source: sasview/sansmodels/src/sans/models/c_extensions/elliptical_cylinder.c @ e52eeea

/**
 * Scattering model for a cylinder with elliptical cross-section
 */

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


/**
 * Function to evaluate 1D scattering function
 * @param pars: parameters of the cylinder
 * @param q: q-value
 * @return: function value
 */
double elliptical_cylinder_analytical_1D(EllipticalCylinderParameters *pars, double q) {
        double dp[7];

        // Fill paramater array
        dp[0] = pars->scale;
        dp[1] = pars->r_minor;
        dp[2] = pars->r_ratio;
        dp[3] = pars->length;
        dp[4] = pars->sldCyl;
        dp[5] = pars->sldSolv;
        dp[6] = pars->background;

        // Call library function to evaluate model
        return EllipCyl20(dp, q);
}

double elliptical_cylinder_kernel(EllipticalCylinderParameters *pars, double q, double alpha, double nu) {
        double qr;
        double qL;
        double Be,Si;
        double r_major;
        double kernel;

        r_major = pars->r_ratio * pars->r_minor;

        qr = q*sin(alpha)*sqrt( r_major*r_major*sin(nu)*sin(nu) + pars->r_minor*pars->r_minor*cos(nu)*cos(nu) );
        qL = q*pars->length*cos(alpha)/2.0;

        if (qr==0){
                Be = 0.5;
        }else{
                Be = NR_BessJ1(qr)/qr;
        }
        if (qL==0){
                Si = 1.0;
        }else{
                Si = sin(qL)/qL;
        }


        kernel = 2.0*Be * Si;
        return kernel*kernel;
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the cylinder
 * @param q: q-value
 * @return: function value
 */
double elliptical_cylinder_analytical_2DXY(EllipticalCylinderParameters *pars, double qx, double qy) {
        double q;
        q = sqrt(qx*qx+qy*qy);
    return elliptical_cylinder_analytical_2D_scaled(pars, q, qx/q, qy/q);
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the cylinder
 * @param q: q-value
 * @param theta: angle theta = angle wrt z axis
 * @param phi: angle phi = angle around y axis (starting from the x+-direction as phi = 0)
 * @return: function value
 */
double elliptical_cylinder_analytical_2D(EllipticalCylinderParameters *pars, double q, double phi) {
    return elliptical_cylinder_analytical_2D_scaled(pars, q, cos(phi), sin(phi));
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the cylinder
 * @param q: q-value
 * @param q_x: q_x / q
 * @param q_y: q_y / q
 * @return: function value
 */
double elliptical_cylinder_analytical_2D_scaled(EllipticalCylinderParameters *pars, double q, double q_x, double q_y) {
        double cyl_x, cyl_y, cyl_z;
        double ell_x, ell_y;
        double q_z;
        double alpha, vol, cos_val;
        double nu, cos_nu;
        double answer;
        //convert angle degree to radian
        double pi = 4.0*atan(1.0);
        double theta = pars->cyl_theta * pi/180.0;
        double phi = pars->cyl_phi * pi/180.0;
        double psi = pars->cyl_psi * pi/180.0;

    //Cylinder orientation
    cyl_x = sin(theta) * cos(phi);
    cyl_y = sin(theta) * sin(phi);
    cyl_z = cos(theta);

    // 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 );

    //ellipse orientation:
        // the elliptical corss section was transformed and projected
        // into the detector plane already through sin(alpha)and furthermore psi remains as same
        // on the detector plane.
        // So, all we need is to calculate the angle (nu) of the minor axis of the ellipse wrt
        // the wave vector q.

        //x- y- component on the detector plane.
    ell_x =  cos(psi);
    ell_y =  sin(psi);

    // calculate the axis of the ellipse wrt q-coord.
    cos_nu = ell_x*q_x + ell_y*q_y;
    nu = acos(cos_nu);

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

        answer = elliptical_cylinder_kernel(pars, q, alpha,nu);

        // Multiply by contrast^2
        answer *= (pars->sldCyl - pars->sldSolv) * (pars->sldCyl - pars->sldSolv);

        //normalize by cylinder volume
        //NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl
    vol = acos(-1.0) * pars->r_minor * pars->r_minor * pars->r_ratio * pars->length;
        answer *= vol;

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

        //Scale
        answer *= pars->scale;

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

        return answer;
}