/*****************************************************************************
* McXtrace, x-ray tracing package
*         Copyright, All rights reserved
*         DTU Physics, Kgs. Lyngby, Denmark
*         Synchrotron SOLEIL, Saint-Aubin, France
*
* Component: Pore_p
*
* %Identification
*
* Written by: Erik B Knudsen and Desiree D. M. Ferreira 
* Date: Feb. 2016
* Version: 1.0
* Release: McXtrace 1.2
* Origin: DTU Physics, DTU Space
*
* Single Pore as part of the Silicon Pore Optics (SPO) as envisioned for the ATHENA+ space telescope.
*
* %Description
* A single pore is simulated, which may have thick walls. The top and bottom are curved cylindrically
* azimuthally, and according to the Wolter I optic lengthwise (sagitally). This is the parabolic part.
* The azimuthal curvature is defined by the radius parameters. This refers to the center of the pore. I.e the top
* and bottom plates have radius of curvature <radius+yheight/2> and <radius-yheight/2> respectively.
* 
* To intersect the Wolter I plates we take advatage of the azimuthal symmetry and only consider the radial component
* of the photon's wavevector.
*
* %Parameters
* Input parameters:
* radius_m: [m] Ring radius of the upper (reflecting) plate of the pore at the intersection with the hyperbolic section.
* radius_p: [m] Ring radius of the upper (reflecting) plate of the pore at the edge furthest away from the focal point.
* yheight:  [m] Height of the pore. (Thus the inner radius is radius_{m,h}-yehight.
* xwidth: [m]  Width of the pore.
* chamferwidth: [m] Width of side walls.
* gap: [m] gap between intersection with parabolic section and actual plate.
* Z0: [m] distance between intersection plane and the focal spot( essentially the focal length).
* mirror_reflec: [ ] Data file containing reflectivities of the reflector surface (TOP).
* side_reflec:  [ ]   Data file containing reflectivities of the side walls (LEFT and RIGHT).
* bottom_reflec: [ ]  Data file containing reflectivities of the bottom surface (BOTTOM).
* R_d: [ ] Default reflectivity value to use if no reflectivity file is given. Useful f.i. is one surface is reflecting and the others absorbing.
* 
* %End
*******************************************************************************/

DEFINE COMPONENT Pore_p
SETTING PARAMETERS (radius_p, radius_m, Z0, xwidth, yheight, gap=0, chamferwidth=0, zdepth=0, string mirror_reflec="", string bottom_reflec="", string side_reflec="", R_d=1, waviness=0, longw=0)

SHARE
%{
  %include "read_table-lib"
  #ifndef MCSPO_INTERSECT_PARABOLOID
  #define MCSPO_INTERSECT_PARABOLOID 1
  int
  intersect_paraboloid (double* l0, double x, double y, double z, double kx, double ky, double kz, double Z0, double radius, double* nx, double* ny, double* nz) {
    /* Intersection routine for a paraboloid as given by the paper by vanspeybroeck and Chase (appl. optics. 1972)*/
    double alpha, thetap, thetah, P, d, e, C0;
    alpha = 0.25 * atan (radius / Z0);
    thetap = alpha;
    thetah = alpha * 3;
    P = Z0 * tan (4 * alpha) * tan (thetap);
    d = Z0 * tan (4 * alpha) * tan (4 * alpha - thetah);
    e = cos (4 * alpha) * (1 + tan (4 * alpha) * tan (thetah));
    C0 = 4 * e * e * P * d / (e * e - 1);

    double kxn = kx, kyn = ky, kzn = kz;
    NORM (kxn, kyn, kzn);

    double A, B, C;
    A = kxn * kxn + kyn * kyn;
    B = 2 * (kxn * x + kyn * y + P * kzn);
    C = x * x + y * y - P * P - 2 * P * (Z0 - z) - C0;
    int status;
    double l1;
    if ((status = solve_2nd_order (l0, &l1, A, B, C)) == 0) {
      /*note that if l1->NULL only the smallest positive solution is returned*/
      /*fprintf(stderr,"Error(%s): No solution to second order eq.\n","Pore_p");*/
      return status;
    }
    /*compute normal vector*/
    x += kxn * (*l0);
    y += kyn * (*l0);
    z += kzn * (*l0);

    double delta_y = -P * pow (P * P + 2 * P * (Z0 - z) + C0, -0.5);
    double rp = sqrt (P * P + 2 * P * (Z0 - z) + C0);

    /* The tilt of the normal vector perpendicular to the optical axis
     * depends only on the displacement in x*/
    *nx = x / rp;
    *ny = y / rp;
    *nz = 0 - delta_y + 0;
    /* the minus sign since a negative slope in rp results in the normal tilting "forward" which
       corresponds to a positive sign in z*/
    NORM (*nx, *ny, *nz);
    return status;
  }
  #endif
%}

DECLARE
%{
  double nExit[3];
  double wExit[3];
  double nEntry[3];
  double wEntry[3];
  double nTop[3];
  double nBottom[3];
  double nRight[3];
  double wRight[3];
  double nLeft[3];
  double wLeft[3];
  double radius_1;
  double radius_2;
  double e_min[3];
  double e_step[3];
  double e_max[3];
  double theta_min[3];
  double theta_step[3];
  double theta_max[3];

  double zentry;

  t_Table reflec_top_table;
  t_Table reflec_bottom_table;
  t_Table reflec_side_table;
  t_Table wave_table[1024];
%}

INITIALIZE
%{
  char* filenames[] = { mirror_reflec, bottom_reflec, side_reflec };
  t_Table* ref_tables[] = { &reflec_top_table, &reflec_bottom_table, &reflec_side_table };
  int i;

  /*read data from files into tables using read_table-lib*/
  for (i = 0; i < 3; i++) {
    char* reflec = filenames[i];
    t_Table* tp = ref_tables[i];
    if (reflec && strlen (reflec)) {
      char** header_parsed;
      /* read 1st block data from file into tp */
      if (Table_Read (tp, reflec, 1) <= 0) {
        exit (fprintf (stderr, "Error(%s): can not read file %s\n", NAME_CURRENT_COMP, reflec));
      }
      header_parsed = Table_ParseHeader (tp->header, "e_min=", "e_max=", "e_step=", "theta_min=", "theta_max=", "theta_step=", NULL);
      if (header_parsed[0] && header_parsed[1] && header_parsed[2] && header_parsed[3] && header_parsed[4] && header_parsed[5]) {
        e_min[i] = strtod (header_parsed[0], NULL);
        e_max[i] = strtod (header_parsed[1], NULL);
        e_step[i] = strtod (header_parsed[2], NULL);
        theta_min[i] = strtod (header_parsed[3], NULL);
        theta_max[i] = strtod (header_parsed[4], NULL);
        theta_step[i] = strtod (header_parsed[5], NULL);
      } else {
        exit (fprintf (stderr, "Error (%s): wrong/missing header line(s) in file %s\n", NAME_CURRENT_COMP, reflec));
      }
      if (!((int)(e_max[i] - e_min[i]) == (int)((tp->rows - 1) * e_step[i]))) {
        exit (fprintf (stderr, "Error (%s): e_step does not match e_min and e_max in file %s\n", NAME_CURRENT_COMP, reflec));
      }
      if (!((int)(theta_max[i] - theta_min[i]) == (int)((tp->columns - 1) * theta_step[i]))) {
        exit (fprintf (stderr, "Error (%s): theta_step does not match theta_min and theta_max in file %s\n", NAME_CURRENT_COMP, reflec));
      }
    } else {
      /*mark the table as unread by setting "rows" to -1
        This will trigger the default reflectivity.*/
      tp->rows = -1;
    }
  }

  /* compute some pore parameters for the parabolic or hyperbolic equations*/
  /* the z coordinate of the entry plane*/
  /*assuming the parameter xi==1*/
  double alpha, thetap, thetah, P, d, e, C0, Z;
  alpha = 0.25 * atan (radius_m / Z0);
  thetap = alpha;
  thetah = alpha * 3;
  P = Z0 * tan (4 * alpha) * tan (thetap);
  d = Z0 * tan (4 * alpha) * tan (4 * alpha - thetah);
  e = cos (4 * alpha) * (1 + tan (4 * alpha) * tan (thetah));
  C0 = 4 * e * e * P * d / (e * e - 1);

  /*solve to get the z-coordinate of the entry plane, assuming radius_1 to be bigger*/
  Z = (pow (radius_p, 2.0) - pow (P, 2.0) - C0) / (2 * P);
  zentry = Z0 - Z;
  double cosa = cos (xwidth / 2.0 / radius_m);
  double sina = sin (xwidth / 2.0 / radius_m);
  /*side wall, entry, and exit planes*/
  nLeft[0] = cosa;
  nLeft[1] = -sina;
  nLeft[2] = 0;
  wLeft[0] = radius_m * (sina);
  wLeft[1] = radius_m * (1 - cosa);
  wLeft[2] = 0;

  nRight[0] = -cosa;
  nRight[1] = -sina;
  nRight[2] = 0;
  wRight[0] = -radius_m * (sina);
  wRight[1] = -radius_m * (1 - cosa);
  wRight[2] = 0;

  nEntry[0] = 0;
  nEntry[1] = 0;
  nEntry[2] = -1;
  wExit[0] = wExit[1] = 0;
  wExit[2] = zentry;

  nExit[0] = 0;
  nExit[1] = 0;
  nExit[2] = 1;
  wExit[0] = wExit[1] = wExit[2] = 0;
%}

TRACE
%{
  enum { LEFT, RIGHT, TOP, BOTTOM, EXIT, NONE } wall;
  t_Table* reflec_table = NULL;
  int hit_pore, hit_chamfer;
  double R;

  /*first do a test prop to see if the photon will enter the pore*/
  double tmpt, tmpx, tmpy, dl;
  tmpt = (zentry - z) / kz;
  tmpx = x + kx * tmpt;
  tmpy = y + ky * tmpt;

  double psi_max, psi_min, psi;
  psi_min = -xwidth * 0.5 / radius_m;
  psi_max = xwidth * 0.5 / radius_m;
  psi = atan2 (tmpx, tmpy + radius_m);

  hit_pore = ((tmpx * tmpx + (tmpy + radius_m) * (tmpy + radius_m) < radius_p * radius_p)
              && (tmpx * tmpx + (tmpy + radius_m) * (tmpy + radius_m) > (radius_p - yheight) * (radius_p - yheight)) && (psi > psi_min && psi < psi_max));
  hit_chamfer = 0;

  if (hit_pore) {
    /*Moving photon to z=zentry. This odd way of writing this, is to handle phase and time automatically.*/
    z -= zentry;
    ALLOW_BACKPROP;
    PROP_Z0;
    z += zentry;

    SCATTER;
    int exit = 0;
    int intersections[5] = { 0, 0, 0, 0, 0 };
    int i_small;
    double l[5] = { 100000.0, 100000.0, 100000.0, 100000.0, 100000.0 };
    double l_small;

    double nx, ny, nz;

    while (!exit) {
      l_small = DBL_MAX;
      wall = NONE;
      double nx, ny, nz;
      double wx, wy, wz;
      int prm_idx; /*index indicating which table parameter set to choose*/
      /*left wall*/
      intersections[LEFT] = plane_intersect (l + LEFT, x, y, z, kx, ky, kz, nLeft[0], nLeft[1], nLeft[2], wLeft[0], wLeft[1], wLeft[2]);
      if (intersections[LEFT] && l[LEFT] > DBL_EPSILON && l[LEFT] < l_small) {
        l_small = l[LEFT];
        i_small = intersections[LEFT];
        wall = LEFT;
      }
      /*right wall*/
      intersections[RIGHT] = plane_intersect (l + RIGHT, x, y, z, kx, ky, kz, nRight[0], nRight[1], nRight[2], wRight[0], wRight[1], wRight[2]);
      if (intersections[RIGHT] && l[RIGHT] > DBL_EPSILON && l[RIGHT] < l_small) {
        l_small = l[RIGHT];
        i_small = intersections[RIGHT];
        wall = RIGHT;
      }
      /*exit plane*/
      intersections[EXIT] = plane_intersect (l + EXIT, x, y, z, kx, ky, kz, nExit[0], nExit[1], nExit[2], wExit[0], wExit[1], wExit[2]);
      if (intersections[EXIT] && l[EXIT] > DBL_EPSILON && l[EXIT] < l_small) {
        l_small = l[EXIT];
        i_small = intersections[EXIT];
        wall = EXIT;
      }
      /*top surface - the real reflecting surface*/
      intersections[TOP] = intersect_paraboloid ((l + TOP), x, y + radius_m, z, kx, ky, kz, Z0, radius_m, &(nTop[0]), &(nTop[1]), &(nTop[2]));
      if (intersections[TOP] && l[TOP] > DBL_EPSILON && l[TOP] < l_small) {
        l_small = l[TOP];
        i_small = intersections[TOP];
        wall = TOP;
      }
      /*bottom surface*/
      intersections[BOTTOM]
          = intersect_paraboloid ((l + BOTTOM), x, y + radius_m, z, kx, ky, kz, Z0, radius_m - yheight, &(nBottom[0]), &(nBottom[1]), &(nBottom[2]));
      if (intersections[BOTTOM] && l[BOTTOM] > DBL_EPSILON && l[BOTTOM] < l_small) {
        l_small = l[BOTTOM];
        i_small = intersections[BOTTOM];
        wall = BOTTOM;
      }

      /*sort intersections ot find the smallest positive one*/
      switch (wall) {
      case LEFT:
        /*handle left wall "reflection"*/
        reflec_table = &reflec_side_table;
        nx = nLeft[0];
        ny = nLeft[1];
        nz = nLeft[2];
        prm_idx = 2;
        break;
      case RIGHT:
        /*handle right wall "reflection"*/
        reflec_table = &reflec_side_table;
        nx = nRight[0];
        ny = nRight[1];
        nz = nRight[2];
        prm_idx = 2;
        break;
      case TOP:
        /*handle top wall reflection*/
        reflec_table = &reflec_top_table;
        nx = nTop[0];
        ny = nTop[1];
        nz = nTop[2];
        prm_idx = 0;
        break;
      case BOTTOM:
        /*handle bottom wall "reflection"*/
        reflec_table = &reflec_bottom_table;
        nx = nBottom[0];
        ny = nBottom[1];
        nz = nBottom[2];
        prm_idx = 1;
        break;
      case EXIT:
        /*photon will exit pore*/
        exit = 1;
        break;
      }
      if (exit) {
        continue;
      }
      PROP_DL (l_small);

      double kix = kx, kiy = ky, kiz = kz;
      double k = sqrt (kx * kx + ky * ky + kz * kz);
      double e = K2E * k;
      double s = scalar_prod (kx, ky, kz, nx, ny, nz);
      double theta = RAD2DEG * (M_PI_2 - acos (s / k)); /*pi_2 since theta is supposed to be the grazing angle*/

      /*if we have waviness alter the normal vector slightly*/
      if (waviness != 0) {
        /*assuming theta to be small we might disregard atan*/
        if (longw) {
          double dtheta;
          if (theta < waviness) {
            dtheta = rand01 () * (theta + waviness) - theta;
          } else {
            dtheta = randpm1 () * waviness;
          }
          double tx, ty, tz;
          vec_prod (tx, ty, tz, 0, 0, 1, nx, ny, nz);
          rotate (nx, ny, nz, nx, ny, nz, dtheta, tx, ty, tz);
        } else {
          /*waviness is also transversal but isotropic*/
          double radius;
          if (theta < waviness) {
            radius = atan (waviness);
            randvec_target_circle (&nx, &ny, &nz, NULL, nx, ny, nx, radius);
          } else {
            radius = (atan (theta) + atan (waviness)) / 2.0;
            randvec_target_circle (&nx, &ny, &nz, NULL, nx, ny, nx + radius - atan (theta), radius);
          }
          NORM (nx, ny, nz);
        }
        /*recompute theta*/
        theta = RAD2DEG * 0.5 * acos (scalar_prod (kx, ky, kz, kix, kiy, kiz) / k / k);
      }
      /*reflect the photon through the surface normal*/
      if (s != 0) {
        kx -= 2 * s * nx;
        ky -= 2 * s * ny;
        kz -= 2 * s * nz;
      }
      SCATTER;
      if (reflec_table == NULL || reflec_table->rows == -1) {
        R = R_d;
      } else {
        R = Table_Value2d (*reflec_table, (e - e_min[prm_idx]) / e_step[prm_idx], (theta - theta_min[prm_idx]) / theta_step[prm_idx]);
      }
      p *= R;
    }
  } else if (hit_chamfer) {
    ABSORB;
  } else {
    /*no hit*/
    ABSORB;
  }
%}

MCDISPLAY
%{
  int k;
  double dth, theta, t0, t1, inner_m, inner_p;
  const int N = 20;

  theta = xwidth / 2.0 / radius_m;
  inner_m = radius_m - yheight;
  inner_p = radius_p - yheight;

  magnify ("");
  line (0, 0, 0, 0, radius_p - radius_m, zentry); /*this extra line indicates the reflecting surface*/
  line (sin (theta) * radius_m, (cos (theta) - 1) * radius_m, 0, sin (theta) * radius_p, cos (theta) * radius_p - radius_m, zentry);
  line (-sin (theta) * radius_m, (cos (theta) - 1) * radius_m, 0, -sin (theta) * radius_p, cos (theta) * radius_p - radius_m, zentry);

  line (sin (theta) * inner_m, cos (theta) * inner_m - radius_m, 0, sin (theta) * inner_p, cos (theta) * inner_p - radius_m, zentry);
  line (-sin (theta) * inner_m, cos (theta) * inner_m - radius_m, 0, -sin (theta) * inner_p, cos (theta) * inner_p - radius_m, zentry);

  line (sin (theta) * radius_m, (cos (theta) - 1) * radius_m, 0, sin (theta) * inner_m, cos (theta) * inner_m - radius_m, 0);
  line (-sin (theta) * radius_m, (cos (theta) - 1) * radius_m, 0, -sin (theta) * inner_m, cos (theta) * inner_m - radius_m, 0);
  line (sin (theta) * radius_p, cos (theta) * radius_p - radius_m, zentry, sin (theta) * inner_p, cos (theta) * inner_p - radius_m, zentry);
  line (-sin (theta) * radius_p, cos (theta) * radius_p - radius_m, zentry, -sin (theta) * inner_p, cos (theta) * inner_p - radius_m, zentry);

  dth = 2 * theta / N;
  for (k = 1; k < N + 1; k++) {
    t0 = -theta + (k - 1) * dth;
    t1 = -theta + k * dth;
    line (sin (t0) * radius_m, cos (t0) * radius_m - radius_m, 0, sin (t1) * radius_m, cos (t1) * radius_m - radius_m, 0);
    line (sin (t0) * inner_m, cos (t0) * inner_m - radius_m, 0, sin (t1) * inner_m, cos (t1) * inner_m - radius_m, 0);

    line (sin (t0) * radius_p, cos (t0) * radius_p - radius_m, zentry, sin (t1) * radius_p, cos (t1) * radius_p - radius_m, zentry);
    line (sin (t0) * inner_p, cos (t0) * inner_p - radius_m, zentry, sin (t1) * inner_p, cos (t1) * inner_p - radius_m, zentry);
  }
%}

END