- (NTH  COUNT POINTLIST) AVGY))
    (SETQ COUNT (+ COUNT 1))
    (SETQ COUNT (+ COUNT 1))
    (SETQ UU (* U U))
    (SETQ VV (* V V))
    (SETQ UV (* U V))
    (SETQ UUU (* U U U))
    (SETQ VVV (* V V V))
    (SETQ UVV (* U V V))
    (SETQ VUU (* V U U))
    (SETQ SUU (+ SUU UU))
    (SETQ SVV (+ SVV VV))
    (SETQ SUV (+ SUV UV))
    (SETQ SUUU (+ SUUU UUU))
    (SETQ SVVV (+ SVVV VVV))
    (SETQ SUVV (+ SUVV UVV))
    (SETQ SVUU (+ SVUU VUU))
    )

  

  ;CREATE A MATRIX
  (SETQ A11 SUU)
  (SETQ A12 SUV)
  (SETQ A21 SUV)
  (SETQ A22 SVV)

  ;CREATE B MATRIX
  (SETQ B1 (/ (+ SUUU SUVV) 2))
  (SETQ B2 (/ (+ SVVV SVUU) 2))

  ;CREATE ATA
  (SETQ ATA11 (+ (* A11 A11) ( * A12 A21)))
  (SETQ ATA12 (+ (* A11 A12) ( * A12 A22)))
  (SETQ ATA21 (+ (* A21 A11) ( * A22 A21)))
  (SETQ ATA22 (+ (* A21 A12) ( * A22 A22)))

  ;DETERMINE DETERMINANT
(SETQ DET (- (* ATA11 ATA22) (* ATA12 ATA21)))
  (SETQ DET (/ 1 DET))
  (SETQ INV11 (* -1 ( * DET ATA22)))
  (SETQ INV12 (* -1(* (* DET ATA12) -1)))
  (SETQ INV21 (* -1(* (* DET ATA21) -1)))
  (SETQ INV22 (* -1(* DET ATA11)))

  ;CREATE ATB
  (SETQ ATB1 (+ (* A11 B1) (* A12 B2)))
  (SETQ ATB2 (+ (* A21 B1) (* A22 B2))) 
 
  ;CREATE X

  (SETQ X1 (+ (* INV11 ATB1) (* INV12 ATB2)))
  (SETQ X2 (+ (* INV21 ATB1) (* INV22 ATB2)))

  (SETQ CX (+ (* X1 -1) AVGX))
  (SETQ CY (+ (* X2 -1) AVGY))

  (COMMAND "POINT" (LIST CX CY))
  (SETQ NRAD (SQRT (+ (* X1 X1) (* X2 X2) (/ (+ SUU SVV) N))))

	(PRINC (STRCAT "\nNominal Radius " (RTOS NRAD 2 4)))
  (SETQ RAD (GETREAL "\nDesign Radius: "))
  
  (COMMAND "CIRCLE" (LIST CX CY) RAD)
 
  (SETQ COUNT 0)
  (REPEAT (SSLENGTH aws)
(SETQ P1 (CDR(ASSOC 10 (ENTGET (SSNAME aws COUNT)))))
(SETQ DIFF (- RAD (DISTANCE P1 (LIST CX CY))))
    (COMMAND "TEXT" P1 "0.025" "90" (RTOS DIFF 2 4))
    
 
   
(SETQ COUNT (+ COUNT 1))
); ende repeat

[drobzz]

If you have Civil 3D you can use menu: Lines/Curves > Create Best Fit Entities > Create Arc