/*******************************************************************************
*
* McXtrace, X-ray tracing package
*         Copyright, All rights reserved
*         DTU Physics, Kgs. Lyngby, Denmark
*         Synchrotron SOLEIL, Saint-Aubin, France
*
* Component: SasView_core_shell_ellipsoid
*
* %Identification
* Written by: Jose Robledo
* Based on sasmodels from SasView
* Origin: FZJ / DTU / ESS DMSC
*
*
* SasView core_shell_ellipsoid model component as sample description.
*
* %Description
*
* SasView_core_shell_ellipsoid component, generated from core_shell_ellipsoid.c in sasmodels.
*
* Example: 
*  SasView_core_shell_ellipsoid_aniso(radius_equat_core, x_core, thick_shell, x_polar_shell, sld_core, sld_shell, sld_solvent, theta, Phi, 
*     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_equat_core=0.0, pd_thick_shell=0.0, pd_theta=0.0, pd_Phi=0.0)
*
* %Parameters
* INPUT PARAMETERS:
* radius_equat_core: [Ang] ([0, inf]) Equatorial radius of core.
* x_core: [None] ([0, inf]) axial ratio of core, X = r_polar/r_equatorial.
* thick_shell: [Ang] ([0, inf]) thickness of shell at equator.
* x_polar_shell: [] ([0, inf]) ratio of thickness of shell at pole to that at equator.
* sld_core: [1e-6/Ang^2] ([-inf, inf]) Core scattering length density.
* sld_shell: [1e-6/Ang^2] ([-inf, inf]) Shell scattering length density.
* sld_solvent: [1e-6/Ang^2] ([-inf, 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_equat_core: [] (0,inf) defined as (dx/x), where x is de mean value and dx the standard devition of the variable.
* pd_thick_shell: [] (0,inf) defined as (dx/x), where x is de mean value and dx the standard devition of the variable.
* pd_theta: [] (0,360) defined as (dx/x), where x is de mean value and dx the standard devition of the variable.
* pd_Phi: [] (0,360) defined as (dx/x), where x is de mean value and dx the standard devition of the variable
*
* %Link
* %End
*******************************************************************************/
DEFINE COMPONENT SasView_core_shell_ellipsoid_aniso
DEFINITION PARAMETERS ()
SETTING PARAMETERS (
        radius_equat_core=20,
        x_core=3,
        thick_shell=30,
        x_polar_shell=1,
        sld_core=2,
        sld_shell=1,
        sld_solvent=6.3,
        theta=0,
        Phi=0,
        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_equat_core=0.0,
        pd_thick_shell=0.0,
        pd_theta=0.0,
        pd_Phi=0.0)


SHARE %{
%include "sas_kernel_header.c"

/* BEGIN Required header for SASmodel core_shell_ellipsoid */
#define HAS_Iqac
#define HAS_FQ
#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_gauss76
#define SAS_HAVE_gauss76

#line 1 "gauss76"
// Created by Andrew Jackson on 4/23/07

 #ifdef GAUSS_N
 # undef GAUSS_N
 # undef GAUSS_Z
 # undef GAUSS_W
 #endif
 #define GAUSS_N 76
 #define GAUSS_Z Gauss76Z
 #define GAUSS_W Gauss76Wt

// Gaussians
constant double Gauss76Wt[76] = {
	.00126779163408536,		//0
	.00294910295364247,
	.00462793522803742,
	.00629918049732845,
	.00795984747723973,
	.00960710541471375,
	.0112381685696677,
	.0128502838475101,
	.0144407317482767,
	.0160068299122486,
	.0175459372914742,		//10
	.0190554584671906,
	.020532847967908,
	.0219756145344162,
	.0233813253070112,
	.0247476099206597,
	.026072164497986,
	.0273527555318275,
	.028587223650054,
	.029773487255905,
	.0309095460374916,		//20
	.0319934843404216,
	.0330234743977917,
	.0339977794120564,
	.0349147564835508,
	.0357728593807139,
	.0365706411473296,
	.0373067565423816,
	.0379799643084053,
	.0385891292645067,
	.0391332242205184,		//30
	.0396113317090621,
	.0400226455325968,
	.040366472122844,
	.0406422317102947,
	.0408494593018285,
	.040987805464794,
	.0410570369162294,
	.0410570369162294,
	.040987805464794,
	.0408494593018285,		//40
	.0406422317102947,
	.040366472122844,
	.0400226455325968,
	.0396113317090621,
	.0391332242205184,
	.0385891292645067,
	.0379799643084053,
	.0373067565423816,
	.0365706411473296,
	.0357728593807139,		//50
	.0349147564835508,
	.0339977794120564,
	.0330234743977917,
	.0319934843404216,
	.0309095460374916,
	.029773487255905,
	.028587223650054,
	.0273527555318275,
	.026072164497986,
	.0247476099206597,		//60
	.0233813253070112,
	.0219756145344162,
	.020532847967908,
	.0190554584671906,
	.0175459372914742,
	.0160068299122486,
	.0144407317482767,
	.0128502838475101,
	.0112381685696677,
	.00960710541471375,		//70
	.00795984747723973,
	.00629918049732845,
	.00462793522803742,
	.00294910295364247,
	.00126779163408536		//75 (indexed from 0)
};

constant double Gauss76Z[76] = {
	-.999505948362153,		//0
	-.997397786355355,
	-.993608772723527,
	-.988144453359837,
	-.981013938975656,
	-.972229228520377,
	-.961805126758768,
	-.949759207710896,
	-.936111781934811,
	-.92088586125215,
	-.904107119545567,		//10
	-.885803849292083,
	-.866006913771982,
	-.844749694983342,
	-.822068037328975,
	-.7980001871612,
	-.77258672828181,
	-.74587051350361,
	-.717896592387704,
	-.688712135277641,
	-.658366353758143,		//20
	-.626910417672267,
	-.594397368836793,
	-.560882031601237,
	-.526420920401243,
	-.491072144462194,
	-.454895309813726,
	-.417951418780327,
	-.380302767117504,
	-.342012838966962,
	-.303146199807908,		//30
	-.263768387584994,
	-.223945802196474,
	-.183745593528914,
	-.143235548227268,
	-.102483975391227,
	-.0615595913906112,
	-.0205314039939986,
	.0205314039939986,
	.0615595913906112,
	.102483975391227,			//40
	.143235548227268,
	.183745593528914,
	.223945802196474,
	.263768387584994,
	.303146199807908,
	.342012838966962,
	.380302767117504,
	.417951418780327,
	.454895309813726,
	.491072144462194,		//50
	.526420920401243,
	.560882031601237,
	.594397368836793,
	.626910417672267,
	.658366353758143,
	.688712135277641,
	.717896592387704,
	.74587051350361,
	.77258672828181,
	.7980001871612,	//60
	.822068037328975,
	.844749694983342,
	.866006913771982,
	.885803849292083,
	.904107119545567,
	.92088586125215,
	.936111781934811,
	.949759207710896,
	.961805126758768,
	.972229228520377,		//70
	.981013938975656,
	.988144453359837,
	.993608772723527,
	.997397786355355,
	.999505948362153		//75
};


#pragma acc declare copyin(Gauss76Wt[0:76], Gauss76Z[0:76])

#endif // SAS_HAVE_gauss76


#ifndef SAS_HAVE_core_shell_ellipsoid
#define SAS_HAVE_core_shell_ellipsoid

#line 1 "core_shell_ellipsoid"

// Converted from Igor function gfn4, using the same pattern as ellipsoid
// for evaluating the parts of the integral.
//     FUNCTION gfn4:    CONTAINS F(Q,A,B,MU)**2  AS GIVEN
//                       BY (53) & (58-59) IN CHEN AND
//                       KOTLARCHYK REFERENCE
//
//       <OBLATE ELLIPSOID>
static double
_cs_ellipsoid_kernel(double qab, double qc,
    double equat_core, double polar_core,
    double equat_shell, double polar_shell,
    double sld_core_shell, double sld_shell_solvent)
{
    const double qr_core = sqrt(square(equat_core*qab) + square(polar_core*qc));
    const double si_core = sas_3j1x_x(qr_core);
    const double volume_core = M_4PI_3*equat_core*equat_core*polar_core;
    const double fq_core = si_core*volume_core*sld_core_shell;

    const double qr_shell = sqrt(square(equat_shell*qab) + square(polar_shell*qc));
    const double si_shell = sas_3j1x_x(qr_shell);
    const double volume_shell = M_4PI_3*equat_shell*equat_shell*polar_shell;
    const double fq_shell = si_shell*volume_shell*sld_shell_solvent;

    return fq_core + fq_shell;
}

static double
form_volume_core_shell_ellipsoid(double radius_equat_core,
    double x_core,
    double thick_shell,
    double x_polar_shell)
{
    const double equat_shell = radius_equat_core + thick_shell;
    const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell;
    double vol = M_4PI_3*equat_shell*equat_shell*polar_shell;
    return vol;
}

static double
radius_from_volume_core_shell_ellipsoid(double radius_equat_core, double x_core, double thick_shell, double x_polar_shell)
{
    const double volume_ellipsoid = form_volume_core_shell_ellipsoid(radius_equat_core, x_core, thick_shell, x_polar_shell);
    return cbrt(volume_ellipsoid/M_4PI_3);
}

static double
radius_from_curvature_core_shell_ellipsoid(double radius_equat_core, double x_core, double thick_shell, double x_polar_shell)
{
    // Trivial cases
    if (1.0 == x_core && 1.0 == x_polar_shell) return radius_equat_core + thick_shell;
    if ((radius_equat_core + thick_shell)*(radius_equat_core*x_core + thick_shell*x_polar_shell) == 0.)  return 0.;

    // see equation (26) in A.Isihara, J.Chem.Phys. 18(1950)1446-1449
    const double radius_equat_tot = radius_equat_core + thick_shell;
    const double radius_polar_tot = radius_equat_core*x_core + thick_shell*x_polar_shell;
    const double ratio = (radius_polar_tot < radius_equat_tot
                          ? radius_polar_tot / radius_equat_tot
                          : radius_equat_tot / radius_polar_tot);
    const double e1 = sqrt(1.0 - ratio*ratio);
    const double b1 = 1.0 + asin(e1) / (e1 * ratio);
    const double bL = (1.0 + e1) / (1.0 - e1);
    const double b2 = 1.0 + 0.5 * ratio * ratio / e1 * log(bL);
    const double delta = 0.75 * b1 * b2;
    const double ddd = 2.0 * (delta + 1.0) * radius_polar_tot * radius_equat_tot * radius_equat_tot;
    return 0.5 * cbrt(ddd);
}

static double
radius_effective_core_shell_ellipsoid(int mode, double radius_equat_core, double x_core, double thick_shell, double x_polar_shell)
{
    const double radius_equat_tot = radius_equat_core + thick_shell;
    const double radius_polar_tot = radius_equat_core*x_core + thick_shell*x_polar_shell;

    switch (mode) {
    default:
    case 1: // average outer curvature
        return radius_from_curvature_core_shell_ellipsoid(radius_equat_core, x_core, thick_shell, x_polar_shell);
    case 2: // equivalent volume sphere
        return radius_from_volume_core_shell_ellipsoid(radius_equat_core, x_core, thick_shell, x_polar_shell);
    case 3: // min outer radius
        return (radius_polar_tot < radius_equat_tot ? radius_polar_tot : radius_equat_tot);
    case 4: // max outer radius
        return (radius_polar_tot > radius_equat_tot ? radius_polar_tot : radius_equat_tot);
    }
}

static void
Fq_core_shell_ellipsoid(double q,
    double *F1,
    double *F2,
    double radius_equat_core,
    double x_core,
    double thick_shell,
    double x_polar_shell,
    double core_sld,
    double shell_sld,
    double solvent_sld)
{
    const double sld_core_shell = core_sld - shell_sld;
    const double sld_shell_solvent = shell_sld - solvent_sld;

    const double polar_core = radius_equat_core*x_core;
    const double equat_shell = radius_equat_core + thick_shell;
    const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell;

    // translate from [-1, 1] => [0, 1]
    const double m = 0.5;
    const double b = 0.5;
    double total_F1 = 0.0;     //initialize intergral
    double total_F2 = 0.0;     //initialize intergral
    for(int i=0;i<GAUSS_N;i++) {
        const double cos_theta = GAUSS_Z[i]*m + b;
        const double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
        double fq = _cs_ellipsoid_kernel(q*sin_theta, q*cos_theta,
            radius_equat_core, polar_core,
            equat_shell, polar_shell,
            sld_core_shell, sld_shell_solvent);
        total_F1 += GAUSS_W[i] * fq;
        total_F2 += GAUSS_W[i] * fq * fq;
    }
    total_F1 *= m;
    total_F2 *= m;

    // convert to [cm-1]
    *F1 = 1.0e-2 * total_F1;
    *F2 = 1.0e-4 * total_F2;
}


static double
Iqac_core_shell_ellipsoid(double qab, double qc,
    double radius_equat_core,
    double x_core,
    double thick_shell,
    double x_polar_shell,
    double core_sld,
    double shell_sld,
    double solvent_sld)
{
    const double sld_core_shell = core_sld - shell_sld;
    const double sld_shell_solvent = shell_sld - solvent_sld;

    const double polar_core = radius_equat_core*x_core;
    const double equat_shell = radius_equat_core + thick_shell;
    const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell;

    double fq = _cs_ellipsoid_kernel(qab, qc,
                  radius_equat_core, polar_core,
                  equat_shell, polar_shell,
                  sld_core_shell, sld_shell_solvent);

    //convert to [cm-1]
    return 1.0e-4 * fq * fq;
}


#endif // SAS_HAVE_core_shell_ellipsoid



/* END Required header for SASmodel core_shell_ellipsoid */
%}
    DECLARE
%{
  double shape;
  double my_a_k;
%}

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;
  }

  /*TODO fix absorption*/
  my_a_k = model_abs; /* assume absorption is given in 1/m */

%}


TRACE
%{
  double l0, l1, k, l_full, l, dl, d_Phi;
  double aim_x=0, aim_y=0, aim_z=1, axis_x, axis_y, axis_z;
  double f, solid_angle, kx_i, ky_i, kz_i, q, qx, qy, qz;
  char intersect=0;

  /* Intersection photon trajectory / sample (sample surface) */
  if (shape == 0){
    intersect = cylinder_intersect(&l0, &l1, x, y, z, kx, ky, kz, R, yheight);}
  else if (shape == 1){
    intersect = box_intersect(&l0, &l1, x, y, z, kx, ky, kz, xwidth, yheight, zdepth);}
  else if (shape == 2){
    intersect = sphere_intersect(&l0, &l1, x, y, z, kx, ky, kz, R);}
  if(intersect)
  {
    if(l0 < 0)
      ABSORB;

    /* Photon enters at l0. */
    k = sqrt(kx*kx + ky*ky + kz*kz);
    l_full = (l1 - l0);          /* Length of full path through sample */
    dl = rand01()*(l1 - l0) + l0;    /* Point of scattering */
    PROP_DL(dl);                     /* Point of scattering */
    l = (dl-l0);                   /* Penetration in sample */

    kx_i=kx;
    ky_i=ky;
    kz_i=kz;
    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(&kx, &ky, &kz, &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(&kx, &ky, &kz, &solid_angle,
        aim_x, aim_y, aim_z, focus_xw, focus_yh, ROT_A_CURRENT_COMP);
    } else {
      randvec_target_circle(&kx, &ky, &kz, &solid_angle, aim_x, aim_y, aim_z, focus_r);
    }
    NORM(kx, ky, kz);
    kx *= k;
    ky *= k;
    kz *= k;
    qx = (kx_i-kx);
    qy = (ky_i-ky);
    qz = (kz_i-kz);
    q = sqrt(qx*qx+qy*qy+qz*qz);
    
    double trace_radius_equat_core=radius_equat_core;
    double trace_thick_shell=thick_shell;
    if ( pd_radius_equat_core!=0.0 || pd_thick_shell!=0.0 ){
    trace_radius_equat_core = (randnorm()*pd_radius_equat_core+1.0)*radius_equat_core;
    trace_thick_shell = (randnorm()*pd_thick_shell+1.0)*thick_shell;
    }

        
    double trace_theta=theta, dtheta=0.0;
    double trace_Phi=Phi, dPhi=0.0;
    if ( pd_theta!=0.0 || pd_Phi!=0.0 ){
    trace_theta = ((rand01()-0.5)*pd_theta + 1.0)*theta;
    dtheta = trace_theta-theta;
    trace_Phi = ((rand01()-0.5)*pd_Phi + 1.0)*Phi;
    dPhi = trace_Phi-Phi;
    }


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

    double qab=0.0, qc=0.0;
    QACRotation rotation;

    qac_rotation(&rotation, trace_theta, trace_Phi, dtheta, dPhi);
    qac_apply(&rotation, qx, qy, &qab, &qc);
    Iq_out = Iqac_core_shell_ellipsoid(qab, qc, trace_radius_equat_core, x_core, trace_thick_shell, x_polar_shell, sld_core, sld_shell, sld_solvent );


    float vol;
    vol = 1;

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

    
    p *= l_full*solid_angle/(4*PI)*Iq_out*exp(-my_a_k*(l+l1));


    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

