real_T bisection2(real_T a, real_T b, real_T tol)
{
real_T p;
const mxArray *y;
static const int32_T iv0[2] = { 1, 16 };
const mxArray *m0;
static const char_T cv0[16] = { 'W', 'r', 'o', 'n', 'g', ' ', 'c', 'h', 'o',
'i', 'c', 'e', ' ', 'b', 'r', 'o' };
real_T err;
/* provide the equation you want to solve with R.H.S = 0 form. */
/* Write the L.H.S by using inline function */
/* Give initial guesses. */
/* Solves it by method of bisection. */
/* A very simple code and very handy! */
if ((muDoubleScalarPower(a - 1.5, 3.0) + 10.0) * (muDoubleScalarPower(b - 1.5,
3.0) + 10.0) > 0.0) {
EMLRTPUSHRTSTACK(&emlrtRSI);
EMLRTPUSHRTSTACK(&b_emlrtRSI);
y = NULL;
m0 = mxCreateCharArray(2, iv0);
emlrtInitCharArray(16, m0, cv0);
emlrtAssign(&y, m0);
error(y, &emlrtMCI);
EMLRTPOPRTSTACK(&b_emlrtRSI);
EMLRTPOPRTSTACK(&emlrtRSI);
} else {
p = (a + b) / 2.0;
err = muDoubleScalarAbs(b - a);
while (err >= tol) {
if ((muDoubleScalarPower(a - 1.5, 3.0) + 10.0) * (muDoubleScalarPower(p -
1.5, 3.0) + 10.0) < 0.0) {
b = p;
} else {
a = p;
}
p = (a + b) / 2.0;
err = muDoubleScalarAbs(b - a);
emlrtBreakCheck();
}
}
return p;
}
void drr_SK_Simplified(const emxArray_boolean_T *voxel_data, const real_T
voxel_size_mm[3], const real_T detector_dimensions[2], real_T pixel_size_mm,
const real_T voxel_corner_min[3], const real_T T_carm[16], emxArray_real_T
*projection)
{
int32_T ix;
int32_T i;
uint32_T voxDim[3];
real_T voxPlanes__max[3];
real_T source[3];
real_T pixel_size_mmel__hn[3];
real_T pixel_size_mmel__wn[3];
real_T corner[3];
real_T b_ix;
real_T iy;
int32_T ih;
int32_T iw;
real_T tnext[3];
real_T tstep[3];
real_T b_voxPlanes__max[3];
real_T ray_source2pixel[3];
real_T b_ray_source2pixel[3];
real_T pixel_point_mm[3];
real_T t_plane_min[3];
real_T t_plane_max[3];
boolean_T exitg8;
boolean_T exitg7;
real_T iz;
boolean_T exitg6;
real_T t_larger[4];
boolean_T exitg5;
boolean_T exitg4;
boolean_T exitg3;
real_T t_smaller[4];
real_T temp;
int32_T itmp;
boolean_T exitg2;
real_T tmax;
boolean_T exitg1;
real_T tx;
real_T ty;
real_T tz;
/* function [projection] = drr (voxel_data, voxel_size_mm, detector_dimensions, pixel_size_mm, isocenter_mm, cbct_angles_deg) */
/* Creates a 2D projection at each cbct_angle of voxel_data. the projection */
/* axis is defined by the isocenter to which the source and center of */
/* the detector are aligned. This simulation assumes standard Cone Beam CT */
/* geometry (source to isocenter distance is 100 cm and source to detector */
/* distance is 150cm). */
/* */
/* voxel_data: must be a 3 dimensional matrix (typically of CT data) */
/* voxel_size_mm: a 3 element vector listing the size (in mm) of the voxels */
/* along each dimension */
/* detector_dimension: a 2 element vector listing the dimensions (number of */
/* pixels) in each dimension (u,v) */
/* pixel_size_mm: a number defining the height and width of each pixel */
/* (assumes square pixel) */
/* isocenter_mm: a 3 element vector pointing from the origin (corner) of the */
/* matrix element(1,1,1) to the isocenter */
/* cbct_angles_deg: a list of angles to generate projections */
/* */
/* Retrun Variable */
/* projection: a 3D matrix with the 3rd dimension representing the angle of */
/* roatation */
/* */
/* { */
/* Author: Michael M. Folkerts [email protected] */
/* Institution: UCSD Physics, UTSW Radiation Oncology */
/* Updated: 2014-July. */
/* Notes: Siddon's Incremental algorithm | modified to read in 3D matlab matrix | Simplified Input | No guarantees!! */
/* */
/* References: */
/* R.L. Siddon, */
/* "Fast calculation of the exact radiological path for a three-dimensional CT */
/* array," Medical Physics 12, 252-255 (1985). */
/* */
/* F. Jacobs, E. Sundermann, B. De Sutter, M. Christiaens and I. Lemahieu, */
/* "A fast algorithm to calculate the exact radiological path through a pixel_size_mmel or voxel space," */
/* Journal of Computing and Information Technology 6, 89-94 (1998). */
/* */
/* G. Han, Z. Liang and J. You, */
/* "A fast ray tracing technique for TCT and ECT studies," */
/* IEEE Medical Imaging Conference 1999. */
/* } */
/* if(0) */
/* voxel_data = OUTPUTgrid; */
/* voxel_size_mm = voxel_size; */
/* detector_dimensions = detector_dimension; */
/* pixel_size_mm = pixel_size; */
/* isocenter_mm = isocenter; */
/* T_carm: Transformation matrix of C-arm (that is set at the middle of */
/* detector & source) with respect to Voxel coordinates */
/* tic; */
/* this will verify the size: */
if (eml_ndims_varsized(*(int32_T (*)[3])voxel_data->size) != 3) {
EMLRTPUSHRTSTACK(&emlrtRSI);
error();
EMLRTPOPRTSTACK(&emlrtRSI);
}
/* constants: */
/* .0001; */
/* .0001; */
/* sounce to imager(detector) distance */
/* source to axis distance %% RRI set the coordinate at the middle between source and the detector */
/* initialize memory for speed: */
ix = projection->size[0] * projection->size[1];
projection->size[0] = (int32_T)emlrtIntegerCheckR2009b
(emlrtNonNegativeCheckR2009b(detector_dimensions[0], &b_emlrtDCI), &emlrtDCI);
projection->size[1] = (int32_T)emlrtIntegerCheckR2009b
(emlrtNonNegativeCheckR2009b(detector_dimensions[1], &d_emlrtDCI),
&c_emlrtDCI);
emxEnsureCapacity((emxArray__common *)projection, ix, (int32_T)sizeof(real_T),
&emlrtRTEI);
i = (int32_T)emlrtIntegerCheckR2009b(emlrtNonNegativeCheckR2009b
(detector_dimensions[0], &f_emlrtDCI), &e_emlrtDCI) * (int32_T)
emlrtIntegerCheckR2009b(emlrtNonNegativeCheckR2009b(detector_dimensions[1],
&h_emlrtDCI), &g_emlrtDCI) - 1;
for (ix = 0; ix <= i; ix++) {
projection->data[ix] = 0.0;
}
for (ix = 0; ix < 3; ix++) {
voxDim[ix] = (uint32_T)voxel_data->size[ix];
}
/* [size(voxel_data,1), size(voxel_data,2), size(voxel_data,3)]; */
/* difine voxel boundaries: */
/* vector from origin to source */
/* vector from origin to CENTER of detector */
/* define pixel_size_mmel vectors: */
/* define upper lefthand corner of detector: */
for (i = 0; i < 3; i++) {
voxPlanes__max[i] = voxel_corner_min[i] + voxel_size_mm[i] * (real_T)
voxDim[i];
/* define up: */
/* up = [0,0,1]; */
/* width of projection image */
/* height of projection image */
/* direction from the detector to the source */
/* end initialization timer: */
/* init_time = toc */
/* start tracing timer: */
/* tic; */
source[i] = 550.0 * T_carm[4 + i] + T_carm[12 + i];
b_ix = -pixel_size_mm * T_carm[i];
/* length of pixel_size_mmel */
iy = pixel_size_mm * T_carm[8 + i];
/* vector pointing left, parallel to detector */
/* define incremental vectors: */
pixel_size_mmel__hn[i] = -iy;
pixel_size_mmel__wn[i] = -b_ix;
corner[i] = (-550.0 * T_carm[4 + i] + T_carm[12 + i]) +
(detector_dimensions[0] * b_ix + detector_dimensions[1] * iy) / 2.0;
}
emlrtForLoopVectorCheckR2011b(1.0, 1.0, detector_dimensions[0], mxDOUBLE_CLASS,
(int32_T)detector_dimensions[0], &d_emlrtRTEI,
&emlrtContextGlobal, 0);
ih = 0;
while (ih <= (int32_T)detector_dimensions[0] - 1) {
/* if(mod(ih,100)==0),fprintf('height:\t%i...\n',ih);end */
emlrtForLoopVectorCheckR2011b(1.0, 1.0, detector_dimensions[1],
mxDOUBLE_CLASS, (int32_T)detector_dimensions[1], &c_emlrtRTEI,
&emlrtContextGlobal, 0);
iw = 0;
while (iw <= (int32_T)detector_dimensions[1] - 1) {
/* ray to be traced */
/* find parametrized (t) voxel plane (min or max) intersections: */
/* PLANE = P1 + t(P2-P1) */
/* SK added */
/* t_x = (i-x1) / (x2-x1), t_y = (j-y1) / (y2-y1), t_z = (k-z1) / (z2-z1) */
for (i = 0; i < 3; i++) {
b_ix = (corner[i] + ((1.0 + (real_T)ih) - 1.0) * pixel_size_mmel__hn[i])
+ ((1.0 + (real_T)iw) - 1.0) * pixel_size_mmel__wn[i];
/* ray end point */
iy = b_ix - source[i];
tnext[i] = voxel_corner_min[i] - source[i];
tstep[i] = iy + 2.2250738585072014E-308;
b_voxPlanes__max[i] = voxPlanes__max[i] - source[i];
ray_source2pixel[i] = iy + 2.2250738585072014E-308;
b_ray_source2pixel[i] = iy;
pixel_point_mm[i] = b_ix;
}
rdivide(tnext, tstep, t_plane_min);
rdivide(b_voxPlanes__max, ray_source2pixel, t_plane_max);
/* compute (parametric) intersection values */
/* tmin = max { min{tx(0), tx(Nx)}, min{ty(0), ty(Ny)], min{tz(0), tz(Nz)}, 0.0 } */
/* tmax = min { max{tx(0), tx(Nx)}, max{ty(0), ty(Ny)], max{tz(0), tz(Nz)}, 1.0 } */
/* t_larger = [ max([t_plane_min(1), t_plane_max(1)]), max([t_plane_min(2), t_plane_max(2)]), max([t_plane_min(3), t_plane_max(3)]), 1.0 ]; */
/* t_smaller = [ min([t_plane_min(1), t_plane_max(1)]), min([t_plane_min(2), t_plane_max(2)]), min([t_plane_min(3), t_plane_max(3)]), 0.0 ]; */
i = 1;
b_ix = t_plane_min[0];
if (muDoubleScalarIsNaN(t_plane_min[0])) {
ix = 2;
exitg8 = FALSE;
while ((exitg8 == 0U) && (ix < 3)) {
i = 2;
if (!muDoubleScalarIsNaN(t_plane_max[0])) {
b_ix = t_plane_max[0];
exitg8 = TRUE;
} else {
ix = 3;
}
}
}
if ((i < 2) && (t_plane_max[0] > b_ix)) {
b_ix = t_plane_max[0];
}
i = 1;
iy = t_plane_min[1];
if (muDoubleScalarIsNaN(t_plane_min[1])) {
ix = 2;
exitg7 = FALSE;
while ((exitg7 == 0U) && (ix < 3)) {
i = 2;
if (!muDoubleScalarIsNaN(t_plane_max[1])) {
iy = t_plane_max[1];
exitg7 = TRUE;
} else {
ix = 3;
}
}
}
if ((i < 2) && (t_plane_max[1] > iy)) {
iy = t_plane_max[1];
}
i = 1;
iz = t_plane_min[2];
if (muDoubleScalarIsNaN(t_plane_min[2])) {
ix = 2;
exitg6 = FALSE;
while ((exitg6 == 0U) && (ix < 3)) {
i = 2;
if (!muDoubleScalarIsNaN(t_plane_max[2])) {
iz = t_plane_max[2];
exitg6 = TRUE;
} else {
ix = 3;
}
}
}
if ((i < 2) && (t_plane_max[2] > iz)) {
iz = t_plane_max[2];
}
t_larger[0] = b_ix;
t_larger[1] = iy;
t_larger[2] = iz;
t_larger[3] = 1.0;
i = 1;
b_ix = t_plane_min[0];
if (muDoubleScalarIsNaN(t_plane_min[0])) {
ix = 2;
exitg5 = FALSE;
while ((exitg5 == 0U) && (ix < 3)) {
i = 2;
if (!muDoubleScalarIsNaN(t_plane_max[0])) {
b_ix = t_plane_max[0];
exitg5 = TRUE;
} else {
ix = 3;
}
}
}
if ((i < 2) && (t_plane_max[0] < b_ix)) {
b_ix = t_plane_max[0];
}
i = 1;
iy = t_plane_min[1];
if (muDoubleScalarIsNaN(t_plane_min[1])) {
ix = 2;
exitg4 = FALSE;
while ((exitg4 == 0U) && (ix < 3)) {
i = 2;
if (!muDoubleScalarIsNaN(t_plane_max[1])) {
iy = t_plane_max[1];
exitg4 = TRUE;
} else {
ix = 3;
}
}
}
if ((i < 2) && (t_plane_max[1] < iy)) {
iy = t_plane_max[1];
}
i = 1;
iz = t_plane_min[2];
if (muDoubleScalarIsNaN(t_plane_min[2])) {
ix = 2;
exitg3 = FALSE;
while ((exitg3 == 0U) && (ix < 3)) {
i = 2;
if (!muDoubleScalarIsNaN(t_plane_max[2])) {
iz = t_plane_max[2];
exitg3 = TRUE;
} else {
ix = 3;
}
}
}
if ((i < 2) && (t_plane_max[2] < iz)) {
iz = t_plane_max[2];
}
t_smaller[0] = b_ix;
t_smaller[1] = iy;
t_smaller[2] = iz;
t_smaller[3] = 0.0;
i = 1;
temp = t_smaller[0];
itmp = 0;
if (muDoubleScalarIsNaN(t_smaller[0])) {
ix = 2;
exitg2 = FALSE;
while ((exitg2 == 0U) && (ix < 5)) {
i = ix;
if (!muDoubleScalarIsNaN(t_smaller[ix - 1])) {
temp = t_smaller[ix - 1];
exitg2 = TRUE;
} else {
ix++;
}
}
}
if (i < 4) {
while (i + 1 < 5) {
if (t_smaller[i] > temp) {
temp = t_smaller[i];
itmp = i;
}
i++;
}
}
i = 1;
tmax = t_larger[0];
if (muDoubleScalarIsNaN(t_larger[0])) {
ix = 2;
exitg1 = FALSE;
while ((exitg1 == 0U) && (ix < 5)) {
i = ix;
if (!muDoubleScalarIsNaN(t_larger[ix - 1])) {
tmax = t_larger[ix - 1];
exitg1 = TRUE;
} else {
ix++;
}
}
}
if (i < 4) {
while (i + 1 < 5) {
if (t_larger[i] < tmax) {
tmax = t_larger[i];
}
i++;
}
}
for (ix = 0; ix < 3; ix++) {
pixel_point_mm[ix] = (real_T)(pixel_point_mm[ix] < source[ix]) * -2.0 +
1.0;
}
if (temp < tmax) {
/* if ray intersects volume */
/* find index for each dimension: */
for (i = 0; i < 3; i++) {
b_ix = muDoubleScalarFloor((((b_ray_source2pixel[i] * temp + source[i])
- voxel_corner_min[i]) + 2.2250738585072014E-308) / voxel_size_mm[i]);
/* (parametric) intersection values... */
/* makes 0 or 1 */
tnext[i] = (voxel_corner_min[i] + ((b_ix + (pixel_point_mm[i] + 1.0) /
2.0) * voxel_size_mm[i] - source[i])) / (b_ray_source2pixel[i] +
2.2250738585072014E-308);
/* parametric value for next plane intersection */
iy = voxel_size_mm[i] / (b_ray_source2pixel[i] +
2.2250738585072014E-308);
tstep[i] = muDoubleScalarAbs(iy);
b_ray_source2pixel[i] = iy;
t_plane_min[i] = b_ix;
}
/* parametric step size */
/* address special cases... */
if (temp == t_plane_max[emlrtBoundsCheck(itmp + 1, &c_emlrtBCI) - 1]) {
/* if intersection is a "max" plane */
if (itmp + 1 == 1) {
t_plane_min[0] = (real_T)voxDim[0] - 1.0;
} else if (itmp + 1 == 2) {
t_plane_min[1] = (real_T)voxDim[1] - 2.0;
} else {
t_plane_min[2] = (real_T)voxDim[2] - 2.0;
}
tnext[itmp] = temp + tstep[itmp];
/* next plane crossing */
} else {
t_plane_min[itmp] = 0.0;
tnext[itmp] = temp + tstep[itmp];
/* next plane crossing */
}
/* voxel index values(add one for matlab): */
b_ix = t_plane_min[0] + 1.0;
iy = t_plane_min[1] + 1.0;
iz = t_plane_min[2] + 1.0;
tx = tnext[0];
ty = tnext[1];
tz = tnext[2];
i = 0;
/* uncomment to generate P-matrix: */
/* pixel_size_mmNum = 1; */
/* len = norm(ray_source2pixel); % ray length */
while ((temp + 0.0001 < tmax) && (!(b_ix * iy * iz == 0.0))) {
if ((tx < ty) && (tx < tz)) {
/* 실제 DRR을 그리지 않고, 한점이라도 지나면 해당 점에 포함시킴 */
if (voxel_data->data[((emlrtDynamicBoundsCheck((int32_T)
emlrtIntegerCheckR2009b(b_ix, &o_emlrtDCI), 1,
voxel_data->size[0], &j_emlrtBCI) + voxel_data->size[0] *
(emlrtDynamicBoundsCheck((int32_T)
emlrtIntegerCheckR2009b(iy, &p_emlrtDCI), 1,
voxel_data->size[1], &k_emlrtBCI) - 1)) + voxel_data->size[0]
* voxel_data->size[1] *
(emlrtDynamicBoundsCheck((int32_T)
emlrtIntegerCheckR2009b(iz, &q_emlrtDCI), 1, voxel_data->
size[2], &l_emlrtBCI) - 1)) - 1]) {
i = 255;
tmax = rtMinusInf;
}
temp = tx;
tx += tstep[0];
b_ix += pixel_point_mm[0];
} else if (ty < tz) {
/* 실제 DRR을 그리지 않고, 한점이라도 지나면 해당 점에 포함시킴 */
if (voxel_data->data[((emlrtDynamicBoundsCheck((int32_T)
emlrtIntegerCheckR2009b(b_ix, &l_emlrtDCI), 1,
voxel_data->size[0], &g_emlrtBCI) + voxel_data->size[0] *
(emlrtDynamicBoundsCheck((int32_T)
emlrtIntegerCheckR2009b(iy, &m_emlrtDCI), 1,
voxel_data->size[1], &h_emlrtBCI) - 1)) + voxel_data->size[0]
* voxel_data->size[1] *
(emlrtDynamicBoundsCheck((int32_T)
emlrtIntegerCheckR2009b(iz, &n_emlrtDCI), 1, voxel_data->
size[2], &i_emlrtBCI) - 1)) - 1]) {
i = 255;
tmax = rtMinusInf;
}
temp = ty;
ty += tstep[1];
iy += pixel_point_mm[1];
} else {
/* 실제 DRR을 그리지 않고, 한점이라도 지나면 해당 점에 포함시킴 */
if (voxel_data->data[((emlrtDynamicBoundsCheck((int32_T)
emlrtIntegerCheckR2009b(b_ix, &i_emlrtDCI), 1,
voxel_data->size[0], &d_emlrtBCI) + voxel_data->size[0] *
(emlrtDynamicBoundsCheck((int32_T)
emlrtIntegerCheckR2009b(iy, &j_emlrtDCI), 1,
voxel_data->size[1], &e_emlrtBCI) - 1)) + voxel_data->size[0]
* voxel_data->size[1] *
(emlrtDynamicBoundsCheck((int32_T)
emlrtIntegerCheckR2009b(iz, &k_emlrtDCI), 1, voxel_data->
size[2], &f_emlrtBCI) - 1)) - 1]) {
i = 255;
tmax = rtMinusInf;
}
temp = tz;
tz += tstep[2];
iz += pixel_point_mm[2];
}
emlrtBreakCheck();
}
/* end while */
projection->data[(emlrtDynamicBoundsCheck((int32_T)(1.0 + (real_T)ih), 1,
projection->size[0], &m_emlrtBCI) + projection->size[0] *
(emlrtDynamicBoundsCheck((int32_T)(1.0 + (real_T)iw),
1, projection->size[1], &n_emlrtBCI) - 1)) - 1] = (real_T)i;
} else {
/* if no intersections */
projection->data[(emlrtDynamicBoundsCheck((int32_T)(1.0 + (real_T)ih), 1,
projection->size[0], &emlrtBCI) + projection->size[0] *
(emlrtDynamicBoundsCheck((int32_T)(1.0 + (real_T)iw),
1, projection->size[1], &b_emlrtBCI) - 1)) - 1] = 0.0;
}
/* if intersections */
/* uncomment to generate P-matrix: */
/* rayCount = rayCount + 1; */
iw++;
emlrtBreakCheck();
}
/* width */
/* fprintf('\n'); */
ih++;
emlrtBreakCheck();
}
/* height */
/* uncomment to generate P-matrix: */
/* matrix = matrix(1:mtxCount-1,:); */
/* stop trace timer: */
/* trace_time = toc */
/* fprintf('\n') */
/* function */
/* } */
}
