EMAN::ChaoProjector Class Reference

Fast real space projection using Bi-Linear interpolation. More...

#include <projector.h>

Inheritance diagram for EMAN::ChaoProjector:

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Collaboration diagram for EMAN::ChaoProjector:

[legend]

List of all members.

Public Member Functions
EMData *	project3d (EMData *vol) const
	Project an 3D image into a 2D image.
EMData *	backproject3d (EMData *imagestack) const
	Back-project a 2D image into a 3D image.
string	get_name () const
	Get the projector's name.
string	get_desc () const
TypeDict	get_param_types () const
	Get processor parameter information in a dictionary.
Static Public Member Functions
static Projector *	NEW ()
Private Member Functions
int	getnnz (Vec3i volsize, int ri, Vec3i origin, int *nray, int *nnz) const
int	cb2sph (float *cube, Vec3i volsize, int ri, Vec3i origin, int nnz0, int *ptrs, int *cord, float *sphere) const
int	sph2cb (float *sphere, Vec3i volsize, int nray, int ri, int nnz0, int *ptrs, int *cord, float *cube) const
int	fwdpj3 (Vec3i volsize, int nray, int nnz, float *dm, Vec3i origin, int ri, int *ptrs, int *cord, float *x, float *y) const
int	bckpj3 (Vec3i volsize, int nray, int nnz, float *dm, Vec3i origin, int ri, int *ptrs, int *cord, float *x, float *y) const
int	ifix (float a) const
void	setdm (vector< float > anglelist, string const angletype, float *dm) const

---

Detailed Description

Fast real space projection using Bi-Linear interpolation.

(C. Yang)

Definition at line 365 of file projector.h.

---

Member Function Documentation

EMData * ChaoProjector::project3d

(

EMData *

image

)

const [virtual]

Project an 3D image into a 2D image.

Returns:

A 2D image from the projection.

Implements EMAN::Projector.

Definition at line 1585 of file projector.cpp.

References anglelist, cb2sph(), cord, cube, dm, EMDeleteArray(), fwdpj3(), EMAN::EMData::get_data(), EMAN::Util::get_min(), EMAN::Transform::get_rotation(), EMAN::EMData::get_xsize(), EMAN::EMData::get_ysize(), EMAN::EMData::get_zsize(), getnnz(), EMAN::Dict::has_key(), images, LOGERR, nnz, nrays, NullPointerException, EMAN::Projector::params, phi, ptrs, EMAN::EMData::set_attr(), EMAN::EMData::set_complex(), EMAN::EMData::set_ri(), EMAN::EMData::set_size(), setdm(), EMAN::Dict::size(), sphere, status, theta, and EMAN::EMData::update().

{

        int nrays, nnz, status, j;
        float *dm;
        int   *ptrs, *cord;
        float *sphere, *images;

        int nxvol = vol->get_xsize();
        int nyvol = vol->get_ysize();
        int nzvol = vol->get_zsize();
        Vec3i volsize(nxvol,nyvol,nzvol);

        int dim = Util::get_min(nxvol,nyvol,nzvol);
        if (nzvol == 1) {
                LOGERR("The ChaoProjector needs a volume!");
                return 0;
        }
        Vec3i origin(0,0,0);
        // If a sensible origin isn't passed in, choose the middle of
        // the cube.
        if (params.has_key("origin_x")) {origin[0] = params["origin_x"];}
        else {origin[0] = nxvol/2+1;}
        if (params.has_key("origin_y")) {origin[1] = params["origin_y"];}
        else {origin[1] = nyvol/2+1;}
        if (params.has_key("origin_z")) {origin[2] = params["origin_z"];}
        else {origin[2] = nzvol/2+1;}

        int ri;
        if (params.has_key("radius")) {ri = params["radius"];}
        else {ri = dim/2 - 1;}

        // retrieve the voxel values
        float *cube = vol->get_data();

        // count the number of voxels within a sphere centered at icent,
        // with radius ri
        status = getnnz(volsize, ri, origin, &nrays, &nnz);
        // need to check status...

        // convert from cube to sphere
        sphere = new float[nnz];
        ptrs   = new int[nrays+1];
        cord   = new int[3*nrays];
        if (sphere == NULL || ptrs == NULL || cord == NULL) {
                fprintf(stderr,"ChaoProjector::project3d, failed to allocate!\n");
                exit(1);
        }
        for (int i = 0; i<nnz; i++) sphere[i] = 0.0;
        for (int i = 0; i<nrays+1; i++) ptrs[i] = 0;
        for (int i = 0; i<3*nrays; i++) cord[i] = 0;

        status = cb2sph(cube, volsize, ri, origin, nnz, ptrs, cord, sphere);
        // check status

        int nangles = 0;
        vector<float> anglelist;
        string angletype = "SPIDER";
        // Do we have a list of angles?
        if (params.has_key("anglelist")) {
                anglelist = params["anglelist"];
                nangles = anglelist.size() / 3;
        } else {
                Transform* t3d = params["transform"];
                if ( t3d == NULL ) throw NullPointerException("The transform object (required for projection), was not specified");
                // This part was modified by David Woolford -
                // Before this the code worked only for SPIDER and EMAN angles,
                // but the framework of the Transform3D allows for a generic implementation
                // as specified here.
                Dict p = t3d->get_rotation("spider");
                if(t3d) {delete t3d; t3d=0;}

                float phi   = p["phi"];
                float theta = p["theta"];
                float psi   = p["psi"];
                anglelist.push_back(phi);
                anglelist.push_back(theta);
                anglelist.push_back(psi);
                nangles = 1;
        }
        // End David Woolford modifications

        dm = new float[nangles*9];
        setdm(anglelist, angletype, dm);

                // return images
        EMData *ret = new EMData();
        ret->set_size(nxvol, nyvol, nangles);
        ret->set_complex(false);
        ret->set_ri(true);

        images = ret->get_data();

        for (j = 1; j <= nangles; j++) {
                status = fwdpj3(volsize, nrays, nnz   , &dm(1,j), origin, ri,
                                                ptrs   ,  cord, sphere, &images(1,1,j));
        // check status?
        }

        // deallocate all temporary work space
        EMDeleteArray(dm);
        EMDeleteArray(ptrs);
        EMDeleteArray(cord);
        EMDeleteArray(sphere);

        if (!params.has_key("anglelist")) {
                Transform* t3d = params["transform"];
                ret->set_attr("xform.projection",t3d);
                if(t3d) {delete t3d; t3d=0;}
        }
        ret->update();
        return ret;
}

EMData * ChaoProjector::backproject3d

(

EMData *

image

)

const [virtual]

Back-project a 2D image into a 3D image.

Returns:

A 3D image from the backprojection.

Implements EMAN::Projector.

Definition at line 1704 of file projector.cpp.

References anglelist, bckpj3(), cb2sph(), cord, cube, dm, EMDeleteArray(), EMAN::EMData::get_data(), EMAN::Util::get_min(), EMAN::Transform::get_rotation(), EMAN::EMData::get_xsize(), EMAN::EMData::get_ysize(), EMAN::EMData::get_zsize(), getnnz(), EMAN::Dict::has_key(), images, LOGERR, nnz, nrays, NullPointerException, EMAN::Projector::params, phi, ptrs, EMAN::EMData::set_complex(), EMAN::EMData::set_ri(), EMAN::EMData::set_size(), setdm(), EMAN::Dict::size(), sph2cb(), sphere, status, theta, EMAN::EMData::to_zero(), and EMAN::EMData::update().

{
        int nrays, nnz, status, j;
        float *dm;
        int   *ptrs, *cord;
        float *sphere, *images, *cube;

        int nximg   = imagestack->get_xsize();
        int nyimg   = imagestack->get_ysize();
        int nslices = imagestack->get_zsize();

        int dim = Util::get_min(nximg,nyimg);
        Vec3i volsize(nximg,nyimg,dim);

        Vec3i origin(0,0,0);
        // If a sensible origin isn't passed in, choose the middle of
        // the cube.
        if (params.has_key("origin_x")) {origin[0] = params["origin_x"];}
        else {origin[0] = nximg/2+1;}
        if (params.has_key("origin_y")) {origin[1] = params["origin_y"];}
        else {origin[1] = nyimg/2+1;}
        if (params.has_key("origin_z")) {origin[1] = params["origin_z"];}
        else {origin[2] = dim/2+1;}

        int ri;
        if (params.has_key("radius")) {ri = params["radius"];}
        else {ri = dim/2 - 1;}

        // retrieve the voxel values
        images = imagestack->get_data();

        // count the number of voxels within a sphere centered at icent,
        // with radius ri
        status = getnnz(volsize, ri, origin, &nrays, &nnz);
        // need to check status...

        // convert from cube to sphere
        sphere = new float[nnz];
        ptrs   = new int[nrays+1];
        cord   = new int[3*nrays];
        if (sphere == NULL || ptrs == NULL || cord == NULL) {
                fprintf(stderr,"ChaoProjector::backproject3d, failed to allocate!\n");
                exit(1);
        }
        for (int i = 0; i<nnz; i++) sphere[i] = 0.0;
        for (int i = 0; i<nrays+1; i++) ptrs[i] = 0;
        for (int i = 0; i<3*nrays; i++) cord[i] = 0;

        int nangles = 0;
        vector<float> anglelist;
        string angletype = "SPIDER";
        // Do we have a list of angles?
        if (params.has_key("anglelist")) {
                anglelist = params["anglelist"];
                nangles = anglelist.size() / 3;
        } else {
                Transform* t3d = params["transform"];
                if ( t3d == NULL ) throw NullPointerException("The transform3d object (required for projection), was not specified");
                // This part was modified by David Woolford -
                // Before this the code worked only for SPIDER and EMAN angles,
                // but the framework of the Transform3D allows for a generic implementation
                // as specified here.
                //  This was broken by david.  we need here a loop over all projections and put all angles on stack  PAP 06/28/09
                Dict p = t3d->get_rotation("spider");
                if(t3d) {delete t3d; t3d=0;}

                float phi = p["phi"];
                float theta = p["theta"];
                float psi = p["psi"];
                anglelist.push_back(phi);
                anglelist.push_back(theta);
                anglelist.push_back(psi);
                nangles = 1;
        }

        // End David Woolford modifications

        if (nslices != nangles) {
                LOGERR("the number of images does not match the number of angles");
                return 0;
        }

        dm = new float[nangles*9];
        setdm(anglelist, angletype, dm);

        // return volume
        EMData *ret = new EMData();
        ret->set_size(nximg, nyimg, dim);
        ret->set_complex(false);
        ret->set_ri(true);
        ret->to_zero();

        cube = ret->get_data();
        // cb2sph should be replaced by something that touches only ptrs and cord
        status = cb2sph(cube, volsize, ri, origin, nnz, ptrs, cord, sphere);
        // check status

        for (j = 1; j <= nangles; j++) {
                status = bckpj3(volsize, nrays, nnz, &dm(1,j), origin, ri,
                         ptrs   , cord , &images(1,1,j), sphere);
        // check status?
        }

        status = sph2cb(sphere, volsize, nrays, ri, nnz, ptrs, cord, cube);
        // check status?

        // deallocate all temporary work space
        EMDeleteArray(dm);
        EMDeleteArray(ptrs);
        EMDeleteArray(cord);
        EMDeleteArray(sphere);

        ret->update();
        return ret;
}

string EMAN::ChaoProjector::get_name

(

)

const [inline, virtual]

Get the projector's name.

Each projector is indentified by unique name.

Returns:

The projector's name.

Implements EMAN::Projector.

Definition at line 371 of file projector.h.

                {
                        return "chao";
                }

string EMAN::ChaoProjector::get_desc

(

)

const [inline, virtual]

Implements EMAN::Projector.

Definition at line 376 of file projector.h.

                {
                        return "Fast real space projection generation with Bi-Linear interpolation.";
                }

static Projector* EMAN::ChaoProjector::NEW

(

)

[inline, static]

Definition at line 381 of file projector.h.

                {
                        return new ChaoProjector();
                }

TypeDict EMAN::ChaoProjector::get_param_types

(

)

const [inline, virtual]

Get processor parameter information in a dictionary.

Each parameter has one record in the dictionary. Each record contains its name, data-type, and description.

Returns:

A dictionary containing the parameter info.

Reimplemented from EMAN::Projector.

Definition at line 386 of file projector.h.

References EMAN::EMObject::FLOAT, EMAN::EMObject::FLOATARRAY, EMAN::EMObject::INT, EMAN::TypeDict::put(), and EMAN::EMObject::TRANSFORM.

                {
                        TypeDict d;
                        d.put("transform", EMObject::TRANSFORM);
                        d.put("origin_x",  EMObject::INT);
                        d.put("origin_y",  EMObject::INT);
                        d.put("origin_z",  EMObject::INT);
                        d.put("anglelist", EMObject::FLOATARRAY);
                        d.put("radius",    EMObject::FLOAT);
                        return d;
                }

int ChaoProjector::getnnz	(	Vec3i	volsize,
		int	ri,
		Vec3i	origin,
		int *	nray,
		int *	nnz
	)			const [private]

Definition at line 1227 of file projector.cpp.

References nnz, nrays, nx, ny, and status.

Referenced by backproject3d(), and project3d().

          : count the number of voxels within a sphere centered
            at origin and with a radius ri.

     input:
     volsize contains the size information (nx,ny,nz) about the volume
     ri      radius of the object embedded in the cube.
     origin  coordinates for the center of the volume

     output:
     nnz    total number of voxels within the sphere (of radius ri)
     nrays  number of rays in z-direction.
*/
{
        int  ix, iy, iz, rs, r2, xs, ys, zs, xx, yy, zz;
        int  ftm=0, status = 0;

        r2    = ri*ri;
        *nnz  = 0;
        *nrays = 0;
        int nx = (int)volsize[0];
        int ny = (int)volsize[1];
        int nz = (int)volsize[2];

        int xcent = (int)origin[0];
        int ycent = (int)origin[1];
        int zcent = (int)origin[2];

        // need to add some error checking
        for (ix = 1; ix <=nx; ix++) {
            xs  = ix-xcent;
            xx  = xs*xs;
            for (iy = 1; iy <= ny; iy++) {
                ys = iy-ycent;
                yy = ys*ys;
                ftm = 1;
                for (iz = 1; iz <= nz; iz++) {
                    zs = iz-zcent;
                    zz = zs*zs;
                    rs = xx + yy + zz;
                    if (rs <= r2) {
                        (*nnz)++;
                        if (ftm) {
                           (*nrays)++;
                           ftm = 0;
                        }
                    }
                }
            } // end for iy
        } // end for ix
        return status;
}

int ChaoProjector::cb2sph	(	float *	cube,
		Vec3i	volsize,
		int	ri,
		Vec3i	origin,
		int	nnz0,
		int *	ptrs,
		int *	cord,
		float *	sphere
	)			const [private]

Definition at line 1287 of file projector.cpp.

References cord, cube, nnz, nrays, nx, ny, ptrs, sphere, and status.

Referenced by backproject3d(), and project3d().

{
    int    xs, ys, zs, xx, yy, zz, rs, r2;
    int    ix, iy, iz, jnz, nnz, nrays;
    int    ftm = 0, status = 0;

    int xcent = (int)origin[0];
    int ycent = (int)origin[1];
    int zcent = (int)origin[2];

    int nx = (int)volsize[0];
    int ny = (int)volsize[1];
    int nz = (int)volsize[2];

    r2      = ri*ri;
    nnz     = 0;
    nrays    = 0;
    ptrs(1) = 1;

    for (ix = 1; ix <= nx; ix++) {
       xs  = ix-xcent;
       xx  = xs*xs;
       for ( iy = 1; iy <= ny; iy++ ) {
           ys = iy-ycent;
           yy = ys*ys;
           jnz = 0;

           ftm = 1;
           // not the most efficient implementation
           for (iz = 1; iz <= nz; iz++) {
               zs = iz-zcent;
               zz = zs*zs;
               rs = xx + yy + zz;
               if (rs <= r2) {
                  jnz++;
                  nnz++;
                  sphere(nnz) = cube(iz, iy, ix);

                  //  record the coordinates of the first nonzero ===
                  if (ftm) {
                     nrays++;
                     cord(1,nrays) = iz;
                     cord(2,nrays) = iy;
                     cord(3,nrays) = ix;
                     ftm = 0;
                  }
               }
            } // end for (iz..)
            if (jnz > 0) {
                ptrs(nrays+1) = ptrs(nrays) + jnz;
            }  // endif (jnz)
       } // end for iy
    } // end for ix
    if (nnz != nnz0) status = -1;
    return status;
}

int ChaoProjector::sph2cb	(	float *	sphere,
		Vec3i	volsize,
		int	nray,
		int	ri,
		int	nnz0,
		int *	ptrs,
		int *	cord,
		float *	cube
	)			const [private]

Definition at line 1346 of file projector.cpp.

References cord, cube, nnz, nx, ny, ptrs, sphere, and status.

Referenced by backproject3d().

{
    int       status=0;
    int       r2, i, j, ix, iy, iz,  nnz;

    int nx = (int)volsize[0];
    int ny = (int)volsize[1];
    // int nz = (int)volsize[2];

    r2      = ri*ri;
    nnz     = 0;
    ptrs(1) = 1;

    // no need to initialize
    // for (i = 0; i<nx*ny*nz; i++) cube[i]=0.0;

    nnz = 0;
    for (j = 1; j <= nrays; j++) {
       iz = cord(1,j);
       iy = cord(2,j);
       ix = cord(3,j);
       for (i = ptrs(j); i<=ptrs(j+1)-1; i++, iz++) {
           nnz++;
           cube(iz,iy,ix) = sphere(nnz);
       }
    }
    if (nnz != nnz0) status = -1;
    return status;
}

int ChaoProjector::fwdpj3	(	Vec3i	volsize,
		int	nray,
		int	nnz,
		float *	dm,
		Vec3i	origin,
		int	ri,
		int *	ptrs,
		int *	cord,
		float *	x,
		float *	y
	)			const [private]

Definition at line 1381 of file projector.cpp.

References cord, dm, ifix(), nx, ptrs, status, x, and y.

Referenced by project3d().

{
    /*
        purpose:  y <--- proj(x)
        input  :  volsize  the size (nx,ny,nz) of the volume
                  nrays    number of rays within the compact spherical
                           representation
                  nnz      number of voxels within the sphere
                  dm       an array of size 9 storing transformation
                           associated with the projection direction
                  origin   coordinates of the center of the volume
                  ri       radius of the sphere
                  ptrs     the beginning address of each ray
                  cord     the coordinates of the first point in each ray
                  x        3d input volume
                  y        2d output image
    */

    int    iqx, iqy, i, j, xc, yc, zc;
    float  ct, dipx, dipy, dipx1m, dipy1m, xb, yb, dm1, dm4;
    int    status = 0;

    int xcent = origin[0];
    int ycent = origin[1];
    int zcent = origin[2];

    int nx = volsize[0];

    dm1 = dm(1);
    dm4 = dm(4);

    if ( nx > 2*ri ) {
        for (i = 1; i <= nrays; i++) {
            zc = cord(1,i)-zcent;
            yc = cord(2,i)-ycent;
            xc = cord(3,i)-xcent;

            xb = zc*dm(1)+yc*dm(2)+xc*dm(3) + xcent;
            yb = zc*dm(4)+yc*dm(5)+xc*dm(6) + ycent;

            for (j = ptrs(i); j< ptrs(i+1); j++) {
               iqx = ifix(xb);
               iqy = ifix(yb);

               ct   = x(j);
               dipx =  xb - (float)(iqx);
               dipy = (yb - (float)(iqy)) * ct;

               dipy1m = ct - dipy;
               dipx1m = 1.0f - dipx;

               y(iqx  ,iqy)   = y(iqx  ,iqy)   + dipx1m*dipy1m;
               y(iqx+1,iqy)   = y(iqx+1,iqy)   + dipx*dipy1m;
               y(iqx+1,iqy+1) = y(iqx+1,iqy+1) + dipx*dipy;
               y(iqx  ,iqy+1) = y(iqx  ,iqy+1) + dipx1m*dipy;

               xb += dm1;
               yb += dm4;
           }
        }
    }
    else {
        fprintf(stderr, " nx must be greater than 2*ri\n");
        exit(1);
    }
    return status;
}

int ChaoProjector::bckpj3	(	Vec3i	volsize,
		int	nray,
		int	nnz,
		float *	dm,
		Vec3i	origin,
		int	ri,
		int *	ptrs,
		int *	cord,
		float *	x,
		float *	y
	)			const [private]

Definition at line 1457 of file projector.cpp.

References cord, dm, ifix(), nx, ptrs, status, x, and y.

Referenced by backproject3d().

{
    int       i, j, iqx,iqy, xc, yc, zc;
    float     xb, yb, dx, dy, dx1m, dy1m, dxdy;
    int       status = 0;

    int xcent = origin[0];
    int ycent = origin[1];
    int zcent = origin[2];

    int nx = volsize[0];

    if ( nx > 2*ri) {
        for (i = 1; i <= nrays; i++) {
            zc = cord(1,i) - zcent;
            yc = cord(2,i) - ycent;
            xc = cord(3,i) - xcent;

            xb = zc*dm(1)+yc*dm(2)+xc*dm(3) + xcent;
            yb = zc*dm(4)+yc*dm(5)+xc*dm(6) + ycent;

            for (j = ptrs(i); j <ptrs(i+1); j++) {
                iqx = ifix((float)(xb));
                iqy = ifix((float)(yb));

                dx = xb - (float)(iqx);
                dy = yb - (float)(iqy);
                dx1m = 1.0f - dx;
                dy1m = 1.0f - dy;
                dxdy = dx*dy;
/*
c               y(j) = y(j) + dx1m*dy1m*x(iqx  , iqy)
c     &                     + dx1m*dy  *x(iqx  , iqy+1)
c     &                     + dx  *dy1m*x(iqx+1, iqy)
c     &                     + dx  *dy  *x(iqx+1, iqy+1)
c
c              --- faster version of the above commented out
c                  code (derived by summing the following table
c                  of coefficients along  the colunms) ---
c
c                        1         dx        dy      dxdy
c                     ------   --------  --------  -------
c                      x(i,j)   -x(i,j)   -x(i,j)    x(i,j)
c                                        x(i,j+1) -x(i,j+1)
c                              x(i+1,j)           -x(i+1,j)
c                                                x(i+1,j+1)
c
*/
               y(j) += x(iqx,iqy)
                    +  dx*(-x(iqx,iqy)+x(iqx+1,iqy))
                    +  dy*(-x(iqx,iqy)+x(iqx,iqy+1))
                    +  dxdy*( x(iqx,iqy) - x(iqx,iqy+1)
                             -x(iqx+1,iqy) + x(iqx+1,iqy+1) );

               xb += dm(1);
               yb += dm(4);
            } // end for j
        } // end for i
     }
    else {
        fprintf(stderr, "bckpj3: nx must be greater than 2*ri\n");
    }

    return status;
}

int ChaoProjector::ifix

(

float

a

)

const [private]

Definition at line 1530 of file projector.cpp.

Referenced by bckpj3(), and fwdpj3().

{
    int ia;

    if (a>=0) {
       ia = (int)floor(a);
    }
    else {
       ia = (int)ceil(a);
    }
    return ia;
}

void ChaoProjector::setdm	(	vector< float >	anglelist,
		string const	angletype,
		float *	dm
	)			const [private]

Definition at line 1547 of file projector.cpp.

References anglelist, dgr_to_rad, dm, phi, and theta.

Referenced by backproject3d(), and project3d().

{ // convert Euler angles to transformations, dm is an 9 by nangles array

        float  psi, theta, phi;
        double cthe, sthe, cpsi, spsi, cphi, sphi;
        int    j;

        int nangles = anglelist.size() / 3;

        // now convert all angles
        for (j = 1; j <= nangles; j++) {
                phi   = static_cast<float>(anglelist(1,j)*dgr_to_rad);
                theta = static_cast<float>(anglelist(2,j)*dgr_to_rad);
                psi   = static_cast<float>(anglelist(3,j)*dgr_to_rad);

                //              cout << phi << " " << theta << " " << psi << endl;
                cthe  = cos(theta);
                sthe  = sin(theta);
                cpsi  = cos(psi);
                spsi  = sin(psi);
                cphi  = cos(phi);
                sphi  = sin(phi);

                dm(1,j)=static_cast<float>(cphi*cthe*cpsi-sphi*spsi);
                dm(2,j)=static_cast<float>(sphi*cthe*cpsi+cphi*spsi);
                dm(3,j)=static_cast<float>(-sthe*cpsi);
                dm(4,j)=static_cast<float>(-cphi*cthe*spsi-sphi*cpsi);
                dm(5,j)=static_cast<float>(-sphi*cthe*spsi+cphi*cpsi);
                dm(6,j)=static_cast<float>(sthe*spsi);
                dm(7,j)=static_cast<float>(sthe*cphi);
                dm(8,j)=static_cast<float>(sthe*sphi);
                dm(9,j)=static_cast<float>(cthe);
        }
}

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The documentation for this class was generated from the following files:

• projector.h
• projector.cpp