# Fwd: sph2cart octave definition matches neither mathematical nor phsics definitions Classic List Threaded 1 message (please keep the help list copied on all emails. message forwarded below.)---------- Forwarded message ---------From: J.A. (Hans) Piest Date: Wed, Feb 12, 2020 at 6:46 AMSubject: sph2cart octave definition matches neither mathematical nor phsics definitionsTo: <[hidden email]>, <[hidden email]>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 ------------------------------------------------------------------------------------ example publication: CRDS of thin layers : www.darklands-sewer-system.eu/outlet/FTP/CavityRingdownPaper.pdf sailing: SV Morgenster bottom-up : www.darklands-sewer-system.eu/outlet/FTP/bottom-up-small.mov SV Morgenster top-down  : www.darklands-sewer-system.eu/outlet/FTP/top-down-small.mov rowing: 8+ : www.darklands-sewer-system.eu/outlet/FTP/RowingTheClubAcht-28February2015-small.mp4 sph2cart.csv (2K) Download Attachment sph2cart.ods (16K) Download Attachment