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/*******************************************************************************
*
* McXtrace, x-ray tracing package
* Copyright, All rights reserved
* DTU Physics, Kgs. Lyngby, Denmark
* Synchrotron SOLEIL, Saint-Aubin, France
*
* Component: Mirror_toroid_pothole
*
* %Identification
*
* Written by: Erik B Knudsen
* Date: Jul 2016
* Version: 1.0
* Origin: DTU Physics
* Modified by: Padovani Antoine, 5th August 2022.
*
* Toroidal shape mirror (in XZ)
*
* %Description
* This is an implementation of a toroidal mirror which may be curved in two dimensions.
* To avoid solving quartic equations, the intersection is computed as a combination of
* two intersections. First, the ray is intersected with a cylinder to catch (almost) the small
* radius curvature. Secondly, the ray is the intersected with an ellipsoid, with the curvatures
* matching that of the torus.
*
* The first incarnation (Mirror_toroid.comp) the mirror curves outwards (a bump), but this incarnation (Mirror_toroid_pothole) curves inwards (a pothole).
*
* Example: Mirror_toroid_pothole( radius=0.1, radius_o=1000, xwidth=5e-2, zdepth=2e-1,R0=1, coating="")
*
* %Parameters
* R0: [1] Reflectivity of mirror.
* xwidth: [m] Width of mirror.
* zdepth: [m] Length of mirror.
* coating: [str] Datafile containing either mirror material constants or reflectivity numbers.
* radius: [m] Curvature radius
* radius_o:[m] Curvature radius, outwards
*
* %End
*******************************************************************************/
DEFINE COMPONENT Mirror_toroid_pothole
SETTING PARAMETERS (zdepth=0.1, xwidth=0.01, radius, radius_o,R0=0,string coating="")
SHARE
%{
#include <complex.h>
%include "read_table-lib"
%include "reflectivity-lib"
struct potholestruct {
double e_min,e_max,e_step,theta_min,theta_max,theta_step;
int use_reflec_table;
};
%}
DECLARE
%{
struct potholestruct prms;
t_Table reflec_table;
t_Reflec re;
%}
INITIALIZE
%{
if (coating && strlen(coating)){
char **header_parsed;
t_Table *tp=&reflec_table;
/* read 1st block data from file into tp */
if (Table_Read(tp, coating, 1) <= 0)
{
exit(fprintf(stderr,"Error: %s: cannot read file %s\n",NAME_CURRENT_COMP, coating));
}
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])
{
prms.e_min=strtod(header_parsed[0],NULL);
prms.e_max=strtod(header_parsed[1],NULL);
prms.e_step=strtod(header_parsed[2],NULL);
prms.theta_min=strtod(header_parsed[3],NULL);
prms.theta_max=strtod(header_parsed[4],NULL);
prms.theta_step=strtod(header_parsed[5],NULL);
} else {
exit(fprintf(stderr,"Error: %s: wrong/missing header line(s) in file %s\n", NAME_CURRENT_COMP, coating));
}
if (((tp->rows-2)*prms.e_step) > (prms.e_max-prms.e_min))
{
exit(fprintf(stderr,"Error: %s: e_step does not match e_min and e_max in file %s (<)\n",NAME_CURRENT_COMP, coating));
}
if ((prms.e_max-prms.e_min) > ((tp->rows)*prms.e_step))
{
exit(fprintf(stderr,"Error: %s: e_step does not match e_min and e_max in file %s (>)\n",NAME_CURRENT_COMP, coating));
}
if (((tp->columns-2)*prms.theta_step) > (prms.theta_max-prms.theta_min))
{
exit(fprintf(stderr,"Error: %s: theta_step does not match theta_min and theta_max in file %s (<)\n",NAME_CURRENT_COMP,coating));
}
if ((prms.theta_max-prms.theta_min) > ((tp->columns)*prms.theta_step))
{
exit(fprintf(stderr,"Error: %s: theta_step does not match theta_min and theta_max in file %s (>)\n",NAME_CURRENT_COMP,coating));
}
prms.use_reflec_table=1;
}else{
prms.use_reflec_table=0;
}
%}
TRACE
%{
int status;
double l0,l1,l2,l3,tx,ty,tz;
do {
/*TODO check the permutation of coordinates and the actual position of the cylinder.*/
status= cylinder_intersect(&l0,&l1,x,z,y-radius,kx,kz,ky, radius, zdepth);
if (!status) break; /* no interaction with the cylinder*/
//if(status & (02|04)) break; /*we exit the top/bottom of the cylinder*/
if(status & (24)) break;
//if(status & (8|16)) break; /*we exit the top/bottom of the cylinder*/
/*if the first intersection is behind the particle - this means the ray is on the wrong side of the mirror*/
if(l1<0) break;
do {
/*this to do a test propagation*/
double op[12];
op[0]=x; op[1]=y; op[2]=z; op[3]=kx; op[4]=ky; op[5]=kz; op[6]=phi; op[7]=t; op[8]=Ex; op[9]=Ey; op[10]=Ez; op[12]=p;
mcPROP_DL(l1);
(tx)=x;(ty)=y; (tz)=z;
x=op[0]; y=op[1]; z=op[2]; kx=op[3]; ky=op[4]; kz=op[5]; phi=op[6]; t=op[7]; Ex=op[8]; Ey=op[9]; Ez=op[10]; p=op[12];
}while(0);
/*check mirror limits of intersectio point.*/
if(tz<-zdepth/2.0 || tz>zdepth/2.0) break;
/*check if the width is OK*/
double xmax=acos(xwidth/(2.0*radius))*radius;
if(tx<-xmax || tx>xmax) break;
status=ellipsoid_intersect(&l2,&l3,x,y-radius,z,kx,ky,kz,radius,radius,radius_o+radius,NULL);
if (!status) break;
if(l3<0) break; /*This shouldn't be possible*/
/*the mirror is indeed hit*/
PROP_DL(l3);
SCATTER;
double nx,ny,nz;
nx=2*x/(radius*radius);
ny=2*(y-radius)/(radius*radius);/*ellipsoid is displaced to put Origin on the surface*/
nz=2*z/((radius+radius_o)*(radius+radius_o));
NORM(nx,ny,nz);
/*By definition the normal vector points out from the ellipsoid*/
double s=scalar_prod(kx,ky,kz,nx,ny,nz);
double k=sqrt(scalar_prod(kx,ky,kz,kx,ky,kz));
kx=kx-2*s*nx;
ky=ky-2*s*ny;
kz=kz-2*s*nz;
/*find energy, and glancing angle*/
if (prms.use_reflec_table){
/*the get ref. by call to Table_value2d*/
double R;
double theta=RAD2DEG*(acos(s/k)-M_PI_2);
double e=K2E*k;
R=Table_Value2d(reflec_table,fabs((e-prms.e_min)/prms.e_step), fabs(((theta-prms.theta_min)/prms.theta_step)));
p*=R;
/*update phase - as an approximation turn by 180 deg.*/
phi+=M_PI;
}else{
p*=R0;
}
}while(0);
%}
MCDISPLAY
%{
//See parametric equation used for the 3D view here: https://en.wikipedia.org/wiki/Torus#Geometry or here:https://web.maths.unsw.edu.au/~rsw/Torus/index.php
//Because the code above doesn't actually reproduce a torus exactly but uses a cylinder and an ellipsoid to construct the toroidal mirror (to avoid solving quartic equations),
//there's a slight mismatch between the 3D view (exact torus) and the actual toroidal mirror coded above.
double x0,y0,z0,x1,y1,z1,theta,phi,phi_total,theta_total,theta_beginning,phi_beginning,theta_end,phi_end;
//int N=50; too many points, makes the 3D matlab viewer bug
int N=10;
phi_total = RAD2DEG*(zdepth/(radius+radius_o));//degrees
theta_total = RAD2DEG*(xwidth/radius);
//fix theta=0 and phi=180 degrees respectively
theta=0;
phi=180;
//then start at the beginning of the theta or phi range in order to map the flat surface (xwidth, zdepth) on the torus.
theta_beginning=theta-(theta_total/2);
phi_beginning=phi-(phi_total/2);
theta_end = theta+(theta_total/2);
phi_end = phi+(phi_total/2);
theta = theta_beginning;
phi = phi_beginning;
while (theta<=theta_end){
phi=180-(phi_total/2);
x0=radius*sin(DEG2RAD*theta);
y0=(radius_o+radius*cos(DEG2RAD*theta))*cos(DEG2RAD*phi)+(radius_o+radius);
z0=(radius_o+radius*cos(DEG2RAD*theta))*sin(DEG2RAD*phi);
while (phi<=phi_end){
x1=radius*sin(DEG2RAD*theta);
y1=(radius_o+radius*cos(DEG2RAD*theta))*cos(DEG2RAD*phi)+(radius_o+radius);
z1=(radius_o+radius*cos(DEG2RAD*theta))*sin(DEG2RAD*phi);
line(x0,y0,z0,x1,y1,z1);
x0=x1;
y0=y1;
z0=z1;
phi+=phi_total/N;
}
theta+=theta_total/N;
}
theta = theta_beginning;
phi = phi_beginning;
while (phi<=phi_end){
theta=-(theta_total/2);
x0=radius*sin(DEG2RAD*theta);
y0=(radius_o+radius*cos(DEG2RAD*theta))*cos(DEG2RAD*phi)+(radius_o+radius);
z0=(radius_o+radius*cos(DEG2RAD*theta))*sin(DEG2RAD*phi);
while (theta<=theta_end){
x1=radius*sin(DEG2RAD*theta);
y1=(radius_o+radius*cos(DEG2RAD*theta))*cos(DEG2RAD*phi)+(radius_o+radius);
z1=(radius_o+radius*cos(DEG2RAD*theta))*sin(DEG2RAD*phi);
line(x0,y0,z0,x1,y1,z1);
x0=x1;
y0=y1;
z0=z1;
theta+=theta_total/N;
}
phi+=phi_total/N;
}
%}
END
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