Equation for circle points in 3D

  • #1
2
0
Summary:
Calculate the coordinates of consecutive points based on ABC points lying on a circle in 3D space
Hello,

I am trying to solve a problem and I would like to ask for help.

I have 3 points (A, B, C) in 3D space that are assumed to be on a circle.

EXAMPLE 1
1637915795573.png
1637915918290.png
EXAMPLE 2
1637920200382.png
1637916124402.png

My goal is to create an algebraic formula to calculate the coordinates for 10 points on a circle composed of ABC points at any distance from each other.

1637916560383.png
1637916587355.png

MY IDEA

My first idea was to create a triangle inscribed in a circle from the ABC points and then the radius of the circle.
First, I calculate the lengths of the triangle's legs by recalculating the lengths of |AB| |AC| and |CB| vectors.

1637920433604.png

I calculate the radius length using the formula (https://www.physicsforums.com/threads/equation-of-a-circle-through-3-points-in-3d-space.173847/):
1637920084001.png

And at this step, I have now stopped
 

Answers and Replies

  • #2
35,812
12,540
The center has a distance r to all these points. Can you find its coordinates as function of e.g. a, (b-a) and (c-a), e.g. the position of a and two sides? This is completely analogous to the two-dimensional problem.
 
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  • #3
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The center has a distance r to all these points. Can you find its coordinates as function of e.g. a, (b-a) and (c-a), e.g. the position of a and two sides? This is completely analogous to the two-dimensional problem.
Thank you for your answer.
I am testing the formula for the circle center coordinates in the "Cartesian coordinates from cross- and dot-products" section on the website : https://en.wikipedia.org/wiki/Circu...sian_coordinates_from_cross-_and_dot-products
 
  • #4
jim mcnamara
Mentor
4,521
3,360
Hint: think bisector - the problem says 'lies on a circle' which has to imply that the points are not collinear.
 

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