Thread: [SOLVED] Adjacent points

Hi!

I am implementing the computation of spherical harmonics for the simulation of non-radially oscillating stars.
Therefore, I need to define a grid of points regularly distributed on a sphere.
For defining the position of these points I want to use a icosahedron and subdivide its faces (iteratively) to create a finer grid.
This grid is then projected on a sphere having the same center as the icosahedron.

I have the following questions:
1) For the computation I need to define somehow, which points of the resulting surface grid (of the subdicided icosahedron) are adjacent since I will have to compute the projected surface area of each triangle.
Triangles may not be calculated twice (or more times). Is there a formalism for such a problem?

2) I will have to interpolate a grid of points P (on a sphere) onto another grid of points Q. Therefore, I need to find for every point of Q at least the 3 closest points of P to interpolate.
Is there a more efficient way than just computing for every single point of Q the distances to all points of P and select the 3 closest points for interpolation?

I hope my questions were formulated clear enough... I would also be happy about any helping reference to a website or literature.

Thanks in advance for your answers!

Cheers, Wolfgang.

Originally Posted by jacqueslaflute

Hi!

I am implementing the computation of spherical harmonics for the simulation of non-radially oscillating stars.
Therefore, I need to define a grid of points regularly distributed on a sphere.
For defining the position of these points I want to use a icosahedron and subdivide its faces (iteratively) to create a finer grid.
This grid is then projected on a sphere having the same center as the icosahedron.

I have the following questions:
1) For the computation I need to define somehow, which points of the resulting surface grid (of the subdicided icosahedron) are adjacent since I will have to compute the projected surface area of each triangle.
Triangles may not be calculated twice (or more times). Is there a formalism for such a problem?

2) I will have to interpolate a grid of points P (on a sphere) onto another grid of points Q. Therefore, I need to find for every point of Q at least the 3 closest points of P to interpolate.
Is there a more efficient way than just computing for every single point of Q the distances to all points of P and select the 3 closest points for interpolation?

I hope my questions were formulated clear enough... I would also be happy about any helping reference to a website or literature.

Thanks in advance for your answers!

Cheers, Wolfgang.

I think you will probably not get a satisfactory answer here (though I could
be wrong).

I would suggest that you Google for "triangulation sphere" possibly
with "computational geometry" also in the search string.

RonL