/******************************************************************************* * * McStas, neutron ray-tracing package * Copyright (C) 1997-2008, All rights reserved * Risoe National Laboratory, Roskilde, Denmark * Institut Laue Langevin, Grenoble, France * * Component: SasView_core_shell_cylinder * * %Identification * Written by: Jose Robledo * Based on sasmodels from SasView * Origin: FZJ / DTU / ESS DMSC * * * SasView core_shell_cylinder model component as sample description. * * %Description * * SasView_core_shell_cylinder component, generated from core_shell_cylinder.c in sasmodels. * * Example: * SasView_core_shell_cylinder_aniso(sld_core, sld_shell, sld_solvent, radius, thickness, length, 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=0.0, pd_thickness=0.0, pd_length=0.0, pd_theta=0.0, pd_phi=0.0) * * %Parameters * INPUT PARAMETERS: * sld_core: [1e-6/Ang^2] ([-inf, inf]) Cylinder core scattering length density. * sld_shell: [1e-6/Ang^2] ([-inf, inf]) Cylinder shell scattering length density. * sld_solvent: [1e-6/Ang^2] ([-inf, inf]) Solvent scattering length density. * radius: [Ang] ([0, inf]) Cylinder core radius. * thickness: [Ang] ([0, inf]) Cylinder shell thickness. * length: [Ang] ([0, inf]) Cylinder length. * 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. * pd_thickness: [] (0,inf) defined as (dx/x), where x is de mean value and dx the standard devition of the variable. * pd_length: [] (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_cylinder_aniso SETTING PARAMETERS ( sld_core=4, sld_shell=4, sld_solvent=1, radius=20, thickness=20, length=400, theta=60, phi=60, 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, pd_thickness=0.0, pd_length=0.0, pd_theta=0.0, pd_phi=0.0) SHARE %{ %include "sas_kernel_header.c" /* BEGIN Required header for SASmodel core_shell_cylinder */ #define HAS_Iqac #define HAS_FQ #define FORM_VOL #ifndef SAS_HAVE_polevl #define SAS_HAVE_polevl #line 1 "polevl" /* polevl.c * p1evl.c * * Evaluate polynomial * * * * SYNOPSIS: * * int N; * double x, y, coef[N+1], polevl[]; * * y = polevl( x, coef, N ); * * * * DESCRIPTION: * * Evaluates polynomial of degree N: * * 2 N * y = C + C x + C x +...+ C x * 0 1 2 N * * Coefficients are stored in reverse order: * * coef[0] = C , ..., coef[N] = C . * N 0 * * The function p1evl() assumes that C_N = 1.0 and is * omitted from the array. Its calling arguments are * otherwise the same as polevl(). * * * SPEED: * * In the interest of speed, there are no checks for out * of bounds arithmetic. This routine is used by most of * the functions in the library. Depending on available * equipment features, the user may wish to rewrite the * program in microcode or assembly language. * */ /* Cephes Math Library Release 2.1: December, 1988 Copyright 1984, 1987, 1988 by Stephen L. Moshier Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ #pragma acc routine seq static double polevl( double x, pconstant double *coef, int N ) { int i = 0; double ans = coef[i]; while (i < N) { i++; ans = ans * x + coef[i]; } return ans; } /* p1evl() */ /* N * Evaluate polynomial when coefficient of x is 1.0. * Otherwise same as polevl. */ #pragma acc routine seq static double p1evl( double x, pconstant double *coef, int N ) { int i=0; double ans = x+coef[i]; while (i < N-1) { i++; ans = ans*x + coef[i]; } return ans; } #endif // SAS_HAVE_polevl #ifndef SAS_HAVE_sas_J1 #define SAS_HAVE_sas_J1 #line 1 "sas_J1" /* j1.c * * Bessel function of order one * * * * SYNOPSIS: * * double x, y, j1(); * * y = j1( x ); * * * * DESCRIPTION: * * Returns Bessel function of order one of the argument. * * The domain is divided into the intervals [0, 8] and * (8, infinity). In the first interval a 24 term Chebyshev * expansion is used. In the second, the asymptotic * trigonometric representation is employed using two * rational functions of degree 5/5. * * * * ACCURACY: * * Absolute error: * arithmetic domain # trials peak rms * DEC 0, 30 10000 4.0e-17 1.1e-17 * IEEE 0, 30 30000 2.6e-16 1.1e-16 * * */ /* Cephes Math Library Release 2.8: June, 2000 Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier */ #if FLOAT_SIZE>4 //Cephes double pression function constant double RPJ1[8] = { -8.99971225705559398224E8, 4.52228297998194034323E11, -7.27494245221818276015E13, 3.68295732863852883286E15, 0.0, 0.0, 0.0, 0.0 }; constant double RQJ1[8] = { 6.20836478118054335476E2, 2.56987256757748830383E5, 8.35146791431949253037E7, 2.21511595479792499675E10, 4.74914122079991414898E12, 7.84369607876235854894E14, 8.95222336184627338078E16, 5.32278620332680085395E18 }; constant double PPJ1[8] = { 7.62125616208173112003E-4, 7.31397056940917570436E-2, 1.12719608129684925192E0, 5.11207951146807644818E0, 8.42404590141772420927E0, 5.21451598682361504063E0, 1.00000000000000000254E0, 0.0} ; constant double PQJ1[8] = { 5.71323128072548699714E-4, 6.88455908754495404082E-2, 1.10514232634061696926E0, 5.07386386128601488557E0, 8.39985554327604159757E0, 5.20982848682361821619E0, 9.99999999999999997461E-1, 0.0 }; constant double QPJ1[8] = { 5.10862594750176621635E-2, 4.98213872951233449420E0, 7.58238284132545283818E1, 3.66779609360150777800E2, 7.10856304998926107277E2, 5.97489612400613639965E2, 2.11688757100572135698E2, 2.52070205858023719784E1 }; constant double QQJ1[8] = { 7.42373277035675149943E1, 1.05644886038262816351E3, 4.98641058337653607651E3, 9.56231892404756170795E3, 7.99704160447350683650E3, 2.82619278517639096600E3, 3.36093607810698293419E2, 0.0 }; #pragma acc declare copyin( RPJ1[0:8], RQJ1[0:8], PPJ1[0:8], PQJ1[0:8], QPJ1[0:8], QQJ1[0:8]) #pragma acc routine seq static double cephes_j1(double x) { double w, z, p, q, abs_x, sign_x; const double Z1 = 1.46819706421238932572E1; const double Z2 = 4.92184563216946036703E1; // 2017-05-18 PAK - mathematica and mpmath use J1(-x) = -J1(x) if (x < 0) { abs_x = -x; sign_x = -1.0; } else { abs_x = x; sign_x = 1.0; } if( abs_x <= 5.0 ) { z = abs_x * abs_x; w = polevl( z, RPJ1, 3 ) / p1evl( z, RQJ1, 8 ); w = w * abs_x * (z - Z1) * (z - Z2); return( sign_x * w ); } w = 5.0/abs_x; z = w * w; p = polevl( z, PPJ1, 6)/polevl( z, PQJ1, 6 ); q = polevl( z, QPJ1, 7)/p1evl( z, QQJ1, 7 ); // 2017-05-19 PAK improve accuracy using trig identies // original: // const double THPIO4 = 2.35619449019234492885; // const double SQ2OPI = 0.79788456080286535588; // double sin_xn, cos_xn; // SINCOS(abs_x - THPIO4, sin_xn, cos_xn); // p = p * cos_xn - w * q * sin_xn; // return( sign_x * p * SQ2OPI / sqrt(abs_x) ); // expanding p*cos(a - 3 pi/4) - wq sin(a - 3 pi/4) // [ p(sin(a) - cos(a)) + wq(sin(a) + cos(a)) / sqrt(2) // note that sqrt(1/2) * sqrt(2/pi) = sqrt(1/pi) const double SQRT1_PI = 0.56418958354775628; double sin_x, cos_x; SINCOS(abs_x, sin_x, cos_x); p = p*(sin_x - cos_x) + w*q*(sin_x + cos_x); return( sign_x * p * SQRT1_PI / sqrt(abs_x) ); } #else //Single precission version of cephes constant float JPJ1[8] = { -4.878788132172128E-009, 6.009061827883699E-007, -4.541343896997497E-005, 1.937383947804541E-003, -3.405537384615824E-002, 0.0, 0.0, 0.0 }; constant float MO1J1[8] = { 6.913942741265801E-002, -2.284801500053359E-001, 3.138238455499697E-001, -2.102302420403875E-001, 5.435364690523026E-003, 1.493389585089498E-001, 4.976029650847191E-006, 7.978845453073848E-001 }; constant float PH1J1[8] = { -4.497014141919556E+001, 5.073465654089319E+001, -2.485774108720340E+001, 7.222973196770240E+000, -1.544842782180211E+000, 3.503787691653334E-001, -1.637986776941202E-001, 3.749989509080821E-001 }; #pragma acc declare copyin( JPJ1[0:8], MO1J1[0:8], PH1J1[0:8]) #pragma acc routine seq static float cephes_j1f(float xx) { float x, w, z, p, q, xn; const float Z1 = 1.46819706421238932572E1; // 2017-05-18 PAK - mathematica and mpmath use J1(-x) = -J1(x) x = xx; if( x < 0 ) x = -xx; if( x <= 2.0 ) { z = x * x; p = (z-Z1) * x * polevl( z, JPJ1, 4 ); return( xx < 0. ? -p : p ); } q = 1.0/x; w = sqrt(q); p = w * polevl( q, MO1J1, 7); w = q*q; // 2017-05-19 PAK improve accuracy using trig identies // original: // const float THPIO4F = 2.35619449019234492885; /* 3*pi/4 */ // xn = q * polevl( w, PH1J1, 7) - THPIO4F; // p = p * cos(xn + x); // return( xx < 0. ? -p : p ); // expanding cos(a + b - 3 pi/4) is // [sin(a)sin(b) + sin(a)cos(b) + cos(a)sin(b)-cos(a)cos(b)] / sqrt(2) xn = q * polevl( w, PH1J1, 7); float cos_xn, sin_xn; float cos_x, sin_x; SINCOS(xn, sin_xn, cos_xn); // about xn and 1 SINCOS(x, sin_x, cos_x); p *= M_SQRT1_2*(sin_xn*(sin_x+cos_x) + cos_xn*(sin_x-cos_x)); return( xx < 0. ? -p : p ); } #endif #if FLOAT_SIZE>4 #define sas_J1 cephes_j1 #else #define sas_J1 cephes_j1f #endif //Finally J1c function that equals 2*J1(x)/x #pragma acc routine seq static double sas_2J1x_x(double x) { return (x != 0.0 ) ? 2.0*sas_J1(x)/x : 1.0; } #endif // SAS_HAVE_sas_J1 #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_cylinder #define SAS_HAVE_core_shell_cylinder #line 1 "core_shell_cylinder" // vd = volume * delta_rho // besarg = q * R * sin(theta) // siarg = q * L/2 * cos(theta) static double _cyl(double vd, double besarg, double siarg) { return vd * sas_sinx_x(siarg) * sas_2J1x_x(besarg); } static double form_volume_core_shell_cylinder(double radius, double thickness, double length) { return M_PI*square(radius+thickness)*(length+2.0*thickness); } static double radius_from_excluded_volume_core_shell_cylinder(double radius, double thickness, double length) { const double radius_tot = radius + thickness; const double length_tot = length + 2.0*thickness; return 0.5*cbrt(0.75*radius_tot*(2.0*radius_tot*length_tot + (radius_tot + length_tot)*(M_PI*radius_tot + length_tot))); } static double radius_from_volume_core_shell_cylinder(double radius, double thickness, double length) { const double volume_outer_cyl = form_volume_core_shell_cylinder(radius,thickness,length); return cbrt(volume_outer_cyl/M_4PI_3); } static double radius_from_diagonal_core_shell_cylinder(double radius, double thickness, double length) { const double radius_outer = radius + thickness; const double length_outer = length + 2.0*thickness; return sqrt(radius_outer*radius_outer + 0.25*length_outer*length_outer); } static double radius_effective_core_shell_cylinder(int mode, double radius, double thickness, double length) { switch (mode) { default: case 1: //cylinder excluded volume return radius_from_excluded_volume_core_shell_cylinder(radius, thickness, length); case 2: // equivalent volume sphere return radius_from_volume_core_shell_cylinder(radius, thickness, length); case 3: // outer radius return radius + thickness; case 4: // half outer length return 0.5*length + thickness; case 5: // half min outer length return (radius < 0.5*length ? radius + thickness : 0.5*length + thickness); case 6: // half max outer length return (radius > 0.5*length ? radius + thickness : 0.5*length + thickness); case 7: // half outer diagonal return radius_from_diagonal_core_shell_cylinder(radius,thickness,length); } } static void Fq_core_shell_cylinder(double q, double *F1, double *F2, double core_sld, double shell_sld, double solvent_sld, double radius, double thickness, double length) { // precalculate constants const double core_r = radius; const double core_h = 0.5*length; const double core_vd = form_volume_core_shell_cylinder(radius,0,length) * (core_sld-shell_sld); const double shell_r = (radius + thickness); const double shell_h = (0.5*length + thickness); const double shell_vd = form_volume_core_shell_cylinder(radius,thickness,length) * (shell_sld-solvent_sld); double total_F1 = 0.0; double total_F2 = 0.0; for (int i=0; i 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; double trace_thickness = thickness; double trace_length = length; if (pd_radius != 0.0 || pd_thickness != 0.0 || pd_length != 0.0) { trace_radius = (randnorm () * pd_radius + 1.0) * radius; trace_thickness = (randnorm () * pd_thickness + 1.0) * thickness; trace_length = (randnorm () * pd_length + 1.0) * length; } 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_cylinder (qab, qc, sld_core, sld_shell, sld_solvent, trace_radius, trace_thickness, trace_length); 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