source: sasview/sansmodels/src/c_extensions/fcc.c @ fb732dc

/*
 * Scattering model for a SC_ParaCrystal
 */
#include "fcc.h"
#include "libSphere.h"
#include <math.h>
#include <stdio.h>

/**
 * Function to evaluate 1D scattering function
 * @param pars: parameters of the FCC_ParaCrystal
 * @param q: q-value
 * @return: function value
 */
double fcc_analytical_1D(FCParameters *pars, double q) {
        double dp[7];
        double result;

        dp[0] = pars->scale;
        dp[1] = pars->dnn;
        dp[2] = pars->d_factor;
        dp[3] = pars->radius;
        dp[4] = pars->sldSph;
        dp[5] = pars->sldSolv;
        dp[6] = pars->background;

        result = FCC_ParaCrystal(dp, q);
        // This FIXES a singualrity the kernel in libigor.
        if ( result == INFINITY || result == NAN){
                result = pars->background;
        }
        return result;
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the FCC_ParaCrystal
 * @param q: q-value
 * @return: function value
 */
double fc_analytical_2DXY(FCParameters *pars, double qx, double qy){
        double q;
        q = sqrt(qx*qx+qy*qy);
        return fc_analytical_2D_scaled(pars, q, qx/q, qy/q);
}

double fc_analytical_2D(FCParameters *pars, double q, double phi) {
        return fc_analytical_2D_scaled(pars, q, cos(phi), sin(phi));
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the FCCCrystalModel
 * @param q: q-value
 * @param q_x: q_x / q
 * @param q_y: q_y / q
 * @return: function value
 */
double fc_analytical_2D_scaled(FCParameters *pars, double q, double q_x, double q_y) {
        double b3_x, b3_y, b3_z, b1_x, b1_y;
        double q_z;
        double alpha, cos_val_b3, cos_val_b2, cos_val_b1;
        double a1_dot_q, a2_dot_q,a3_dot_q;
        double answer;
        double Pi = 4.0*atan(1.0);
        double aa, Da, qDa_2, latticeScale, Zq, Fkq, Fkq_2;

        double dp[5];
  //convert angle degree to radian
  double theta = pars->theta * Pi/180.0;
  double phi = pars->phi * Pi/180.0;
  double psi = pars->psi * Pi/180.0;
        dp[0] = 1.0;
        dp[1] = pars->radius;
        dp[2] = pars->sldSph;
        dp[3] = pars->sldSolv;
        dp[4] = 0.0;

        aa = pars->dnn;
        Da = pars->d_factor*aa;
        qDa_2 = pow(q*Da,2.0);
        //contrast = pars->sldSph - pars->sldSolv;

        latticeScale = 4.0*(4.0/3.0)*Pi*(dp[1]*dp[1]*dp[1])/pow(aa*sqrt(2.0),3.0);
        // q vector
        q_z = 0.0; // for SANS; assuming qz is negligible
        /// Angles here are respect to detector coordinate
        ///  instead of against q coordinate in PRB 36(46), 3(6), 1754(3854)
    // b3 axis orientation
    b3_x = sin(theta) * cos(phi);//negative sign here???
    b3_y = sin(theta) * sin(phi);
    b3_z = cos(theta);
    cos_val_b3 =  b3_x*q_x + b3_y*q_y + b3_z*q_z;
    alpha = acos(cos_val_b3);
    // b1 axis orientation
    b1_x = sin(psi);
    b1_y = cos(psi);
        cos_val_b1 = (b1_x*q_x + b1_y*q_y);
    // b2 axis orientation
        cos_val_b2 = sin(acos(cos_val_b1));
        // alpha correction
        cos_val_b2 *= sin(alpha);
        cos_val_b1 *= sin(alpha);

    // Compute the angle btw vector q and the a3 axis
    a3_dot_q = 0.5*aa*q*(cos_val_b2+cos_val_b1);

    // a1 axis
    a1_dot_q = 0.5*aa*q*(cos_val_b2+cos_val_b3);

    // a2 axis
    a2_dot_q = 0.5*aa*q*(cos_val_b3+cos_val_b1);

    // The following test should always pass
    if (fabs(cos_val_b3)>1.0) {
        printf("fcc_ana_2D: Unexpected error: cos(alpha)>1\n");
        return 0;
    }
    // Get Fkq and Fkq_2
    Fkq = exp(-0.5*pow(Da/aa,2.0)*(a1_dot_q*a1_dot_q+a2_dot_q*a2_dot_q+a3_dot_q*a3_dot_q));
    Fkq_2 = Fkq*Fkq;
    // Call Zq=Z1*Z2*Z3
    Zq = (1.0-Fkq_2)/(1.0-2.0*Fkq*cos(a1_dot_q)+Fkq_2);
    Zq = Zq * (1.0-Fkq_2)/(1.0-2.0*Fkq*cos(a2_dot_q)+Fkq_2);
    Zq = Zq * (1.0-Fkq_2)/(1.0-2.0*Fkq*cos(a3_dot_q)+Fkq_2);

        // Use SphereForm directly from libigor
        answer = SphereForm(dp,q)*Zq;

        //consider scales
        answer *= latticeScale * pars->scale;

        // This FIXES a singualrity the kernel in libigor.
        if ( answer == INFINITY || answer == NAN){
                answer = 0.0;
        }

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

        return answer;
}