#How to find the parameters of a circle based on 3 points on circumference
I spent some hours with WolframAlpha, paper and a text editor to distill the mathematical formula to find the center coordinates of a circle and its radius. I tested it with a few random coordinates and it returned precise results each time.
I provide here a Go code for my testing. It's very trivial to convert it into any other language.
Laszlo
| package main | |
| import ( | |
| "fmt" | |
| "math" | |
| ) | |
| func main() { | |
| x1:=1.91 | |
| y1:=1.06 | |
| x2:=3.28 | |
| y2:=9.69 | |
| x3:=8.24 | |
| y3:=1.16 | |
| D1:=y2-y1 | |
| D2:=y1-y3 | |
| D3:=y3-y2 | |
| D4:=x1-x2 | |
| D5:=x3-x1 | |
| D6:=x2-x3 | |
| S1:=x1*x1+y1*y1 | |
| S2:=x2*x2+y2*y2 | |
| S3:=x3*x3+y3*y3 | |
| T1:=2*(x3*D1+x2*D2+x1*D3) | |
| x:=(D3*S1+D2*S2+D1*S3)/T1 | |
| y:=(D6*S1+D5*S2+D4*S3)/T1 | |
| r:=0.5*math.Sqrt( | |
| (D4*D4+D1*D1)* | |
| (D5*D5+D2*D2)* | |
| (D6*D6+D3*D3)/ | |
| (x1*D3+x2*D2+x3*D1)/ | |
| (x1*D3+x2*D2+x3*D1)) | |
| fmt.Println("x= ",x,"y=",y,"r=",r) | |
| } |