source: sasmodels/sasmodels/models/sc_paracrystal.c @ 50beefe

double form_volume(double radius);

double Iq(double q,
          double dnn,
          double d_factor,
          double radius,
          double sphere_sld,
          double solvent_sld);

double Iqxy(double qx, double qy,
            double dnn,
            double d_factor,
            double radius,
            double sphere_sld,
            double solvent_sld,
            double theta,
            double phi,
            double psi);

double form_volume(double radius)
{
    return sphere_volume(radius);
}

static double
sc_eval(double theta, double phi, double temp3, double temp4, double temp5)
{
    double cnt, snt;
    SINCOS(theta, cnt, snt);

    double cnp, snp;
    SINCOS(phi, cnp, snp);

        double temp6 = snt;
        double temp7 = -1.0*temp3*snt*cnp;
        double temp8 = temp3*snt*snp;
        double temp9 = temp3*cnt;
        double result = temp6/((1.0-temp4*cos((temp7))+temp5)*
                               (1.0-temp4*cos((temp8))+temp5)*
                               (1.0-temp4*cos((temp9))+temp5));
        return (result);
}

static double
sc_integrand(double dnn, double d_factor, double qq, double xx, double yy)
{
    //Function to calculate integrand values for simple cubic structure

        double da = d_factor*dnn;
        double temp1 = qq*qq*da*da;
        double temp2 = cube(-expm1(-temp1));
        double temp3 = qq*dnn;
        double temp4 = 2.0*exp(-0.5*temp1);
        double temp5 = exp(-1.0*temp1);

        double integrand = temp2*sc_eval(yy,xx,temp3,temp4,temp5)/M_PI_2;

        return(integrand);
}

double Iq(double q,
          double dnn,
          double d_factor,
          double radius,
          double sphere_sld,
          double solvent_sld)
{
        const double va = 0.0;
        const double vb = M_PI_2; //orientation average, outer integral

    double summ=0.0;
    double answer=0.0;

        for(int i=0;i<150;i++) {
                //setup inner integral over the ellipsoidal cross-section
                double summj=0.0;
                double zi = ( Gauss150Z[i]*(vb-va) + va + vb )/2.0;
                for(int j=0;j<150;j++) {
                        //150 gauss points for the inner integral
                        double zij = ( Gauss150Z[j]*(vb-va) + va + vb )/2.0;
                        double tmp = Gauss150Wt[j] * sc_integrand(dnn,d_factor,q,zi,zij);
                        summj += tmp;
                }
                //now calculate the value of the inner integral
                answer = (vb-va)/2.0*summj;

                //now calculate outer integral
                double tmp = Gauss150Wt[i] * answer;
                summ += tmp;
        }               //final scaling is done at the end of the function, after the NT_FP64 case

        answer = (vb-va)/2.0*summ;

        //Volume fraction calculated from lattice symmetry and sphere radius
        // NB: 4/3 pi r^3 / dnn^3 = 4/3 pi(r/dnn)^3
        const double latticeScale = sphere_volume(radius/dnn);

        answer *= sphere_form(q, radius, sphere_sld, solvent_sld)*latticeScale;

        return answer;
}

double Iqxy(double qx, double qy,
          double dnn,
          double d_factor,
          double radius,
          double sphere_sld,
          double solvent_sld,
          double theta,
          double phi,
          double psi)
{
    double q, zhat, yhat, xhat;
    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat);

    const double qd = q*dnn;
    const double arg = 0.5*square(qd*d_factor);
    const double tanh_qd = tanh(arg);
    const double cosh_qd = cosh(arg);
    const double Zq = tanh_qd/(1. - cos(qd*zhat)/cosh_qd)
                    * tanh_qd/(1. - cos(qd*yhat)/cosh_qd)
                    * tanh_qd/(1. - cos(qd*xhat)/cosh_qd);

    const double Fq = sphere_form(q, radius, sphere_sld, solvent_sld)*Zq;
    //the occupied volume of the lattice
    const double lattice_scale = sphere_volume(radius/dnn);
    return lattice_scale * Fq;
}