Plotting points evenly around an origin

[wizzy]

TL;DR

Can anyone help w/ how to plot the given number of points evenly around a sphere using the start and end degrees for phi and theta?

Say I have phi starting at 0 and ending at 360 degrees. Theta starts at 0 and ends at 360, and I input 10 points for phi and theta. I am trying to 3d plot phi * theta number of points around a center point.

I can plot a coordinate around a sphere using the following, which I think is correct. The axes I'm using on my project is x, y is up, and z is depth (in, out).

Real radius;
Radian theta;
Radian phi;

Vector3 result;
result.x = radius * Cos(phi) * Sin(theta);
result.z = radius * Sin(phi) * Sin(theta);
result.y = radius * Cos(theta);

But I don't understand how to get the number of points evenly distributed which should be, if I'm not mistaken, 100 points (phi's no. of points * theta's no. of points).

 

[Baluncore]

Welcome to PF.
You cannot map an evenly spaced Cartesian grid onto a sphere.

If you want the points to be evenly distributed over the surface of the sphere, you will need to first consider tiling or tessellation of the sphere with a combination of pentagons and hexagons, then place the points at the centres of the polygonal faces.
https://en.wikipedia.org/wiki/Truncated_icosahedron#Spherical
https://en.wikipedia.org/wiki/Geodesic_polyhedron

 

[Baluncore]

Another way might be to consider a method used to generate random points on a sphere, which goes something like this;

The phi coordinate is selected by a random number Ua between 0 and 1;
phi = Ua * 2 * Pi.

The theta coordinate is determined by selecting another random number Ub between 0 and 1; then solving for theta = Acos( 1 – 2 * Ub ).

The x, y and z coordinates are then;
x = r * Sin( theta ) * Cos( phi )
y = r * Sin( theta ) * Sin( phi )
z = r * Cos( theta )

How could you generate an orderly sequence of Ua and Ub to cover the sphere with evenly spaced points ?

 

[Baluncore]

The Fibonacci Sphere distributes points evenly over a sphere.

Const As Integer n = 100
Const Double TwoPi = 8 * Atn( 1 )
Const As Double golden_ratio = ( Sqrt( 5.0 ) + 1.0 ) / 2.0
Const As Double golden_angle = ( 2 - golden_ratio ) * TwoPi

Type geog
    As Double lat, lon
    As Double x, y, z
End Type

Dim As geog a( 1 To n )

Dim As Double r = 1
Dim As Integer i
For i = 1 To n
    With a( i )
        .lat = Asin( 2 * i / ( n + 1 ) - 1 )
        .lon = golden_angle * i
        .x = r * Cos( .lat ) * Cos( .lon )
        .y = r * Cos( .lat ) * Sin( .lon )
        .z = r * Sin( .lat )
    End With
Next i