pearl-polar-coordinates.ipf

Go to the documentation of this file.

#pragma rtGlobals=3
#pragma version = 1.1
#pragma IgorVersion = 6.1
#pragma ModuleName = PearlPolarCoordinates

// author: matthias.muntwiler@psi.ch
// Copyright (c) 2011-13 Paul Scherrer Institut
// $Id$

variable cart2polar(variable xx, variable yy, variable zz, variable* radius, variable* theta, variable* phi){
    // converts a 3-vector from Cartesian to polar coordinates
    variable xx, yy, zz
    variable &radius, &theta, &phi// angles in degrees
    
    radius = sqrt(xx^2 + yy^2 + zz^2)
    
    if (radius > 0)
        theta = acos(zz / radius) * 180 / pi
    else
        theta = 0
    endif
        
    if (xx > 0)
        phi = atan(yy / xx) * 180 / pi
    else if (xx < 0)
        phi = atan(yy / xx) * 180 / pi + 180
    else
        if (yy > 0)
            phi = 90
        else
            phi = 270
        endif
    endif
};

variable cart2polar_wave(wave in, wave out){
    // converts a wave of 3-vectors from Cartesian to polar coordinates
    wave in// wave with dimensions (3, N), N >= 1, (x, y, z)
    wave out// wave same dimensions as in, (radius, theta, phi)
        // angles in degrees
    
    out[0][] = sqrt(in[0][q]^2 + in[1][q]^2 + in[2][q]^2)
    out[1][] = acos(in[2][q] / out[0][q]) * 180 / pi
    out[2][] = atan(in[1][q] / in[0][q]) * 180 / pi + 180 * (in[0][q] < 0)
    out[2][] = numtype(out[2][q]) == 0 ? out[2][q] : 90 + 180 * (in[1][q] < 0)
};

variable polar2cart(variable radius, variable theta, variable phi, variable* xx, variable* yy, variable* zz){
    // converts a 3-vector from Cartesian to polar coordinates
    variable radius, theta, phi// angles in degrees
    variable &xx, &yy, &zz
    
    xx = radius * sin(theta * pi / 180) * cos(phi * pi / 180)
    yy = radius * sin(theta * pi / 180) * sin(phi * pi / 180)
    zz = radius * cos(theta * pi / 180)
};

variable polar2cart_wave(wave in, wave out){
    // converts a wave of 3-vectors from polar to Cartesian coordinates
    wave in// wave with dimensions (3, N), N >= 1, (radius, theta, phi)
        // angles in degrees
    wave out// wave same dimensions as in, (x, y, z)
    
    out[0][] = in[0][q] * sin(in[1][q] * pi / 180) * cos(in[2][q] * pi / 180)
    out[1][] = in[0][q] * sin(in[1][q] * pi / 180) * sin(in[2][q] * pi / 180)
    out[2][] = in[0][q] * cos(in[1][q] * pi / 180)
};

variable polar_distance(variable polar1, variable azim1, variable polar2, variable azim2){
    // returns the angle between two spherical coordinates
    variable polar1, azim1
        // angles in degrees
    variable polar2, azim2
        // angles in degrees
    
    variable xx1, yy1, zz1
    variable xx2, yy2, zz2
    
    polar2cart(1, polar1, azim1, xx1, yy1, zz1)
    polar2cart(1, polar2, azim2, xx2, yy2, zz2)
    
    variable vv
    vv = (xx1 * xx2 + yy1 * yy2 + zz1 * zz2) / sqrt(xx1^2 + yy1^2 + zz1^2) / sqrt(xx2^2 + yy2^2 + zz2^2)
    return acos(vv) * 180 / pi
};