Finding the (x, y, z) of a point on a sphere

[Bazil]

Hi,

I have two known points on a sphere P1(x1, y1, z1) and P2(x2, y2, z2). I know the angle between them on the plane from the origin.

I wish to divide that angle by n to create n - 1 new points on the sphere surface on the arc between P1 and P2.

How do i find the x, y, z of these points. Or at least the first point with n = 3?

(n = 2 is done by midpoint of chord and scaling).

tia,

Bryan

 

[vrmuth]

I have two known points on a sphere P1(x1, y1, z1) and P2(x2, y2, z2). I know the angle between them on the plane from the origin.
I wish to divide that angle by n to create n - 1 new points on the sphere surface on the arc between P1 and P2.
How do i find the x, y, z of these points.

Just to make it clear, is the origin center ? Radius known ?
this thread may be useful https://www.physicsforums.com/showthread.php?t=173847

 

[Bazil]

Hi,

thx for answering - i had long given up

Yes the sphere is centred at the origin and i know the radius.

The other thread didn't appear to apply - but i don't know enough to be sure.

I have solved the problem using coordinate geometry but wondered if there was a more elegant solution using vectors...