Given 3 points how to find the centre and radius of a circle in 3 D?

  • Thread starter ukmj
  • Start date
  • #1
2
0
Given 3 points how to find the centre and radius of a circle in 3 D??

Say the 3 points are (a,b,c),(a1.b1,c1) and (a2,b2,c2)...
 

Answers and Replies

  • #2
exk
119
0
Do you mean a sphere? Are these arbitrary points anywhere in the sphere or on the surface?
 
  • #3
1,250
2
Here is the equation of the points {x_i,y_i} for i = 1,2,3 in terms of the variables x and y:

[tex]
\left|
\begin{array}{llll}
x^2+y^2 & x & y & 1 \\
x_1^2+y_1^2 & x_1 & y_1 & 1 \\
x_2^2+y_2^2 & x_2 & y_2 & 1 \\
x_3^2+y_3^2 & x_3 & y_3 & 1
\end{array}
\right|=0
[/tex]
 
  • #4
Borek
Mentor
28,651
3,144
Do you mean a sphere? Are these arbitrary points anywhere in the sphere or on the surface?

Three points are not enough to define the sphere. Four will do the trick (unless they will not, but you need four at least). Points inside the sphere do not belong to the sphere. IMHO question is very precise.
 
  • #5
exk
119
0
Borek you are absolutely right. I just wanted to make sure.
 
  • #6
mathwonk
Science Advisor
Homework Helper
2020 Award
11,113
1,317
one might find the plane through the three points, then choosing two pairs of points, find the plane perpendicular bisector of the segments they determine.

these three planes should meet at the center of the circle.
 

Related Threads on Given 3 points how to find the centre and radius of a circle in 3 D?

Replies
3
Views
2K
Replies
18
Views
40K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
6
Views
10K
Replies
2
Views
23K
Replies
5
Views
65K
Replies
1
Views
1K
Top