/*-----------------------------------------------------------------------------  File        : integral_line.h  Description : This CImg plug-in defines function to track integral lines.  Copyright   : David Tschumperle - http://www.greyc.ensicaen.fr/~dtschump/  License     : CeCILL  This software is governed by the CeCILL  license under French law and  abiding by the rules of distribution of free software.  You can  use,  modify and/ or redistribute the software under the terms of the CeCILL  license as circulated by CEA, CNRS and INRIA at the following URL  "http://www.cecill.info".  As a counterpart to the access to the source code and  rights to copy,  modify and redistribute granted by the license, users are provided only  with a limited warranty  and the software's author,  the holder of the  economic rights,  and the successive licensors  have only  limited  liability.  In this respect, the user's attention is drawn to the risks associated  with loading,  using,  modifying and/or developing or reproducing the  software by the user in light of its specific status of free software,  that may mean  that it is complicated to manipulate,  and  that  also  therefore means  that it is reserved for developers  and  experienced  professionals having in-depth computer knowledge. Users are therefore  encouraged to load and test the software's suitability as regards their  requirements in conditions enabling the security of their systems and/or  data to be ensured and,  more generally, to use and operate it in the  same conditions as regards security.  The fact that you are presently reading this means that you have had  knowledge of the CeCILL license and that you accept its terms.  ------------------------------------------------------------------------------*/#ifndef cimg_plugin_integral_line#define cimg_plugin_integral_line#define pcimg_valign2d(i,j) \    { restype &u = W(i,j,0,0), &v = W(i,j,0,1); \    if (u*curru + v*currv<0) { u=-u; v=-v; }}#define pcimg_valign3d(i,j,k) \    { restype &u = W(i,j,k,0), &v = W(i,j,k,1), &w = W(i,j,k,2); \    if (u*curru + v*currv + w*currw<0) { u=-u; v=-v; w=-w; }}CImgList<typename cimg::largest<float,T>::type> get_integral_line(const float x, const float y, const float z=0, const float L=1000,                                                                  const float dl=0.5f, const unsigned int interpolation=3) const {  typedef typename cimg::largest<float,T>::type restype;  CImgList<restype> tracking;  CImg<restype> W = (*this)*dl;  const unsigned int    dx1 = width-1,    dy1 = height-1;  const float    L2 = L/2,    cu = (float)(dl*W((int)x,(int)y,(int)z,0)),    cv = (float)(dl*W((int)x,(int)y,(int)z,1));  float    pu = cu,    pv = cv,    X = x,    Y = y;  // 3D integral lines  //-------------------  switch (W.dimv()) {  case 3: {    const unsigned int      dz1 = depth-1;    const float      cw = (float)(dl*W((int)x,(int)y,(int)z,2));    float      pw = cw,      Z = z;    switch (interpolation) {    case 0: { // Nearest neighbor      for (float l=0; l<L2 && X>=0 && X<=dx1 && Y>=0 && Y<=dy1 && Z>=0 && Z<=dz1; l+=dl) {        tracking.insert(CImg<restype>::vector(X,Y,Z));        const int          cx = (int)(X+0.5f),          cy = (int)(Y+0.5f),          cz = (int)(Z+0.5f);        float          u = (float)(dl*W(cx,cy,cz,0)),          v = (float)(dl*W(cx,cy,cz,1)),          w = (float)(dl*W(cx,cy,cz,2));        if ((pu*u + pv*v + pw*w)<0) { u=-u; v=-v; w=-w; }        X+=(pu=u); Y+=(pv=v); Z+=(pw=w);      }      pu = cu;      pv = cv;      pw = cw;      X  = x;      Y  = y;      Z  = z;      for (float l=0; l<L2 && X>=0 && X<=dx1 && Y>=0 && Y<=dy1 && Z>=0 && Z<=dz1; l+=dl) {        const int          cx = (int)(X+0.5f),          cy = (int)(Y+0.5f),          cz = (int)(Z+0.5f);        float          u = (float)(dl*W(cx,cy,cz,0)),          v = (float)(dl*W(cx,cy,cz,1)),          w = (float)(dl*W(cx,cy,cz,2));        if ((pu*u + pv*v + pw*w)<0) { u=-u; v=-v; w=-w; }        X-=(pu=u); Y-=(pv=v); Z-=(pw=w);        tracking.insert(CImg<restype>::vector(X,Y,Z),0);      }    } break;    case 1: { // Linear      for (float l=0; l<L2 && X>=0 && X<=dx1 && Y>=0 && Y<=dy1 && Z>=0 && Z<=dz1; l+=dl) {        tracking.insert(CImg<restype>::vector(X,Y,Z));        const int          cx = (int)X, px = (cx-1<0)?0:cx-1, nx = (cx+1>dx1)?dx1:cx+1,          cy = (int)Y, py = (cy-1<0)?0:cy-1, ny = (cy+1>dy1)?dy1:cy+1,          cz = (int)Z, pz = (cz-1<0)?0:cz-1, nz = (cz+1>dz1)?dz1:cz+1;        const float          curru = (float)W(cx,cy,cz,0),          currv = (float)W(cx,cy,cz,1),          currw = (float)W(cx,cy,cz,2);        pcimg_valign3d(px,py,pz); pcimg_valign3d(cx,py,pz); pcimg_valign3d(nx,py,pz);        pcimg_valign3d(px,cy,pz); pcimg_valign3d(cx,cy,pz); pcimg_valign3d(nx,cy,pz);        pcimg_valign3d(px,ny,pz); pcimg_valign3d(cx,ny,pz); pcimg_valign3d(nx,ny,pz);        pcimg_valign3d(px,py,cz); pcimg_valign3d(cx,py,cz); pcimg_valign3d(nx,py,cz);        pcimg_valign3d(px,cy,cz);                           pcimg_valign3d(nx,cy,cz);        pcimg_valign3d(px,ny,cz); pcimg_valign3d(cx,ny,cz); pcimg_valign3d(nx,ny,cz);        pcimg_valign3d(px,py,nz); pcimg_valign3d(cx,py,nz); pcimg_valign3d(nx,py,nz);        pcimg_valign3d(px,cy,nz); pcimg_valign3d(cx,cy,nz); pcimg_valign3d(nx,cy,nz);        pcimg_valign3d(px,ny,nz); pcimg_valign3d(cx,ny,nz); pcimg_valign3d(nx,ny,nz);        float          u = (float)(dl*W.linear_pix3d(X,Y,Z,0)),          v = (float)(dl*W.linear_pix3d(X,Y,Z,1)),          w = (float)(dl*W.linear_pix3d(X,Y,Z,2));        if ((pu*u + pv*v + pw*w)<0) { u=-u; v=-v; w=-w; }        X+=(pu=u); Y+=(pv=v); Z+=(pw=w);      }      pu = cu;      pv = cv;      pw = cw;      X  = x;      Y  = y;      Z  = z;      for (float l=0; l<L2 && X>=0 && X<=dx1 && Y>=0 && Y<=dy1 && Z>=0 && Z<=dz1; l+=dl) {        const int          cx = (int)X, px = (cx-1<0)?0:cx-1, nx = (cx+1>dx1)?dx1:cx+1,          cy = (int)Y, py = (cy-1<0)?0:cy-1, ny = (cy+1>dy1)?dy1:cy+1,          cz = (int)Z, pz = (cz-1<0)?0:cz-1, nz = (cz+1>dz1)?dz1:cz+1;        const float          curru = (float)W(cx,cy,cz,0),          currv = (float)W(cx,cy,cz,1),          currw = (float)W(cx,cy,cz,2);        pcimg_valign3d(px,py,pz); pcimg_valign3d(cx,py,pz); pcimg_valign3d(nx,py,pz);        pcimg_valign3d(px,cy,pz); pcimg_valign3d(cx,cy,pz); pcimg_valign3d(nx,cy,pz);        pcimg_valign3d(px,ny,pz); pcimg_valign3d(cx,ny,pz); pcimg_valign3d(nx,ny,pz);        pcimg_valign3d(px,py,cz); pcimg_valign3d(cx,py,cz); pcimg_valign3d(nx,py,cz);        pcimg_valign3d(px,cy,cz);                           pcimg_valign3d(nx,cy,cz);        pcimg_valign3d(px,ny,cz); pcimg_valign3d(cx,ny,cz); pcimg_valign3d(nx,ny,cz);        pcimg_valign3d(px,py,nz); pcimg_valign3d(cx,py,nz); pcimg_valign3d(nx,py,nz);        pcimg_valign3d(px,cy,nz); pcimg_valign3d(cx,cy,nz); pcimg_valign3d(nx,cy,nz);        pcimg_valign3d(px,ny,nz); pcimg_valign3d(cx,ny,nz); pcimg_valign3d(nx,ny,nz);        float          u = (float)(dl*W.linear_pix3d(X,Y,Z,0)),          v = (float)(dl*W.linear_pix3d(X,Y,Z,1)),          w = (float)(dl*W.linear_pix3d(X,Y,Z,2));        if ((pu*u+pv*v+pw*w)<0) { u=-u; v=-v; w=-w; }        X-=(pu=u); Y-=(pv=v); Z-=(pw=w);        tracking.insert(CImg<restype>::vector(X,Y,Z),0);      }    } break;    case 2: { // 2nd order Runge Kutta      for (float l=0; l<L2 && X>=0 && X<=dx1 && Y>=0 && Y<=dy1 && Z>=0 && Z<=dz1; l+=dl) {        tracking.insert(CImg<restype>::vector(X,Y,Z));        const int          cx = (int)X, px = (cx-1<0)?0:cx-1, nx = (cx+1>dx1)?dx1:cx+1,          cy = (int)Y, py = (cy-1<0)?0:cy-1, ny = (cy+1>dy1)?dy1:cy+1,          cz = (int)Z, pz = (cz-1<0)?0:cz-1, nz = (cz+1>dz1)?dz1:cz+1;        const float          curru = (float)W(cx,cy,cz,0),          currv = (float)W(cx,cy,cz,1),          currw = (float)W(cx,cy,cz,2);        pcimg_valign3d(px,py,pz); pcimg_valign3d(cx,py,pz); pcimg_valign3d(nx,py,pz);        pcimg_valign3d(px,cy,pz); pcimg_valign3d(cx,cy,pz); pcimg_valign3d(nx,cy,pz);        pcimg_valign3d(px,ny,pz); pcimg_valign3d(cx,ny,pz); pcimg_valign3d(nx,ny,pz);        pcimg_valign3d(px,py,cz); pcimg_valign3d(cx,py,cz); pcimg_valign3d(nx,py,cz);        pcimg_valign3d(px,cy,cz);                           pcimg_valign3d(nx,cy,cz);        pcimg_valign3d(px,ny,cz); pcimg_valign3d(cx,ny,cz); pcimg_valign3d(nx,ny,cz);        pcimg_valign3d(px,py,nz); pcimg_valign3d(cx,py,nz); pcimg_valign3d(nx,py,nz);        pcimg_valign3d(px,cy,nz); pcimg_valign3d(cx,cy,nz); pcimg_valign3d(nx,cy,nz);        pcimg_valign3d(px,ny,nz); pcimg_valign3d(cx,ny,nz); pcimg_valign3d(nx,ny,nz);        const float          u0 = (float)(0.5f*dl*W.linear_pix3d(X,Y,Z,0)),          v0 = (float)(0.5f*dl*W.linear_pix3d(X,Y,Z,1)),          w0 = (float)(0.5f*dl*W.linear_pix3d(X,Y,Z,2));        float          u = (float)(dl*W.linear_pix3d(X+u0,Y+v0,Z+w0,0)),          v = (float)(dl*W.linear_pix3d(X+u0,Y+v0,Z+w0,1)),          w = (float)(dl*W.linear_pix3d(X+u0,Y+v0,Z+w0,2));        if ((pu*u+pv*v+pw*w)<0) { u=-u; v=-v; w=-w; }        X+=(pu=u); Y+=(pv=v); Z+=(pw=w);      }      pu = cu;      pv = cv;      pw = cw;      X  = x;      Y  = y;      Z  = z;      for (float l=0; l<L2 && X>=0 && X<=dx1 && Y>=0 && Y<=dy1 && Z>=0 && Z<=dz1; l+=dl) {        const int          cx = (int)X, px = (cx-1<0)?0:cx-1, nx = (cx+1>dx1)?dx1:cx+1,          cy = (int)Y, py = (cy-1<0)?0:cy-1, ny = (cy+1>dy1)?dy1:cy+1,          cz = (int)Z, pz = (cz-1<0)?0:cz-1, nz = (cz+1>dz1)?dz1:cz+1;        const float          curru = (float)W(cx,cy,cz,0),          currv = (float)W(cx,cy,cz,1),          currw = (float)W(cx,cy,cz,2);        pcimg_valign3d(px,py,pz); pcimg_valign3d(cx,py,pz); pcimg_valign3d(nx,py,pz);        pcimg_valign3d(px,cy,pz); pcimg_valign3d(cx,cy,pz); pcimg_valign3d(nx,cy,pz);        pcimg_valign3d(px,ny,pz); pcimg_valign3d(cx,ny,pz); pcimg_valign3d(nx,ny,pz);        pcimg_valign3d(px,py,cz); pcimg_valign3d(cx,py,cz); pcimg_valign3d(nx,py,cz);        pcimg_valign3d(px,cy,cz);                           pcimg_valign3d(nx,cy,cz);        pcimg_valign3d(px,ny,cz); pcimg_valign3d(cx,ny,cz); pcimg_valign3d(nx,ny,cz);        pcimg_valign3d(px,py,nz); pcimg_valign3d(cx,py,nz); pcimg_valign3d(nx,py,nz);        pcimg_valign3d(px,cy,nz); pcimg_valign3d(cx,cy,nz); pcimg_valign3d(nx,cy,nz);        pcimg_valign3d(px,ny,nz); pcimg_valign3d(cx,ny,nz); pcimg_valign3d(nx,ny,nz);        const float          u0 = (float)(0.5f*dl*W.linear_pix3d(X,Y,Z,0)),          v0 = (float)(0.5f*dl*W.linear_pix3d(X,Y,Z,1)),          w0 = (float)(0.5f*dl*W.linear_pix3d(X,Y,Z,2));        float          u = (float)(dl*W.linear_pix3d(X+u0,Y+v0,Z+w0,0)),          v = (float)(dl*W.linear_pix3d(X+u0,Y+v0,Z+w0,1)),          w = (float)(dl*W.linear_pix3d(X+u0,Y+v0,Z+w0,2));        if ((pu*u+pv*v+pw*w)<0) { u=-u; v=-v; w=-w; }        X-=(pu=u); Y-=(pv=v); Z-=(pw=w);        tracking.insert(CImg<restype>::vector(X,Y,Z),0);      }    } break;    case 3: {  // 4nd order Runge Kutta      for (float l=0; l<L2 && X>=0 && X<=dx1 && Y>=0 && Y<=dy1 && Z>=0 && Z<=dz1; l+=dl) {        tracking.insert(CImg<restype>::vector(X,Y,Z));        const int          cx = (int)X, px = (cx-1<0)?0:cx-1, nx = (cx+1>dx1)?dx1:cx+1,          cy = (int)Y, py = (cy-1<0)?0:cy-1, ny = (cy+1>dy1)?dy1:cy+1,          cz = (int)Z, pz = (cz-1<0)?0:cz-1, nz = (cz+1>dz1)?dz1:cz+1;        const float          curru = (float)W(cx,cy,cz,0),          currv = (float)W(cx,cy,cz,1),          currw = (float)W(cx,cy,cz,2);        pcimg_valign3d(px,py,pz); pcimg_valign3d(cx,py,pz); pcimg_valign3d(nx,py,pz);        pcimg_valign3d(px,cy,pz); pcimg_valign3d(cx,cy,pz); pcimg_valign3d(nx,cy,pz);        pcimg_valign3d(px,ny,pz); pcimg_valign3d(cx,ny,pz); pcimg_valign3d(nx,ny,pz);        pcimg_valign3d(px,py,cz); pcimg_valign3d(cx,py,cz); pcimg_valign3d(nx,py,cz);        pcimg_valign3d(px,cy,cz);                           pcimg_valign3d(nx,cy,cz);        pcimg_valign3d(px,ny,cz); pcimg_valign3d(cx,ny,cz); pcimg_valign3d(nx,ny,cz);        pcimg_valign3d(px,py,nz); pcimg_valign3d(cx,py,nz); pcimg_valign3d(nx,py,nz);        pcimg_valign3d(px,cy,nz); pcimg_valign3d(cx,cy,nz); pcimg_valign3d(nx,cy,nz);