Spherical Harmonics

This function generates the Spherical Harmonics basis functions of degree L and order M.

Description

This function generates the Spherical Harmonics basis functions of degree L and order M.

SYNTAX: [Ymn,THETA,PHI,X,Y,Z]=spharm4(L,M,RES,PLOT_FLAG);

INPUTS:

L - Spherical harmonic degree, [1x1]
M - Spherical harmonic order, [1x1]
RES - Vector of # of points to use [#Theta x #Phi points],[1x2] or [2x1]
PLOT_FLAG - Binary flag to generates a figure of the spherical harmonic surfaces (DEFAULT=1)

OUTPUTS:
 
Ymn - Spherical harmonics coordinates, [RES(1) x RES(2)]
THETA - Circumferential coordinates, [RES(1) x RES(2)]
PHI - Latitudinal coordinates, [RES(1) x RES(2)]
X,Y,Z - Cartesian coordinates of magnitude, squared, spherical harmonic surface points, [RES(1) x RES(2)]

NOTE: It is very important to keep the various usages of THETA and PHI straight. For this function THETA is the Azimuthal/Longitude/Circumferential coordinate and is defined on the interval [0,2*pi], whereas PHI is the Altitude/Latitude/Elevation and is defined on the interval [0,pi]. Also note that the conversion to cartesian coordinates requires that PHI be offset by pi/2 so that the conversion is on the interval [-pi/2,pi/2].

• MATLAB release: MATLAB 7 (R14)

[Michael Kleder]

Nice.

[GOUTAM BISWAS]

 

[Oliver Müller]

This is a very good starting point for me and my work - thanx ;-)

[Ritter Dieter]

 

[Ting HUANG]

There's something wrong with the dimension of Ymn.
"[THETA,PHI]=meshgrid(THETA,PHI);"
should be "[THETA,PHI]=ndgrid(THETA,PHI);" (line 53)

[Tamar Kashti]

Nice start point. Note that the function is mainly for ploting Ylm's, since the output is a matrix of different angles (theta,phi). The opposite convation of (theta,phi) is confusing.

[GOUTAM BISWAS]

 

[B L]

Great, math is correct, but Matlab 7 doesn't know what setfig is:
??? Undefined command/function 'setfig'.

Error in ==> spharm4 at 92
  setfig(gcf,10,5,12);

Easy to tweak for my needs.

[Miguel Neto]

 

[Anamika Gupto]

 

[bapitha anbalagan]

sir,
i am final year M.E. student. i want the matlab coding for harmonic elimination in PWM AC chopper using genetic algorithm.

[Seo Lee]

Nice start point. Note that the function is mainly for ploting Ylm's, since the output is a matrix of different angles (theta,phi).

[Jon Casey]

 

[Jacek]

Nice work .

One minor comment: the output argument Ymn has the elevation and azimuth dimensions flipped with respect to the input RES argument, due to the nature of meshgrid. Thus, the rows of the output Ymn refer to elevation, while the columns of the output Ymn refer to azimuth.

[Etai Rosenkrantz]

 

[Rush]

just one question, let's say i want to find spherical harmonics with m=-1 and l=1, it gives me error statements. im sure it has to do with the modulus sign. if so, why do we put the modulus sign? thanx.