/*******************************************************************************
*
* McStas, neutron ray-tracing package
*         Copyright (C) 1997-2008, All rights reserved
*         Risoe National Laboratory, Roskilde, Denmark
*         Institut Laue Langevin, Grenoble, France
*
* Component: SasView_sc_paracrystal
*
* %Identification
* Written by: Jose Robledo
* Based on sasmodels from SasView
* Origin: FZJ / DTU / ESS DMSC
*
*
* SasView sc_paracrystal model component as sample description.
*
* %Description
*
* SasView_sc_paracrystal component, generated from sc_paracrystal.c in sasmodels.
*
* Example: 
*  SasView_sc_paracrystal(dnn, d_factor, radius, sld, sld_solvent, 
*     model_scale=1.0, model_abs=0.0, xwidth=0.01, yheight=0.01, zdepth=0.005, R=0, 
*     int target_index=1, target_x=0, target_y=0, target_z=1,
*     focus_xw=0.5, focus_yh=0.5, focus_aw=0, focus_ah=0, focus_r=0, 
*     pd_radius=0.0)
*
* %Parameters
* INPUT PARAMETERS:
* dnn: [Ang] ([0.0, inf]) Nearest neighbor distance.
* d_factor: [] ([-inf, inf]) Paracrystal distortion factor.
* radius: [Ang] ([0.0, inf]) Radius of sphere.
* sld: [1e-6/Ang^2] ([0.0, inf]) Sphere scattering length density.
* sld_solvent: [1e-6/Ang^2] ([0.0, inf]) Solvent scattering length density.
* Optional parameters:
* model_abs: [ ] Absorption cross section density at 2200 m/s.
* model_scale: [ ] Global scale factor for scattering kernel. For systems without inter-particle interference, the form factors can be related to the scattering intensity by the particle volume fraction.
* xwidth: [m] ([-inf, inf]) Horiz. dimension of sample, as a width.
* yheight: [m] ([-inf, inf]) vert . dimension of sample, as a height for cylinder/box
* zdepth: [m] ([-inf, inf]) depth of sample
* R: [m] Outer radius of sample in (x,z) plane for cylinder/sphere.
* target_x: [m] relative focus target position.
* target_y: [m] relative focus target position.
* target_z: [m] relative focus target position.
* target_index: [ ] Relative index of component to focus at, e.g. next is +1.
* focus_xw: [m] horiz. dimension of a rectangular area.
* focus_yh: [m], vert. dimension of a rectangular area.
* focus_aw: [deg], horiz. angular dimension of a rectangular area.
* focus_ah: [deg], vert. angular dimension of a rectangular area.
* focus_r: [m] case of circular focusing, focusing radius.
* pd_radius: [] (0,inf) defined as (dx/x), where x is de mean value and dx the standard devition of the variable
*
* %Link
* %End
*******************************************************************************/
DEFINE COMPONENT SasView_sc_paracrystal

SETTING PARAMETERS (
        dnn=220.0,
        d_factor=0.06,
        radius=40.0,
        sld=3.0,
        sld_solvent=6.3,
        model_scale=1.0,
        model_abs=0.0,
        xwidth=0.01,
        yheight=0.01,
        zdepth=0.005,
        R=0,
        target_x=0,
        target_y=0,
        target_z=1,
        int target_index=1,
        focus_xw=0.5,
        focus_yh=0.5,
        focus_aw=0,
        focus_ah=0,
        focus_r=0,
        pd_radius=0.0)


SHARE %{
%include "sas_kernel_header.c"

/* BEGIN Required header for SASmodel sc_paracrystal */
#define HAS_Iqabc
#define HAS_Iq
#define FORM_VOL

#ifndef SAS_HAVE_sas_3j1x_x
#define SAS_HAVE_sas_3j1x_x

#line 1 "sas_3j1x_x"
/**
* Spherical Bessel function 3*j1(x)/x
*
* Used for low q to avoid cancellation error.
* Note that the values differ from sasview ~ 5e-12 rather than 5e-14, but
* in this case it is likely cancellation errors in the original expression
* using double precision that are the source.
*/
double sas_3j1x_x(double q);

// The choice of the number of terms in the series and the cutoff value for
// switching between series and direct calculation depends on the numeric
// precision.
//
// Point where direct calculation reaches machine precision:
//
//   single machine precision eps 3e-8 at qr=1.1 **
//   double machine precision eps 4e-16 at qr=1.1
//
// Point where Taylor series reaches machine precision (eps), where taylor
// series matches direct calculation (cross) and the error at that point:
//
//   prec   n eps  cross  error
//   single 3 0.28  0.4   6.2e-7
//   single 4 0.68  0.7   2.3e-7
//   single 5 1.18  1.2   7.5e-8
//   double 3 0.01  0.03  2.3e-13
//   double 4 0.06  0.1   3.1e-14
//   double 5 0.16  0.2   5.0e-15
//
// ** Note: relative error on single precision starts increase on the direct
// method at qr=1.1, rising from 3e-8 to 5e-5 by qr=1e3.  This should be
// safe for the sans range, with objects of 100 nm supported to a q of 0.1
// while maintaining 5 digits of precision.  For usans/sesans, the objects
// are larger but the q is smaller, so again it should be fine.
//
// See explore/sph_j1c.py for code to explore these ranges.

// Use 4th order series
#if FLOAT_SIZE>4
#define SPH_J1C_CUTOFF 0.1
#else
#define SPH_J1C_CUTOFF 0.7
#endif
#pragma acc routine seq
double sas_3j1x_x(double q)
{
    // 2017-05-18 PAK - support negative q
    if (fabs(q) < SPH_J1C_CUTOFF) {
        const double q2 = q*q;
        return (1.0 + q2*(-3./30. + q2*(3./840. + q2*(-3./45360.))));// + q2*(3./3991680.)))));
    } else {
        double sin_q, cos_q;
        SINCOS(q, sin_q, cos_q);
        return 3.0*(sin_q/q - cos_q)/(q*q);
    }
}


#endif // SAS_HAVE_sas_3j1x_x


#ifndef SAS_HAVE_sphere_form
#define SAS_HAVE_sphere_form

#line 1 "sphere_form"
double sphere_volume(double radius);
double sphere_form(double q, double radius, double sld, double solvent_sld);

    
#pragma acc routine seq
double sphere_volume(double radius)
{
    return M_4PI_3*cube(radius);
}
    
#pragma acc routine seq
double sphere_form(double q, double radius, double sld, double solvent_sld)
{
    const double fq = sphere_volume(radius) * sas_3j1x_x(q*radius);
    const double contrast = (sld - solvent_sld);
    return 1.0e-4*square(contrast * fq);
}



#endif // SAS_HAVE_sphere_form


#ifndef SAS_HAVE_gauss150
#define SAS_HAVE_gauss150

#line 1 "gauss150"
// Created by Andrew Jackson on 4/23/07

 #ifdef GAUSS_N
 # undef GAUSS_N
 # undef GAUSS_Z
 # undef GAUSS_W
 #endif
 #define GAUSS_N 150
 #define GAUSS_Z Gauss150Z
 #define GAUSS_W Gauss150Wt


// Note: using array size 152 rather than 150 so that it is a multiple of 4.
// Some OpenCL devices prefer that vectors start and end on nice boundaries.
constant double Gauss150Z[152]={
  	-0.9998723404457334,
  	-0.9993274305065947,
  	-0.9983473449340834,
  	-0.9969322929775997,
  	-0.9950828645255290,
  	-0.9927998590434373,
  	-0.9900842691660192,
  	-0.9869372772712794,
  	-0.9833602541697529,
  	-0.9793547582425894,
  	-0.9749225346595943,
  	-0.9700655145738374,
  	-0.9647858142586956,
  	-0.9590857341746905,
  	-0.9529677579610971,
  	-0.9464345513503147,
  	-0.9394889610042837,
  	-0.9321340132728527,
  	-0.9243729128743136,
  	-0.9162090414984952,
  	-0.9076459563329236,
  	-0.8986873885126239,
  	-0.8893372414942055,
  	-0.8795995893549102,
  	-0.8694786750173527,
  	-0.8589789084007133,
  	-0.8481048644991847,
  	-0.8368612813885015,
  	-0.8252530581614230,
  	-0.8132852527930605,
  	-0.8009630799369827,
  	-0.7882919086530552,
  	-0.7752772600680049,
  	-0.7619248049697269,
  	-0.7482403613363824,
  	-0.7342298918013638,
  	-0.7198995010552305,
  	-0.7052554331857488,
  	-0.6903040689571928,
  	-0.6750519230300931,
  	-0.6595056411226444,
  	-0.6436719971150083,
  	-0.6275578900977726,
  	-0.6111703413658551,
  	-0.5945164913591590,
  	-0.5776035965513142,
  	-0.5604390262878617,
  	-0.5430302595752546,
  	-0.5253848818220803,
  	-0.5075105815339176,
  	-0.4894151469632753,
  	-0.4711064627160663,
  	-0.4525925063160997,
  	-0.4338813447290861,
  	-0.4149811308476706,
  	-0.3959000999390257,
  	-0.3766465660565522,
  	-0.3572289184172501,
  	-0.3376556177463400,
  	-0.3179351925907259,
  	-0.2980762356029071,
  	-0.2780873997969574,
  	-0.2579773947782034,
  	-0.2377549829482451,
  	-0.2174289756869712,
  	-0.1970082295132342,
  	-0.1765016422258567,
  	-0.1559181490266516,
  	-0.1352667186271445,
  	-0.1145563493406956,
  	-0.0937960651617229,
  	-0.0729949118337358,
  	-0.0521619529078925,
  	-0.0313062657937972,
  	-0.0104369378042598,
  	0.0104369378042598,
  	0.0313062657937972,
  	0.0521619529078925,
  	0.0729949118337358,
  	0.0937960651617229,
  	0.1145563493406956,
  	0.1352667186271445,
  	0.1559181490266516,
  	0.1765016422258567,
  	0.1970082295132342,
  	0.2174289756869712,
  	0.2377549829482451,
  	0.2579773947782034,
  	0.2780873997969574,
  	0.2980762356029071,
  	0.3179351925907259,
  	0.3376556177463400,
  	0.3572289184172501,
  	0.3766465660565522,
  	0.3959000999390257,
  	0.4149811308476706,
  	0.4338813447290861,
  	0.4525925063160997,
  	0.4711064627160663,
  	0.4894151469632753,
  	0.5075105815339176,
  	0.5253848818220803,
  	0.5430302595752546,
  	0.5604390262878617,
  	0.5776035965513142,
  	0.5945164913591590,
  	0.6111703413658551,
  	0.6275578900977726,
  	0.6436719971150083,
  	0.6595056411226444,
  	0.6750519230300931,
  	0.6903040689571928,
  	0.7052554331857488,
  	0.7198995010552305,
  	0.7342298918013638,
  	0.7482403613363824,
  	0.7619248049697269,
  	0.7752772600680049,
  	0.7882919086530552,
  	0.8009630799369827,
  	0.8132852527930605,
  	0.8252530581614230,
  	0.8368612813885015,
  	0.8481048644991847,
  	0.8589789084007133,
  	0.8694786750173527,
  	0.8795995893549102,
  	0.8893372414942055,
  	0.8986873885126239,
  	0.9076459563329236,
  	0.9162090414984952,
  	0.9243729128743136,
  	0.9321340132728527,
  	0.9394889610042837,
  	0.9464345513503147,
  	0.9529677579610971,
  	0.9590857341746905,
  	0.9647858142586956,
  	0.9700655145738374,
  	0.9749225346595943,
  	0.9793547582425894,
  	0.9833602541697529,
  	0.9869372772712794,
  	0.9900842691660192,
  	0.9927998590434373,
  	0.9950828645255290,
  	0.9969322929775997,
  	0.9983473449340834,
  	0.9993274305065947,
  	0.9998723404457334,
  	0., // zero padding is ignored
  	0.  // zero padding is ignored
};

constant double Gauss150Wt[152]={
  	0.0003276086705538,
  	0.0007624720924706,
  	0.0011976474864367,
  	0.0016323569986067,
  	0.0020663664924131,
  	0.0024994789888943,
  	0.0029315036836558,
  	0.0033622516236779,
  	0.0037915348363451,
  	0.0042191661429919,
  	0.0046449591497966,
  	0.0050687282939456,
  	0.0054902889094487,
  	0.0059094573005900,
  	0.0063260508184704,
  	0.0067398879387430,
  	0.0071507883396855,
  	0.0075585729801782,
  	0.0079630641773633,
  	0.0083640856838475,
  	0.0087614627643580,
  	0.0091550222717888,
  	0.0095445927225849,
  	0.0099300043714212,
  	0.0103110892851360,
  	0.0106876814158841,
  	0.0110596166734735,
  	0.0114267329968529,
  	0.0117888704247183,
  	0.0121458711652067,
  	0.0124975796646449,
  	0.0128438426753249,
  	0.0131845093222756,
  	0.0135194311690004,
  	0.0138484622795371,
  	0.0141714592928592,
  	0.0144882814685445,
  	0.0147987907597169,
  	0.0151028518701744,
  	0.0154003323133401,
  	0.0156911024699895,
  	0.0159750356447283,
  	0.0162520081211971,
  	0.0165218992159766,
  	0.0167845913311726,
  	0.0170399700056559,
  	0.0172879239649355,
  	0.0175283451696437,
  	0.0177611288626114,
  	0.0179861736145128,
  	0.0182033813680609,
  	0.0184126574807331,
  	0.0186139107660094,
  	0.0188070535331042,
  	0.0189920016251754,
  	0.0191686744559934,
  	0.0193369950450545,
  	0.0194968900511231,
  	0.0196482898041878,
  	0.0197911283358190,
  	0.0199253434079123,
  	0.0200508765398072,
  	0.0201676730337687,
  	0.0202756819988200,
  	0.0203748563729175,
  	0.0204651529434560,
  	0.0205465323660984,
  	0.0206189591819181,
  	0.0206824018328499,
  	0.0207368326754401,
  	0.0207822279928917,
  	0.0208185680053983,
  	0.0208458368787627,
  	0.0208640227312962,
  	0.0208731176389954,
  	0.0208731176389954,
  	0.0208640227312962,
  	0.0208458368787627,
  	0.0208185680053983,
  	0.0207822279928917,
  	0.0207368326754401,
  	0.0206824018328499,
  	0.0206189591819181,
  	0.0205465323660984,
  	0.0204651529434560,
  	0.0203748563729175,
  	0.0202756819988200,
  	0.0201676730337687,
  	0.0200508765398072,
  	0.0199253434079123,
  	0.0197911283358190,
  	0.0196482898041878,
  	0.0194968900511231,
  	0.0193369950450545,
  	0.0191686744559934,
  	0.0189920016251754,
  	0.0188070535331042,
  	0.0186139107660094,
  	0.0184126574807331,
  	0.0182033813680609,
  	0.0179861736145128,
  	0.0177611288626114,
  	0.0175283451696437,
  	0.0172879239649355,
  	0.0170399700056559,
  	0.0167845913311726,
  	0.0165218992159766,
  	0.0162520081211971,
  	0.0159750356447283,
  	0.0156911024699895,
  	0.0154003323133401,
  	0.0151028518701744,
  	0.0147987907597169,
  	0.0144882814685445,
  	0.0141714592928592,
  	0.0138484622795371,
  	0.0135194311690004,
  	0.0131845093222756,
  	0.0128438426753249,
  	0.0124975796646449,
  	0.0121458711652067,
  	0.0117888704247183,
  	0.0114267329968529,
  	0.0110596166734735,
  	0.0106876814158841,
  	0.0103110892851360,
  	0.0099300043714212,
  	0.0095445927225849,
  	0.0091550222717888,
  	0.0087614627643580,
  	0.0083640856838475,
  	0.0079630641773633,
  	0.0075585729801782,
  	0.0071507883396855,
  	0.0067398879387430,
  	0.0063260508184704,
  	0.0059094573005900,
  	0.0054902889094487,
  	0.0050687282939456,
  	0.0046449591497966,
  	0.0042191661429919,
  	0.0037915348363451,
  	0.0033622516236779,
  	0.0029315036836558,
  	0.0024994789888943,
  	0.0020663664924131,
  	0.0016323569986067,
  	0.0011976474864367,
  	0.0007624720924706,
  	0.0003276086705538,
  	0., // zero padding is ignored
  	0.  // zero padding is ignored
};

#pragma acc declare copyin( Gauss150Wt[0:150], Gauss150Z[0:150] )

#endif // SAS_HAVE_gauss150


#ifndef SAS_HAVE_sc_paracrystal
#define SAS_HAVE_sc_paracrystal

#line 1 "sc_paracrystal"
static double
sc_Zq(double qa, double qb, double qc, double dnn, double d_factor)
{
    // Equations from Matsuoka 9-10-11, multiplied by |q|
    const double a1 = qa;
    const double a2 = qb;
    const double a3 = qc;

    // Matsuoka 13-14-15
    //     Z_k numerator: 1 - exp(a)^2
    //     Z_k denominator: 1 - 2 cos(d a_k) exp(a) + exp(2a)
    // Rewriting numerator
    //         => -(exp(2a) - 1)
    //         => -expm1(2a)
    // Rewriting denominator
    //         => exp(a)^2 - 2 cos(d ak) exp(a) + 1)
    //         => (exp(a) - 2 cos(d ak)) * exp(a) + 1
    const double arg = -0.5*square(dnn*d_factor)*(a1*a1 + a2*a2 + a3*a3);
    const double exp_arg = exp(arg);
    const double Zq = -cube(expm1(2.0*arg))
        / ( ((exp_arg - 2.0*cos(dnn*a1))*exp_arg + 1.0)
          * ((exp_arg - 2.0*cos(dnn*a2))*exp_arg + 1.0)
          * ((exp_arg - 2.0*cos(dnn*a3))*exp_arg + 1.0));

    return Zq;
}

// occupied volume fraction calculated from lattice symmetry and sphere radius
static double
sc_volume_fraction(double radius, double dnn)
{
    return sphere_volume(radius/dnn);
}

static double
form_volume_sc_paracrystal(double radius)
{
    return sphere_volume(radius);
}


static double
Iq_sc_paracrystal(double q, double dnn,
    double d_factor, double radius,
    double sld, double solvent_sld)
{
    // translate a point in [-1,1] to a point in [0, 2 pi]
    const double phi_m = M_PI_4;
    const double phi_b = M_PI_4;
    // translate a point in [-1,1] to a point in [0, pi]
    const double theta_m = M_PI_4;
    const double theta_b = M_PI_4;


    double outer_sum = 0.0;
    for(int i=0; i<GAUSS_N; i++) {
        double inner_sum = 0.0;
        const double theta = GAUSS_Z[i]*theta_m + theta_b;
        double sin_theta, cos_theta;
        SINCOS(theta, sin_theta, cos_theta);
        const double qc = q*cos_theta;
        const double qab = q*sin_theta;
        for(int j=0;j<GAUSS_N;j++) {
            const double phi = GAUSS_Z[j]*phi_m + phi_b;
            double sin_phi, cos_phi;
            SINCOS(phi, sin_phi, cos_phi);
            const double qa = qab*cos_phi;
            const double qb = qab*sin_phi;
            const double form = sc_Zq(qa, qb, qc, dnn, d_factor);
            inner_sum += GAUSS_W[j] * form;
        }
        inner_sum *= phi_m;  // sum(f(x)dx) = sum(f(x)) dx
        outer_sum += GAUSS_W[i] * inner_sum * sin_theta;
    }
    outer_sum *= theta_m;
    const double Zq = outer_sum/M_PI_2;
    const double Pq = sphere_form(q, radius, sld, solvent_sld);

    return sc_volume_fraction(radius, dnn) * Pq * Zq;
}

static double
Iqabc_sc_paracrystal(double qa, double qb, double qc,
    double dnn, double d_factor, double radius,
    double sld, double solvent_sld)
{
    const double q = sqrt(qa*qa + qb*qb + qc*qc);
    const double Pq = sphere_form(q, radius, sld, solvent_sld);
    const double Zq = sc_Zq(qa, qb, qc, dnn, d_factor);
    return sc_volume_fraction(radius, dnn) * Pq * Zq;
}

#endif // SAS_HAVE_sc_paracrystal



/* END Required header for SASmodel sc_paracrystal */
%}
    DECLARE
%{
  double shape;
  double my_a_v;
%}

INITIALIZE
%{
shape=-1;  /* -1:no shape, 0:cyl, 1:box, 2:sphere  */
if (xwidth && yheight && zdepth)
    shape=1;
  else if (R > 0 && yheight)
    shape=0;
  else if (R > 0 && !yheight)
    shape=2;
  if (shape < 0)
    exit(fprintf(stderr, "SasView_model: %s: sample has invalid dimensions.\n"
                         "ERROR     Please check parameter values.\n", NAME_CURRENT_COMP));

  /* now compute target coords if a component index is supplied */
  if (!target_index && !target_x && !target_y && !target_z) target_index=1;
  if (target_index)
  {
    Coords ToTarget;
    ToTarget = coords_sub(POS_A_COMP_INDEX(INDEX_CURRENT_COMP+target_index),POS_A_CURRENT_COMP);
    ToTarget = rot_apply(ROT_A_CURRENT_COMP, ToTarget);
    coords_get(ToTarget, &target_x, &target_y, &target_z);
  }

  if (!(target_x || target_y || target_z)) {
    printf("SasView_model: %s: The target is not defined. Using direct beam (Z-axis).\n",
      NAME_CURRENT_COMP);
    target_z=1;
  }

  my_a_v = model_abs*2200*100; /* Is not yet divided by v. 100: Convert barns -> fm^2 */

%}


TRACE
%{
  double t0, t1, v, l_full, l, l_1, dt, d_phi, my_s;
  double aim_x=0, aim_y=0, aim_z=1, axis_x, axis_y, axis_z;
  double arg, tmp_vx, tmp_vy, tmp_vz, vout_x, vout_y, vout_z;
  double f, solid_angle, vx_i, vy_i, vz_i, q, qx, qy, qz;
  char intersect=0;

  /* Intersection neutron trajectory / sample (sample surface) */
  if (shape == 0){
    intersect = cylinder_intersect(&t0, &t1, x, y, z, vx, vy, vz, R, yheight);}
  else if (shape == 1){
    intersect = box_intersect(&t0, &t1, x, y, z, vx, vy, vz, xwidth, yheight, zdepth);}
  else if (shape == 2){
    intersect = sphere_intersect(&t0, &t1, x, y, z, vx, vy, vz, R);}
  if(intersect)
  {
    if(t0 < 0)
      ABSORB;

    /* Neutron enters at t=t0. */
    v = sqrt(vx*vx + vy*vy + vz*vz);
    l_full = v * (t1 - t0);          /* Length of full path through sample */
    dt = rand01()*(t1 - t0) + t0;    /* Time of scattering */
    PROP_DT(dt);                     /* Point of scattering */
    l = v*(dt-t0);                   /* Penetration in sample */

    vx_i=vx;
    vy_i=vy;
    vz_i=vz;
    if ((target_x || target_y || target_z)) {
      aim_x = target_x-x;            /* Vector pointing at target (anal./det.) */
      aim_y = target_y-y;
      aim_z = target_z-z;
    }
    if(focus_aw && focus_ah) {
      randvec_target_rect_angular(&vx, &vy, &vz, &solid_angle,
        aim_x, aim_y, aim_z, focus_aw, focus_ah, ROT_A_CURRENT_COMP);
    } else if(focus_xw && focus_yh) {
      randvec_target_rect(&vx, &vy, &vz, &solid_angle,
        aim_x, aim_y, aim_z, focus_xw, focus_yh, ROT_A_CURRENT_COMP);
    } else {
      randvec_target_circle(&vx, &vy, &vz, &solid_angle, aim_x, aim_y, aim_z, focus_r);
    }
    NORM(vx, vy, vz);
    vx *= v;
    vy *= v;
    vz *= v;
    qx = V2K*(vx_i-vx);
    qy = V2K*(vy_i-vy);
    qz = V2K*(vz_i-vz);
    q = sqrt(qx*qx+qy*qy+qz*qz);
    
    double trace_radius=radius;
    if ( pd_radius!=0.0 ){
    trace_radius = (randnorm()*pd_radius+1.0)*radius;
    }

        


    // Sample dependent. Retrieved from SasView./////////////////////
    float Iq_out;
    Iq_out = 1;

    Iq_out = Iq_sc_paracrystal(q, dnn, d_factor, trace_radius, sld, sld_solvent);


    float vol;
    vol = 1;

    // Scale by 1.0E2 [SasView: 1/cm  ->   McStas: 1/m]
    Iq_out = model_scale*Iq_out / vol * 1.0E2;

    l_1 = v*t1;
    p *= l_full*solid_angle/(4*PI)*Iq_out*exp(-my_a_v*(l+l_1)/v);
    SCATTER;
  }
%}

MCDISPLAY
%{

  if (shape == 0) {	/* cylinder */
    circle("xz", 0,  yheight/2.0, 0, R);
    circle("xz", 0, -yheight/2.0, 0, R);
    line(-R, -yheight/2.0, 0, -R, +yheight/2.0, 0);
    line(+R, -yheight/2.0, 0, +R, +yheight/2.0, 0);
    line(0, -yheight/2.0, -R, 0, +yheight/2.0, -R);
    line(0, -yheight/2.0, +R, 0, +yheight/2.0, +R);
  }
  else if (shape == 1) { 	/* box */
    double xmin = -0.5*xwidth;
    double xmax =  0.5*xwidth;
    double ymin = -0.5*yheight;
    double ymax =  0.5*yheight;
    double zmin = -0.5*zdepth;
    double zmax =  0.5*zdepth;
    multiline(5, xmin, ymin, zmin,
                 xmax, ymin, zmin,
                 xmax, ymax, zmin,
                 xmin, ymax, zmin,
                 xmin, ymin, zmin);
    multiline(5, xmin, ymin, zmax,
                 xmax, ymin, zmax,
                 xmax, ymax, zmax,
                 xmin, ymax, zmax,
                 xmin, ymin, zmax);
    line(xmin, ymin, zmin, xmin, ymin, zmax);
    line(xmax, ymin, zmin, xmax, ymin, zmax);
    line(xmin, ymax, zmin, xmin, ymax, zmax);
    line(xmax, ymax, zmin, xmax, ymax, zmax);
  }
  else if (shape == 2) {	/* sphere */
    circle("xy", 0,  0.0, 0, R);
    circle("xz", 0,  0.0, 0, R);
    circle("yz", 0,  0.0, 0, R);
  }
%}
END