source: sasview/sansmodels/src/sans/models/c_extensions/spheroid.c @ a807ffd

/**
 * Scattering model for a prolate
 * @author: UTK
 */

#include "spheroid.h"
#include <math.h>
#include "libCylinder.h"
#include <stdio.h>
#include <stdlib.h>

/**
 * Function to evaluate 1D scattering function
 * @param pars: parameters of the prolate
 * @param q: q-value
 * @return: function value
 */
double spheroid_analytical_1D(SpheroidParameters *pars, double q) {
        double dp[9];

        // Fill paramater array
        dp[0] = pars->scale;
        dp[1] = pars->equat_core;
        dp[2] = pars->polar_core;
        dp[3] = pars->equat_shell;
        dp[4] = pars->polar_shell;
        dp[5] = pars->sld_core;
        dp[6] = pars->sld_shell;
        dp[7] = pars->sld_solvent;
        dp[8] = pars->background;

        // Call library function to evaluate model
        return OblateForm(dp, q);
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the prolate
 * @param q: q-value
 * @return: function value
 */
double spheroid_analytical_2DXY(SpheroidParameters *pars, double qx, double qy) {
        double q;
        q = sqrt(qx*qx+qy*qy);
    return spheroid_analytical_2D_scaled(pars, q, qx/q, qy/q);
}


/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the prolate
 * @param q: q-value
 * @param phi: angle phi
 * @return: function value
 */
double spheroid_analytical_2D(SpheroidParameters *pars, double q, double phi) {
    return spheroid_analytical_2D_scaled(pars, q, cos(phi), sin(phi));
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the prolate
 * @param q: q-value
 * @param q_x: q_x / q
 * @param q_y: q_y / q
 * @return: function value
 */
double spheroid_analytical_2D_scaled(SpheroidParameters *pars, double q, double q_x, double q_y) {

        double cyl_x, cyl_y, cyl_z;
        double q_z;
        double alpha, vol, cos_val;
        double answer;
        double Pi = 4.0*atan(1.0);
        double sldcs,sldss;

        //convert angle degree to radian
        double theta = pars->axis_theta * Pi/180.0;
        double phi = pars->axis_phi * Pi/180.0;


    // ellipsoid orientation, the axis of the rotation is consistent with the ploar axis.
    cyl_x = sin(theta) * cos(phi);
    cyl_y = sin(theta) * sin(phi);
    cyl_z = cos(theta);
    //del sld
    sldcs = pars->sld_core - pars->sld_shell;
    sldss = pars->sld_shell- pars->sld_solvent;

    // q vector
    q_z = 0;

    // Compute the angle btw vector q and the
    // axis of the cylinder
    cos_val = cyl_x*q_x + cyl_y*q_y + cyl_z*q_z;

    // The following test should always pass
    if (fabs(cos_val)>1.0) {
        printf("cyl_ana_2D: Unexpected error: cos(alpha)>1\n");
        return 0;
    }

    // Note: cos(alpha) = 0 and 1 will get an
    // undefined value from CylKernel
        alpha = acos( cos_val );

        // Call the IGOR library function to get the kernel: MUST use gfn4 not gf2 because of the def of params.
        answer = gfn4(cos_val,pars->equat_core,pars->polar_core,pars->equat_shell,pars->polar_shell,sldcs,sldss,q);
        //It seems that it should be normalized somehow. How???

        //normalize by cylinder volume
        //NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl
    vol = 4.0*Pi/3.0*pars->equat_shell*pars->equat_shell*pars->polar_shell;
        answer /= vol;

        //convert to [cm-1]
        answer *= 1.0e8;

        //Scale
        answer *= pars->scale;

        // add in the background
        answer += pars->background;

        return answer;
}