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From:
J.A. (Hans) Piest <address@hidden>Date: Wed, Feb 12, 2020 at 6:46 AM
Subject: sph2cart octave definition matches neither mathematical nor phsics definitions
To: <
address@hidden>, <
address@hidden>
Hi guys,
Finally I found out that the spherical coordinates in octave function sph2cart are defined as follows:
x = cos(phi) * cos(theta)
y = cos(phi) * sin(theta)
z = sin(phi)
In physics the coordinates are defined as follows:
x = sin(theta) * cos(phi)
y = sin(theta) * sin(phi)
z = cos(theta)
Mathematics is the same as in physics but with theta and phi interchanged:
x = sin(phi) * cos(theta)
y = sin(phi) * sin(theta)
z = cos(phi)
You can see from e.g. wikipedia => spherical coordinates that
both in mathematics and in physics the x,y,z axes are a righthanded oriented system,
which the default system both in physics and mathematics to use. Only theta and phi have
been interchanged.
E.g. for (theta,phi) = (30°,60°):
octave sph2crt formula : (x,y,z) = ( sqrt(3)/4 , 3/4 , sqrt(3)/2 )
octave sph2crt(pi/6, pi/3) : (x,y,z) = ( 0.43301 , 0.25000 , 0.86603 )
physics formula : (x,y,z) = ( 1/4 , sqrt(3)/4 , sqrt(3)/2 )
mathematics formula : (x,y,z) = ( 3/4 , sqrt(3)/4 , 1/2 )
In the attachment I have compared the outputs of sph2crt(theta,phi,1)
with the outputs of the explicit formulas expressed above:
It show that the formulas for (x,y,z) for physics and mathematics give different results than
those for the explicit octave computation.
I think that it is very important that you give a clear picture of how sph2crt computes x,y,z.
I suggest that you simply put the formula
x = cos(phi) * cos(theta)
y = cos(phi) * sin(theta)
z = sin(phi)
in the manual ... nobody can be confused anymore that way.
regards,
Hans
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rowing:
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