Non-standard spherical coordinates conversion

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Albert Zurita 2023-3-7

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https://ww2.mathworks.cn/matlabcentral/answers/1924785-non-standard-spherical-coordinates-conversion

评论： David Goodmanson 2023-3-9

Hi, I have imported antenna data from CST Microwave Studio, with theta and phi spherical coordinate vectors. However, I noticed the phi vector ranges from -180 to 180 and the theta vector from 0 to 179, which is not the standard spherical coordinate system where phi is [0 180] and theta [0 360]. Is there any conversion function implemented for different conventions?

As an example in my case: phi = -90 and theta = 0 corresponds to the negative X axis. In standard coordinates that point would be expressed by phi = 90 and theta = 180

Here the definition of theta and phi by Wikipedia: https://en.wikipedia.org/wiki/Spherical_coordinate_system#/media/File:3D_Spherical_2.svg

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the cyclist 2023-3-8

I understand how you want the final coordinates to be. (You are calling this "standard", but the Wikipedia page acknowledges that there are multiple conventions used. There is no single standard.) But let's confirm:

phi denotes the polar angle, measured downward from the positive Z axis. It ranges from 0 to 180.
theta denotes the azimuthal angle, measured from the positive X axis, toward the positive Y axis.
0 = pos X axis
90 = pos Y axis
180 = neg X axis
270 = neg Y axis

I cannot figure out the coordinate system you are converting from, based on what you have stated. Can you use the same method I just did above, to describe the angles denoted by phi and theta?

David Goodmanson 2023-3-9

Hi Albert,

given the ranges of the CST phi and theta, the only sensible concusion is that the CST theta is your phi (polar angle) and the CST phi is your theta (azimuthal angle). Since CST theta goes from 0 to 180, it's reasonable to conclude that that angle is measured down from the north pole, (+z axis usually). For CST phi, which goes from -180 to 180, it's likely that phi = 0 is the +x axis with positive azimuthal angle measured counterclockwise from there. All of this is very much one of the standard conventions, subject to verification that you may have to obtain in some way.

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