Calculate Circle Centre

[TURNER]

Hi to all,
Can any body help, I need a formula to calculate X and Y coords of circle centre. The known data is point X1,Y1 and X2,Y2 and R (RADIUS).
From this i need to find Xc,Yc
Thanks.
Turner

[bborb]

One formula won't calculate BOTH "X" and "Y"
If you just need a start to figure it out, any math referencing chords of a circle will help tremendously.

[Andre' B]

Because there are two possible centers you also need to know which direction (clockwize/counterclockwize) you are going when you move from (x1,y1) to (x2,y2).

[Eurisko]

The math isn't pretty, but here's a link to the answer:

http://mathforum.org/library/drmath/view/53179.html

Any good cad program can solve this problem graphically.

Given: 2 points (X1,Y1) & (X2,Y2) on a circle of radius R.

Draw a circle of radius R centered at (X1,Y1)
Draw another circle of radius R centered at (X2,Y2)

The points of intersection of these circles are the possible centers. (XC,YC)

[anorec]

To calculate circle center isn't very easy... I made a little software to 'convert' a Gcode file to DXF file. Just import DXF in any CAD software and pick circle centers or any other informations you need...

Look here

Hope this can help

[Kiwi]

Turner
Attached is a program I'm working on, still a long way to go but may help with your calculating.
Some features are locked.

[oldjohn]

Here:

[Stu_M3]

Point 1 x coord = A
POINT 1 Y COORD = B
POINT 2 X COORD = D
POINT 2 Y COORD = E
CIRCLE RADIUS = F
WHEN THE CIRCLE IS LEFT OF THE LINE FROM POINT P1 TO POINT P2 G=-1

C=F
H=D-A
I=E-B
J=√(H * H + I * I)
K=ACS(H/J)
IF 0>I THEN K = -K
ACS((C*C+J*J-F*F)/2/C/J)
M=A+C*COS(K+G*L)
N=B+C*SIN(K+G*L)

CIRCLE X COORD = M+ SGN M * .005

CIRCLE Y COORD = N+ SGN N *.005

[Kiwi]

I don't see what 'L' represents.
Is the L missing from this line?

L = ACS((C*C+J*J-F*F)/2/C/J)

[Stu_M3]

Quite correct, sorry about that. wrote it down in a hurry.

[BlueChip]

Trig Kalculator from Kentech Inc. will easily perform this calc and many others ... $95.

Info and demo at www.KentechInc.com

[Kiwi]

Looking at the KentechInc web page, it appears like their Kalculator is limited to maximum 90deg arcs.