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

In summary, the conversation is about finding the coordinates of new points on a sphere's surface, given two known points and the angle between them on the plane from the origin. The person also mentions that they have solved the problem using coordinate geometry and wonders if there is a more elegant solution using vectors.
  • #1
Bazil
2
0
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
 
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  • #2
Bazil said:
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
 
Last edited:
  • #3
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...
 

1. How do I find the coordinates of a point on a sphere?

To find the coordinates of a point on a sphere, you can use the formula x = r * cos(theta) * sin(phi), y = r * sin(theta) * sin(phi), and z = r * cos(phi), where x, y, and z are the coordinates of the point, r is the radius of the sphere, and theta and phi are the angles from the x-axis and the z-axis respectively.

2. What is the significance of finding the coordinates of a point on a sphere?

Finding the coordinates of a point on a sphere is important in many applications, such as navigation, astronomy, and computer graphics. It allows us to precisely locate a point on the surface of a sphere, which is a common shape in nature and man-made objects.

3. Can I use any coordinate system to find the coordinates of a point on a sphere?

Yes, you can use any coordinate system to find the coordinates of a point on a sphere. However, the most commonly used coordinate systems are Cartesian coordinates and spherical coordinates. It is important to carefully choose the coordinate system based on the problem at hand.

4. How do I convert the coordinates of a point on a sphere to a different coordinate system?

To convert the coordinates of a point on a sphere to a different coordinate system, you can use transformation equations specific to the two coordinate systems. For example, to convert from spherical coordinates to Cartesian coordinates, you can use the equations x = r * cos(theta) * sin(phi), y = r * sin(theta) * sin(phi), and z = r * cos(phi).

5. Are there any special cases when finding the coordinates of a point on a sphere?

Yes, there are a few special cases when finding the coordinates of a point on a sphere. One of them is when the point is located at the poles (theta = 0 or theta = pi). In this case, the equations for x and y become undefined, and we need to use a different set of equations. Another special case is when the point is located at the equator (phi = pi/2 or phi = 3*pi/2). In this case, the equation for z becomes undefined, and we need to use a different set of equations as well.

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