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|
/*
* Project: The SPD Image correction and azimuthal regrouping
* http://forge.epn-campus.eu/projects/show/azimuthal
*
* Copyright (C) 2005-2010 European Synchrotron Radiation Facility
* Grenoble, France
*
* Principal authors: P. Boesecke (boesecke@esrf.fr)
* R. Wilcke (wilcke@esrf.fr)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* and the GNU Lesser General Public License along with this program.
* If not, see <http://www.gnu.org/licenses/>.
*/
# define ARC_VERSION "arc : V1.9 Peter Boesecke 2011-06-28"
/*+++------------------------------------------------------------------------
NAME
arc --- routines for arc and ang averaging
SYNOPSIS
# include arc.h
HISTORY
2005-10-28 V1.0 Peter Boesecke
2007-04-19 V1.2 PB -Wall compiler warnings resolved
2009-10-02 V1.3 PB arc_lfactor moved to SaxsRoutines,
Success -> 0, SaxsArc -> arc
include only ipol.h and reference.h
2010-03-05 V1.4 PB Problems averaging in a single step:
ang_sum, arc_sum: limits, steps etc. improved,
angular range limited to 360 degrees,
ang_sum: averaging in a single step possible
2010-03-19 V1.5 PB ang_limits parameter changed to use waxs_Range.
ang_range, waxs included
2010-03-20 V1.6 PB ang_limits: condition for min_angle corrected
2010-05-31 V1.7 PB update for waxs.c V1.10
2010-06-02 V1.8 PB maximum regrouping range 360_deg, splitted
in 3 ranges
2011-06-28 V1.9 PB waxs_get_transform and waxs_Transform updated
----------------------------------------------------------------------------*/
/******************************************************************************
* Include Files *
******************************************************************************/
# include "arc.h"
/******************************************************************************
* Private Constants *
******************************************************************************/
static const double arc_rad2deg = 180.0/NUM_PI;
static const double arc_radius_eps = 1e-32;
static const double arc_angle_eps = 1e-32;
static const float arc_twopi = 2.0*NUM_PI;
/******************************************************************************
* Private Definitions *
******************************************************************************/
# define CALC_DIST(A) sqrt((A[0])*(A[0])+(A[1])*(A[1]))
/******************************************************************************
* Routines *
******************************************************************************/
/*+++------------------------------------------------------------------------
NAME
ang_range
SYNOPSIS
int ang_range( int rsys, int proin, int proout,
long dim_1, long dim_2,
float off_1, float pix_1, float cen_1,
float off_2, float pix_2, float cen_2,
float dis, float wvl,
float detrot1, float detrot2, float detrot3,
WaxsCoord *Wmin, WaxsCoord *Wmax, int * pstatus);
DESCRIPTION
Returns the maximum and minimum world coordinates of the cartesian
input image in referecne system rsys. A transformation from
Saxs to Waxs or vice versa is only done if the reference system
rsys is IO_Saxs. In all other cases proin and proout are ignored.
Wmin.s_1 : Wmin_1
Wmin.s_2 : Wmin_2
Wmax.s_1 : Wmax_1
Wmax.s_2 : Wmax_2
RETURN VALUE
-1: inverse projection transformation (WAXS->SAXS)
0: no transformation
1: normal projection transformation (SAXS->WAXS)
-------------------------------------------------------------------------+*/
int ang_range( int rsys, int proin, int proout,
long dim_1, long dim_2,
float off_1, float pix_1, float cen_1,
float off_2, float pix_2, float cen_2,
float dis, float wvl,
float detrot1, float detrot2, float detrot3,
WaxsCoord *Wmin, WaxsCoord *Wmax, int * pstatus)
{
float Off_11, Off_21;
float Ps_11, Ps_21;
float f10, f20, f11, f21;
double K=1.0, rot1=0.0, rot2=0.0, rot3=0.0;
WParams I1params, I0params;
int transform=0; // no transformation
int status=0;
if (pstatus) *pstatus = status;
/* Use waxs_Transform only if reference system is Saxs and if either the
input or the output image is in Saxs projection, but not if both images
are in Saxs projection and the rotations are Zero. */
if ( (rsys==IO_Saxs)&&((proin==IO_ProSaxs)||(proout==IO_ProSaxs))
&&(!((proin==proout)&&(detrot1==0.0)&&(detrot2==0.0)&&(detrot3==0.0))) ) {
K = (double) WAVENUMBER(wvl);
rot1 = (double) detrot1;
rot2 = (double) detrot2;
rot3 = (double) detrot3;
waxs_Init ( &I1params, K, rot1, rot2, rot3 );
waxs_Init ( &I0params, K, 0.0, 0.0, 0.0 );
/* Get coordinate range */
transform=waxs_Range( &I1params, &I0params,
proin, proout,
dim_1, dim_2,
off_1, pix_1, cen_1,
off_2, pix_2, cen_2,
dis, wvl,
Wmin, Wmax, &status);
if (status) goto ang_range_error;
} else {
/* Get world coordinate range of input image */
switch (rsys) {
case IO_Saxs:
// SAXSREF(Off,Ps,O,P,C,S,W)
SAXSREF(Off_11,Ps_11,off_1,pix_1,cen_1,dis,wvl);
SAXSREF(Off_21,Ps_21,off_2,pix_2,cen_2,dis,wvl);
break;
case IO_Normal:
NORMALREF(Off_11,Ps_11,off_1,pix_1,cen_1);
NORMALREF(Off_21,Ps_21,off_2,pix_2,cen_2);
break;
default:
status=-1;
goto ang_range_error;
}
f10 = f20 = A2INDEX(ARRAYSTART+LOWERBORDER);
f11 = A2INDEX(ARRAYSTART+LOWERBORDER+dim_1);
f21 = A2INDEX(ARRAYSTART+LOWERBORDER+dim_2);
if (Wmin) {
Wmin->s_1 = WORLD(f10,Off_11,Ps_11); // W1min_1
Wmin->s_2 = WORLD(f20,Off_21,Ps_21); // W1min_2
}
if (Wmax) {
Wmax->s_1 = WORLD(f11,Off_11,Ps_11); // W1max_1
Wmax->s_2 = WORLD(f21,Off_21,Ps_21); // W1max_2
}
}
return ( transform );
ang_range_error:
if (pstatus) *pstatus = status;
return ( transform );
} // ang_range
/*+++------------------------------------------------------------------------
NAME
ang_limits
SYNOPSIS
void ang_limits( WaxsCoord Wmin, WaxsCoord Wmax,
WaxsCoord *Amin, WaxsCoord *Amax,
int * pstatus);
DESCRIPTION
Returns the maximum and minimum distances of the output image.
The returned distances are absolute values in world distances,
the angles are returned in radian.
Amin.s_1 : minimum radius
Amax.s_1 : maximum radius
Amin.s_2 : minimum angle
Amax.s_2 : maximum angle
| |
| |
G | H | I
| |
_________|_________|_________
edge4| |edge3
| |
D | E | F
| |
_________|_________|_________
edge1| |edge2
| |
A | B | C
| |
| |
RETURN VALUE
void
-------------------------------------------------------------------------+*/
void ang_limits( WaxsCoord Wmin, WaxsCoord Wmax,
WaxsCoord *Amin, WaxsCoord *Amax,
int * pstatus)
{
float edge1[2], edge2[2], edge3[2], edge4[2];
float dist1, dist2, dist3, dist4;
float min_radius, max_radius, min_angle, max_angle;
if (*pstatus) pstatus=0;
edge1[0] = Wmin.s_1; // WORLD(i10,Off_11,Ps_11);
edge1[1] = Wmin.s_2; // WORLD(i20,Off_21,Ps_21);
edge2[0] = Wmax.s_1; // WORLD(i11,Off_11,Ps_11);
edge2[1] = Wmin.s_2; // edge1[1];
edge3[0] = Wmax.s_1; // edge2[0];
edge3[1] = Wmax.s_2; // WORLD(i21,Off_21,Ps_21);
edge4[0] = Wmin.s_1; // edge1[0];
edge4[1] = Wmax.s_2; // edge3[1];
dist1 = CALC_DIST(edge1);
dist2 = CALC_DIST(edge2);
dist3 = CALC_DIST(edge3);
dist4 = CALC_DIST(edge4);
if ( 0.0 < edge1[0] ) {
// A, D, G
if ( 0.0 < edge1[1] ) {
// A
min_radius = dist1;
max_radius = dist3;
min_angle = atan2(edge2[1],edge2[0]);
max_angle = atan2(edge4[1],edge4[0]);
} else {
if ( 0.0 < edge4[1] ) {
// D
min_radius = edge1[0];
max_radius = MAX2(dist2,dist3);
min_angle = atan2(edge1[1],edge1[0]);
max_angle = atan2(edge4[1],edge4[0]);
} else {
// G
min_radius = dist4;
max_radius = dist2;
min_angle = atan2(edge1[1],edge1[0]);
max_angle = atan2(edge3[1],edge3[0]);
}
}
} else {
if ( 0.0 < edge2[0] ) {
// B, E, H
if ( 0.0 < edge2[1] ) {
// B
min_radius = edge1[1];
max_radius = MAX2(dist4,dist3);
min_angle = atan2(edge2[1],edge2[0]);
max_angle = atan2(edge1[1],edge1[0]);
} else {
if ( 0.0 < edge3[1] ) {
// E
min_radius = 0.0;
max_radius = MAX4(dist1, dist2, dist3, dist4);
min_angle = 0.0;
max_angle = arc_twopi;
} else {
// H
min_radius = -edge3[1];
max_radius = MAX2(dist1,dist2);
min_angle = atan2(edge4[1],edge4[0]);
max_angle = atan2(edge3[1],edge3[0]);
}
}
} else {
// C, F, I
if ( 0.0 < edge2[1] ) {
// C
min_radius = dist2;
max_radius = dist4;
min_angle = atan2(edge3[1],edge3[0]);
max_angle = atan2(edge1[1],edge1[0]);
} else {
if ( 0.0 < edge3[1] ) {
// F
min_radius = -edge2[0];
max_radius = MAX2(dist1,dist4);
min_angle = atan2(edge3[1],edge3[0]);
max_angle = atan2(edge2[1],edge2[0]);
} else {
// I
min_radius = dist3;
max_radius = dist1;
min_angle = atan2(edge4[1],edge4[0]);
max_angle = atan2(edge2[1],edge2[0]);
}
}
}
}
// output range of angles is [0..2*pi]
if ( max_angle<min_angle ) max_angle += arc_twopi;
if ( (min_angle<-arc_angle_eps)||(max_angle<=0.0) ) {
min_angle += arc_twopi; max_angle += arc_twopi;
}
if (Amin) {
Amin->s_1 = min_radius; // minimum radius
Amin->s_2 = min_angle; // minimum angle
}
if (Amax) {
Amax->s_1 = max_radius; // maximum radius
Amax->s_2 = max_angle; // maximum angle
}
return;
} // ang_limits
/*---------------------------------------------------------------------------
NAME
arc_sum --- Regrouping of an image from cartesian to radius/arc
SYNOPSIS
void arc_sum ( int rsys,
float * I0Data, float * E0Data,
int I0Dim_1, int I0Dim_2,
float I0Offset_1, float I0PSize_1, float I0Center_1,
float I0Offset_2, float I0PSize_2, float I0Center_2,
float I0SampleDistance, float I0WaveLength,
int I0Pro,
float I0Dummy, float I0DDummy,
float * I1Data, float * E1Data,
int I1Dim_1, int I1Dim_2,
float I1Offset_1, float I1PSize_1, float I1Center_1,
float I1Offset_2, float I1PSize_2, float I1Center_2,
float I1SampleDistance, float I1WaveLength,
float I1DetRot1, float I1DetRot2, float I1DetRot3,
int I1Pro,
float I1Dummy, float I1DDummy,
float AngleMin, float AngleMax,
float Shift_1, float Shift_2,
int vsum, int ave, int testbit, int * pstatus );
PURPOSE
Regrouping of an image radius/arc
DESCRIPTION
The routine regroupes an input image with cartesian coordinates w_1 and w_2
to an image with coordinates radius and arc. The input image is described
with Normal (Offset, Center, PSize) or Saxs coordinates (Offset, Center,
PSize, SampleDistance, WaveLength). Axis 1 of the regrouped image is the
radius, axis 2 the arc. The reference system of output axis 2 is always Normal.
The regrouping is done in the sector between AngleMin and AngleMax. If
AngleMin >= AngleMax nothing is done. AngleMax is limited to AngleMin+2*pi.
The part of the output image outside this range is left unchanged.
(w_1, w_2) -> (radius,arc)
with radius = sqrt(w_1^2+w_2^2), arc = radius*Angle and
cos(Angle)=w_1/radius, sin(Angle)=w_2/radius.
ARGUMENTS
int rsys (i) : reference system
float * I0Data (o) : output image data
float * E0Data (o) : output variance data (ignored if NULL)
int I0Dim_1, (i) :
I0Dim_2 (i) : dimensions of output data arrays
float I0Offset_1,
I0PSize_1,
I0Center_1,
I0Offset_2,
I0Center_2,
I0PSize_2 (i) : output image parameters
I0SampleDistance (i) :
I0WaveLength (i) :
I0Pro () : projection type of input image
float I0Dummy,
I0DDummy (i) : output image dummy definition
float * I1Data (i) : input image data
float * E1Data (i) : input variance data (ignored if NULL)
int I1Dim_1,
I1Dim_2 (i) : dimensions of input data arrays
float I1Offset_1,
I1PSize_1,
I1Center_1,
I1Offset_2,
I1PSize_2,
I1Center_2 (i) : input image parameters
I1SampleDistance (i) :
I1WaveLength (i) :
I1DetRot1,
I1DetRot1,
I1DetRot1 (i) : detector rotations (in radian)
I1Pro () : projection type of output image
float AngleMin,
AngleMax (i) : angular range (in rad)
float Shift_1,
Shift_2 (i) : shift of the output image along axis 1 and 2.
The shift is usually 0.
int vsum (i) : if 1, integrate output values
int ave (i) : if 1, average input values
int testbit (i) : if 1, write debug info
int *pstatus (o) : returned status value
---------------------------------------------------------------------------*/
void arc_sum ( int rsys,
float * I0Data, float * E0Data,
int I0Dim_1, int I0Dim_2,
float I0Offset_1, float I0PSize_1, float I0Center_1,
float I0Offset_2, float I0PSize_2, float I0Center_2,
float I0SampleDistance, float I0WaveLength,
int I0Pro,
float I0Dummy, float I0DDummy,
float * I1Data, float * E1Data,
int I1Dim_1, int I1Dim_2,
float I1Offset_1, float I1PSize_1, float I1Center_1,
float I1Offset_2, float I1PSize_2, float I1Center_2,
float I1SampleDistance, float I1WaveLength,
float I1DetRot1, float I1DetRot2, float I1DetRot3,
int I1Pro,
float I1Dummy, float I1DDummy,
float AngleMin, float AngleMax,
float Shift_1, float Shift_2,
int vsum, int ave, int testbit, int * pstatus )
{
float *pI0Data, *pE0Data;
float Off_10, Ps_10, Off_20, Ps_20;
float Off_11, Ps_11, Off_21, Ps_21;
float I1Value, I1Sum, I1Weight, I1ArcSum, I1ArcSumWeight;
float E1Value, E1Sum, E1Weight, E1ArcSum, E1ArcSumWeight;
double K=1.0, rot1=0.0, rot2=0.0, rot3=0.0;
WParams I1params, I0params;
float Angle, DAngle, AngleLower, AngleUpper;
float MinArc, MaxArc;
float AngleFst, AngleLst;
float MinRadius, MaxRadius, MinAngle, MaxAngle;
float W0_2Fst, W0_2Lst;
float W0_2Min, W0_2Max;
WaxsCoord W1min, W1max, A1min, A1max;
WaxsCoord W0, W1;
int transform=0;
int i_1, i_2;
int i_20, i_22;
float f_11, f_21;
float DDArc, DArc, Arc, Radius;
int NArc, iarc;
float VarDDummy=DDSET(VarDummy);
float factor;
int cnt, varcnt;
int status=0;
if (testbit) printf("arc_sum: AngleMin=% g_deg, AngleMax=% g_deg\n",
AngleMin*arc_rad2deg,AngleMax*arc_rad2deg);
/* Calculate pixel transformations */
switch (rsys) {
case IO_Normal:
if (testbit) printf("arc_sum: The reference system is NORMAL\n");
NORMALREF(Off_11,Ps_11,I1Offset_1,I1PSize_1,I1Center_1);
NORMALREF(Off_21,Ps_21,I1Offset_2,I1PSize_2,I1Center_2);
NORMALREF(Off_10,Ps_10,I0Offset_1,I0PSize_1,I0Center_1);
NORMALREF(Off_20,Ps_20,I0Offset_2,I0PSize_2,I0Center_2);
break;
case IO_Saxs:
if (testbit) printf("arc_sum: The reference system is SAXS\n");
SAXSREF(Off_11,Ps_11,I1Offset_1,I1PSize_1,I1Center_1,I1SampleDistance,I1WaveLength);
SAXSREF(Off_21,Ps_21,I1Offset_2,I1PSize_2,I1Center_2,I1SampleDistance,I1WaveLength);
SAXSREF(Off_10,Ps_10,I0Offset_1,I0PSize_1,I0Center_1,I0SampleDistance,I0WaveLength);
SAXSREF(Off_20,Ps_20,I0Offset_2,I0PSize_2,I0Center_2,I0SampleDistance,I0WaveLength);
break;
default:
fprintf(stderr,"ERROR: The reference system is neither NORMAL nor SAXS (%d)\n",rsys);
status=-1;
goto arc_sum_error;
}
/* Subtract output shift for calculation */
Off_10 = Off_10-Shift_1; Off_20 = Off_20-Shift_2;
if (testbit) {
printf("arc_sum: Off_10 = % f, Ps_10 = % f\n", Off_10,Ps_10);
printf("arc_sum: Off_20 = % f, Ps_20 = % f\n", Off_20,Ps_20);
}
/* loop over I0Data */
/*
* Calculate the number of input image pixels that will have to be averaged
* over for one output image pixel.
*
* Ps_11 and Ps_21 are the input image pixel sizes in x and y direction;
* Ps_10 is the output image pixel size in radial direction, it is set to
* be the smaller one of the input image sizes in x and y direction;
* Ps_20 is the output image pixel size in angular direction, this is an
* input parameter of the routine.
*
* The size of an "unit" pixel is therefore Ps_11 * Ps_21 (= dx * dy) in
* the input image and Ps_10 * Ps_20 (= dr * da) in the output image.
*
* However, dx * dy is the same area over the whole image, whereas dr * da is
* smaller for small values of r and bigger for big values of r.
*
* The area corresponding to dr * da at a given value of r is F = r * dr *
* da.
* Therefore, the number of input image pixels that will fit into an "unit"
* output pixel is
* N = F / (dx * dy), or because of the definition of dr
* N = r * da / MAX(dx,dy)
*
* This is therefore the number of input image pixels that will have to be
* averaged over for one output pixel. The actual value used (variable NAngle
* further below) is an overestimate of this, to make sure that all possible
* input pixels are actually taken into account.
*
* DDArc is an intermediate variable, it corresponds to the number of input
* image pixels at r = 1. It will be used to calculate NArc later.
*/
DDArc = Ps_20/(MIN2(Ps_11,Ps_21));
if (testbit) printf("arc_sum: DDArc = % g_deg\n", DDArc * arc_rad2deg);
/*
* Calculate the minimum and maximum arc values for the input image.
* The dimensions of the output image should have been adjusted with
* ang_limits
*/
transform = ang_range( rsys, I1Pro, I0Pro,
I1Dim_1, I1Dim_2,
I1Offset_1,I1PSize_1,I1Center_1,
I1Offset_2,I1PSize_2,I1Center_2,
I1SampleDistance, I1WaveLength,
I1DetRot1, I1DetRot2, I1DetRot3,
&W1min, &W1max, &status);
if (status) goto arc_sum_error;
if (testbit) {
printf("arc_sum: W1min_1=%g, W1max_1=%g\n", W1min.s_1,W1max.s_1);
printf("arc_sum: W1min_2=%g, W1max_2=%g\n", W1min.s_2,W1max.s_2);
printf("arc_sum: transform=%d\n",transform);
}
ang_limits( W1min, W1max, &A1min, &A1max, &status);
if (status) goto arc_sum_error;
if (testbit) {
printf("arc_sum: A1min.s_1=%lg , A1max.s_1=%lg\n",
A1min.s_1,A1max.s_1);
printf("arc_sum: A1min.s_2=%lg_deg, A1max.s_2=%lg_deg\n",
A1min.s_2*arc_rad2deg,A1max.s_2*arc_rad2deg);
}
MinRadius = A1min.s_1;
MaxRadius = A1max.s_1;
MinAngle = A1min.s_2 + floor(AngleMin/arc_twopi)*arc_twopi;
MaxAngle = A1max.s_2 + floor(AngleMin/arc_twopi)*arc_twopi;
// Calculate coordinate range of Arc in output image
W0_2Fst = WORLD(INDEXSTART+LOWERBORDER,Off_20,Ps_20);
W0_2Lst = WORLD(INDEXSTART+LOWERBORDER+I0Dim_2,Off_20,Ps_20);
if (W0_2Fst <= W0_2Lst) {
W0_2Min = W0_2Fst; W0_2Max = W0_2Lst;
} else {
W0_2Min = W0_2Lst; W0_2Max = W0_2Fst;
}
/* maximum range is AngleMin+2_pi*/
AngleFst = MAX2(AngleMin,MinAngle);
AngleLst = MIN2(AngleMax,MaxAngle);
if (testbit) {
printf("arc_sum: W0_2Min=%g_deg, W0_2Max=%g_deg\n",W0_2Min*arc_rad2deg,W0_2Max*arc_rad2deg);
printf("arc_sum: MinRadius=%g, MaxRadius=%g, MinAngle=%g_deg, MaxAngle=%g_deg\n",
MinRadius, MaxRadius, MinAngle*arc_rad2deg, MaxAngle*arc_rad2deg );
printf("AngleFst=%g_deg, AngleLst=%g_deg\n",
AngleFst*arc_rad2deg, AngleLst*arc_rad2deg );
}
K = (double) WAVENUMBER(I1WaveLength);
rot1 = (double) I1DetRot1;
rot2 = (double) I1DetRot2;
rot3 = (double) I1DetRot3;
waxs_Init ( &I1params, K, rot1, rot2, rot3 );
waxs_Init ( &I0params, K, 0.0, 0.0, 0.0 );
if (testbit) {
printf("I0params\n");
waxs_PrintParams ( stdout, I0params );
printf("I1params\n");
waxs_PrintParams ( stdout, I1params );
}
if (AngleFst < AngleLst) {
/* MinArc and MaxArc depend on the actual radius, i.e. on i_1 */
for (i_1=0;i_1<I0Dim_1;i_1++) {
Radius = WORLD(i_1,Off_10,Ps_10);
if ( Radius > MaxRadius || Radius < MinRadius ) continue;
if (testbit) printf("arc_sum: AngleFst=%g_deg, AngleLst=%g_deg\n",
AngleFst*arc_rad2deg, AngleLst*arc_rad2deg );
if (Radius >= 0 ) {
MinArc = MAX2(Radius*AngleFst,W0_2Min);
MaxArc = MIN2(Radius*AngleLst,W0_2Max);
} else {
MinArc = MAX2(Radius*AngleFst,W0_2Min);
MaxArc = MIN2(Radius*AngleLst,W0_2Max);
}
i_20=MAX2(0,floor(INDEX(MinArc,Off_20,Ps_20)-LOWERBORDER)); // first pixel in range
i_22=MIN2(I0Dim_2,ceil(INDEX(MaxArc,Off_20,Ps_20)-LOWERBORDER)); // first pixel after range
if (testbit>1) {
printf("arc_sum: MinArc=%g, MaxArc=%g\n",MinArc*arc_rad2deg,MaxArc*arc_rad2deg);
printf("arc_sum: i_20=%d, i_22=%d\n",i_20,i_22);
}
/* number of intervals on the arc for averaging */
NArc = MAX2(1,(int) DDArc + 1 );
DArc = Ps_20/(float) NArc;
if (testbit>1)
printf("arc_sum: %d: Radius=%g, NArc=%d, DArc=%g\n",
i_1,Radius,NArc,DArc * arc_rad2deg);
for (i_2=i_20;i_2<i_22;i_2++) {
// Calculate center of first pixel
Arc = WORLD(((float)i_2),Off_20,Ps_20);
/* averaging on the arc */
if ( Radius >= arc_radius_eps ) {
DAngle = DArc/Radius;
AngleLower = WORLD(((float)i_2+LOWERBORDER),Off_20,Ps_20)/Radius; // lower limit
AngleUpper = WORLD(((float)i_2+1+LOWERBORDER),Off_20,Ps_20)/Radius; // upper limit
// restrict integration range to [AngleFst..AngleLst];
AngleLower = MAX2(AngleFst,AngleLower);
AngleUpper = MIN2(AngleLst,AngleUpper);
} else {
DAngle = 0.0;
AngleLower = AngleFst;
AngleUpper = AngleLst;
}
if (testbit>2) {
printf("arc_sum: %d,%d: Arc=%g, MinArc=%g_deg, MaxArc=%g_deg\n",
i_1,i_2,Arc * arc_rad2deg,MinArc * arc_rad2deg,MaxArc * arc_rad2deg);
printf("arc_sum: %d,%d: AngleLower=%g_deg, AngleUpper=%g_deg\n",
i_1,i_2,AngleLower*arc_rad2deg,AngleUpper*arc_rad2deg);
}
cnt = 0;
varcnt = 0;
I1ArcSum = 0.0; I1ArcSumWeight = 0.0;
E1ArcSum = 0.0; E1ArcSumWeight = 0.0;
for (iarc = 0; iarc<NArc; iarc++) {
if ( Radius >= arc_radius_eps ) {
Angle = Arc/Radius;
W0.s_1 = Radius * cos( Angle ); // W_1
W0.s_2 = Radius * sin( Angle ); // W_2
} else {
Angle = 0.0;
W0.s_1 = 0.0; // W_1
W0.s_2 = 0.0; // W_2
}
/* transform saxs-coordinate of unrotated detector (I0params) or Waxs-
projection to saxs-coordinate of rotated detector (I1params) */
//++++++++ W1 = waxs_Transform( &I1params, &I0params, transform, W0 );
W1 = waxs_Transform( &I0params, &I1params, transform, W0 );
if (!W1.status) {
/* averaging range is [AngleFst..AngleLst] */
if ( ( Angle < AngleLower ) || ( AngleUpper < Angle ) ) {
if (testbit>3)
printf("arc_sum: iarc=%d: Angle=%g_deg not in [%g_deg..%g_deg] => continue\n",
iarc,Angle*arc_rad2deg,AngleLower*arc_rad2deg,AngleUpper*arc_rad2deg);
Arc += DArc;
continue;
}
f_11 = INDEX(W1.s_1,Off_11,Ps_11);
f_21 = INDEX(W1.s_2,Off_21,Ps_21);
if ( E0Data ) {
// V0 = V1
if ( Isum2ldwE(I1Data,E1Data,I1Dim_1,I1Dim_2,I1Dummy,I1DDummy,
f_11-0.5, f_21-0.5, f_11+0.5, f_21+0.5,
&I1Sum, &I1Weight, &E1Sum, &E1Weight) ) {
/* then do something with the data */
I1ArcSum += I1Sum;
I1ArcSumWeight += I1Weight;
if ( E1Sum >= 0.0 ) {
E1ArcSum += E1Sum;
E1ArcSumWeight += E1Weight;
varcnt++;
}
cnt++;
} /* if Isum2ldwE ... */
} else {
if ( Isum2ldw(I1Data,I1Dim_1,I1Dim_2,I1Dummy,I1DDummy,
f_11-0.5, f_21-0.5, f_11+0.5, f_21+0.5,
&I1Sum, &I1Weight) ) {
/* then do something with the data */
I1ArcSum += I1Sum;
I1ArcSumWeight += I1Weight;
cnt++;
} /* if Isum2ldw ... */
}
} // if (!W1.status)
Arc += DArc;
} /* for iarc */
if (cnt>0) {
pI0Data = ABSPTR(I0Data,I0Dim_1,I0Dim_2,i_1,i_2);
pE0Data = E0Data-I0Data+pI0Data;
/* The following factor adjusts the size of a rectangular pixel with
the size Ps_11*Ps_21 to a circular pixel with height Ps_10 and
width DArc */
factor = (DArc*Ps_10)/(Ps_11*Ps_21);
I1ArcSum *= factor; I1ArcSumWeight *= factor;
E1ArcSum *= factor; E1ArcSumWeight *= factor;
I1Value = I1ArcSum; if (ave) I1Value /= I1ArcSumWeight;
if ( E0Data && ( varcnt==cnt ) ) {
E1Value = E1ArcSum;
if (ave) E1Value /= E1ArcSumWeight*E1ArcSumWeight;
/* Take into account that the data was averaged in a sector */
} else E1Value = -1.0;
if (vsum) {
/* Multiply with number of covered pixels */
factor = I1ArcSumWeight;
I1Value *= I1ArcSumWeight;
if ( E1Value>=0 ) E1Value *= I1ArcSumWeight*I1ArcSumWeight;
}
UPDATE( *pI0Data, I1Value, I0Dummy, I0DDummy );
if ( E0Data && ( E1Value>=0.0 ) ) {
UPDATE( *pE0Data, E1Value, VarDummy, VarDDummy );
}
}
/* end angular averaging */
} /* for i_2 ... */
} /* for i_1 ... */
} /* if (AngleFst < AngleLst) */
if (pstatus) *pstatus = status;
return;
arc_sum_error:
if (pstatus) *pstatus = status;
return;
} /* arc_sum */
/*---------------------------------------------------------------------------
NAME
ang_sum --- Regrouping of an image from cartesian to polar coordinates
PURPOSE
Regrouping of an image radius/arc
DESCRIPTION
The routine regroupes an input image with cartesian coordinates w_1 and w_2
to an image with polar coordinates. The input image is described with Normal
coordinates (Offset, Center, PSize) or Saxs coordinates (Offset, Center,
PSize, SampleDistance, WaveLength). Axis 1 of the regrouped image is the
radius, axis 2 the angle. The reference system of output axis 2 is always Normal.
The regrouping is done in the sector between AngleMin and AngleMax. If
AngleMin >= AngleMax nothing is done. AngleMax is limited to AngleMin+2*pi.
The part of the output image outside this range is left unchanged.
(w_1, w_2) -> (radius,angle)
with radius = sqrt(w_1^2+w_2^2) and
cos(Angle)=w_1/radius, sin(Angle)=w_2/radius.
SYNOPSIS
void ang_sum ( int rsys,
float * I0Data, float * E0Data,
int I0Dim_1, int I0Dim_2,
float I0Offset_1, float I0PSize_1, float I0Center_1,
float I0Offset_2, float I0PSize_2, float I0Center_2,
float I0SampleDistance, float I0WaveLength,
int I0Pro,
float I0Dummy, float I0DDummy,
float * I1Data, float * E1Data,
int I1Dim_1, int I1Dim_2,
float I1Offset_1, float I1PSize_1, float I1Center_1,
float I1Offset_2, float I1PSize_2, float I1Center_2,
float I1SampleDistance, float I1WaveLength,
float I1DetRot1, float I1DetRot2, float I1DetRot3,
int I1Pro,
float I1Dummy, float I1DDummy,
float AngleMin, float AngleMax,
float Shift_1, float Shift_2,
int vsum, int ave, int testbit, int * pstatus )
ARGUMENTS
int rsys (i) : reference system
float * I0Data (o) : output image data
float * E0Data (o) : output variance data (ignored if NULL)
int I0Dim_1, (i) :
I0Dim_2 (i) : dimensions of output data arrays
float I0Offset_1,
I0PSize_1,
I0Center_1,
I0Offset_2,
I0Center_2,
I0PSize_2 (i) : output image parameters
I0SampleDistance (i) :
I0WaveLength (i) :
I0Pro () : projection type of input image
float I0Dummy,
I0DDummy (i) : output image dummy definition
float * I1Data (i) : input image data
float * E1Data (i) : input variance data (ignored if NULL)
int I1Dim_1,
I1Dim_2 (i) : dimensions of input data arrays
float I1Offset_1,
I1PSize_1,
I1Center_1,
I1Offset_2,
I1PSize_2,
I1Center_2 (i) : input image parameters
I1SampleDistance (i) :
I1WaveLength (i) :
I1DetRot1,
I1DetRot1,
I1DetRot1 (i) : detector rotations (in radian)
I1Pro () : projection type of output image
float AngleMin,
AngleMax (i) : angular range (in rad)
float Shift_1,
Shift_2 (i) : shift of the output image along axis 1 and 2.
The shift is usually 0.
int vsum (i) : if 1, integrate output values
int ave (i) : if 1, average input values
int testbit (i) : if 1, write debug info
int *pstatus (o) : returned status value
---------------------------------------------------------------------------*/
void ang_sum ( int rsys,
float * I0Data, float * E0Data,
int I0Dim_1, int I0Dim_2,
float I0Offset_1, float I0PSize_1, float I0Center_1,
float I0Offset_2, float I0PSize_2, float I0Center_2,
float I0SampleDistance, float I0WaveLength,
int I0Pro,
float I0Dummy, float I0DDummy,
float * I1Data, float * E1Data,
int I1Dim_1, int I1Dim_2,
float I1Offset_1, float I1PSize_1, float I1Center_1,
float I1Offset_2, float I1PSize_2, float I1Center_2,
float I1SampleDistance, float I1WaveLength,
float I1DetRot1, float I1DetRot2, float I1DetRot3,
int I1Pro,
float I1Dummy, float I1DDummy,
float AngleMin, float AngleMax,
float Shift_1, float Shift_2,
int vsum, int ave, int testbit, int * pstatus )
{
float *pI0Data, *pE0Data;
float Off_10, Ps_10, Off_20, Ps_20;
float Off_11, Ps_11, Off_21, Ps_21;
float I1Value, I1Sum, I1Weight, I1CircleSum, I1CircleSumWeight;
float E1Value, E1Sum, E1Weight, E1CircleSum, E1CircleSumWeight;
double K=1.0, rot1=0.0, rot2=0.0, rot3=0.0;
WParams I1params, I0params;
int i_1, i_2;
int i_10, i_11, i_20, i_22;
float f_11, f_21;
float DDAngle, DAngle, Angle, Radius;
float AngleLower, AngleUpper;
float angle, AngleFst, AngleLst;
int NAngle, iangle, ianglefst, ianglelst;
# define N_RANGES 3
float Fst[N_RANGES], Lst[N_RANGES];
int range;
float MinRadius, MaxRadius, MinAngle, MaxAngle;
WaxsCoord W1min, W1max, A1min, A1max;
WaxsCoord W0, W1;
int transform=0;
float VarDDummy=DDSET(VarDummy);
float factor;
int cnt, varcnt;
int status=0;
/* restrict range to 2 pi */
AngleMax = MIN2(AngleMax,AngleMin+arc_twopi);
if (testbit) {
printf("ang_sum: AngleMin=% g_deg, AngleMax=% g_deg\n",
AngleMin*arc_rad2deg,AngleMax*arc_rad2deg);
}
/* Calculate pixel transformations */
switch (rsys) {
case IO_Normal:
if (testbit) printf("ang_sum: The reference system is NORMAL\n");
NORMALREF(Off_11,Ps_11,I1Offset_1,I1PSize_1,I1Center_1);
NORMALREF(Off_21,Ps_21,I1Offset_2,I1PSize_2,I1Center_2);
NORMALREF(Off_10,Ps_10,I0Offset_1,I0PSize_1,I0Center_1);
NORMALREF(Off_20,Ps_20,I0Offset_2,I0PSize_2,I0Center_2);
break;
case IO_Saxs:
if (testbit) printf("ang_sum: The radial reference system is SAXS, the angular NORMAL\n");
SAXSREF(Off_11,Ps_11,I1Offset_1,I1PSize_1,I1Center_1,I1SampleDistance,I1WaveLength);
SAXSREF(Off_21,Ps_21,I1Offset_2,I1PSize_2,I1Center_2,I1SampleDistance,I1WaveLength);
SAXSREF(Off_10,Ps_10,I0Offset_1,I0PSize_1,I0Center_1,I0SampleDistance,I0WaveLength);
NORMALREF(Off_20,Ps_20,I0Offset_2,I0PSize_2,I0Center_2); // Angle reference is NORMAL
break;
default:
fprintf(stderr,"ERROR: The reference system is neither NORMAL nor SAXS (%d)\n",rsys);
status=-1;
goto ang_sum_error;
}
/* Subtract output shift for calculation */
Off_10 = Off_10-Shift_1; Off_20 = Off_20-Shift_2;
if (testbit) {
printf("ang_sum: Off_10 = % f, Ps_10 = % f\n", Off_10,Ps_10);
printf("ang_sum: Off_20 = % f, Ps_20 = % f\n", Off_20,Ps_20);
}
/*
* Calculate the minimum and maximum arc values for the input image.
* The dimensions of the output image should have been adjusted with
* ang_limits
*/
transform = ang_range( rsys, I1Pro, I0Pro,
I1Dim_1, I1Dim_2,
I1Offset_1,I1PSize_1,I1Center_1,
I1Offset_2,I1PSize_2,I1Center_2,
I1SampleDistance, I1WaveLength,
I1DetRot1, I1DetRot2, I1DetRot3,
&W1min, &W1max, &status);
if (status) goto ang_sum_error;
if (testbit) {
printf("ang_sum: W1min_1=%g, W1max_1=%g\n", W1min.s_1,W1max.s_1);
printf("ang_sum: W1min_2=%g, W1max_2=%g\n", W1min.s_2,W1max.s_2);
printf("ang_sum: transform=%d\n",transform);
}
ang_limits( W1min, W1max, &A1min, &A1max, &status);
if (status) goto ang_sum_error;
if (testbit) {
printf("ang_sum: A1min.s_1=%lg , A1max.s_1=%lg\n",
A1min.s_1,A1max.s_1);
printf("ang_sum: A1min.s_2=%lg_deg, A1max.s_2=%lg_deg\n",
A1min.s_2*arc_rad2deg,A1max.s_2*arc_rad2deg);
}
MinRadius = A1min.s_1;
MaxRadius = A1max.s_1;
MinAngle = A1min.s_2 + floor(AngleMin/arc_twopi)*arc_twopi;
MaxAngle = A1max.s_2 + floor(AngleMin/arc_twopi)*arc_twopi;
if (testbit) {
printf("ang_sum: MinRadius=%g, MaxRadius=%g, MinAngle=%g_deg, MaxAngle=%g_deg\n",
MinRadius, MaxRadius, MinAngle*arc_rad2deg, MaxAngle*arc_rad2deg );
}
/* loop over I0Data */
DDAngle = Ps_20/(MIN2(Ps_11,Ps_21));
if (testbit) printf("ang_sum: DDAngle = % g_deg/m\n",
DDAngle * arc_rad2deg);
K = (double) WAVENUMBER(I1WaveLength);
rot1 = (double) I1DetRot1;
rot2 = (double) I1DetRot2;
rot3 = (double) I1DetRot3;
waxs_Init ( &I1params, K, rot1, rot2, rot3 );
waxs_Init ( &I0params, K, 0.0, 0.0, 0.0 );
if (testbit) {
waxs_PrintParams ( stdout, I1params );
}
// REGROUPING BEGIN {
/* Parameters
Ranges:
Output: AngleMin, AngleMax=MIN2(AngleMin+2_pi,AngleMax)
[AngleMin..AngleMax]
Range1: [AngleFst1=AngleMin..AngleLst1=MIN2(AngleMax,MaxAngle-2_pi)
Range2: [AngleFst2=MAX2(AngleMin,MinAngle)..AngleLst2=MIN2(AngleMax,MaxAngle)]
*/
/* maximum range is AngleMin .. AngleMax */
Fst[0] = MAX2(AngleMin,MinAngle);
Lst[0] = MIN2(AngleMax,MaxAngle);
/* 2nd range, if MaxAngle > AngleMax */
Fst[1] = AngleMin;
Lst[1] = MIN2(Fst[0],MaxAngle-arc_twopi);
/* 3rd range, if MaxAngle > AngleMax */
Fst[2] = MAX2(Lst[0],MinAngle+arc_twopi);
Lst[2] = AngleMax;
for (range=0;range<N_RANGES;range++) {
AngleFst = Fst[range];
AngleLst = Lst[range];
if (testbit) {
printf("ang_sum: AngleFst=%g_deg, AngleLst=%g_deg\n",
AngleFst*arc_rad2deg, AngleLst*arc_rad2deg );
}
if (AngleFst < AngleLst) {
// calculate indices of pixel center from indices of lower and upper edges
i_10=MAX2(0,floor(INDEX(MinRadius,Off_10,Ps_10)-LOWERBORDER+0.5));
i_11=MIN2(I0Dim_1,ceil(INDEX(MaxRadius,Off_10,Ps_10)-LOWERBORDER+0.5));
// calculate indices of pixel center from indices of lower and upper edges
i_20=MAX2(0,floor(INDEX(AngleFst,Off_20,Ps_20)-LOWERBORDER)); // first pixel in range
i_22=MIN2(I0Dim_2,ceil(INDEX(AngleLst,Off_20,Ps_20)-LOWERBORDER)); // first pixel after range
if (testbit>1) {
printf("ang_sum: i_10=%d, i_11=%d\n",i_10,i_11);
printf("ang_sum: i_20=%d, i_22=%d\n",i_20,i_22);
}
for (i_1=i_10;i_1<i_11;i_1++) {
Radius = WORLD(i_1,Off_10,Ps_10);
if ( Radius > MaxRadius || Radius < MinRadius ) continue;
/* number of angular intervals for averaging */
NAngle = MAX2(1,(int) (DDAngle * Radius) + 1 );
DAngle = Ps_20/(float) NAngle;
if (testbit>1)
printf("ang_sum: %d: Radius=%g, NAngle=%d, DAngle=%g_deg\n",
i_1,Radius,NAngle,DAngle*arc_rad2deg);
// the integration range is from [AngleFst..AngleLst];
for (i_2=i_20;i_2<i_22;i_2++) {
// use the center of the angular interval to get the pixel value
Angle = WORLD(((float)i_2),Off_20,Ps_20); // output angle
AngleLower = WORLD(((float)i_2+LOWERBORDER),Off_20,Ps_20); // lower limit
AngleUpper = WORLD(((float)i_2+1+LOWERBORDER),Off_20,Ps_20); // upper limit
// restrict integration range to [AngleFst..AngleLst];
AngleLower = MAX2(AngleFst,AngleLower);
AngleUpper = MIN2(AngleLst,AngleUpper);
if (testbit>2)
printf("ang_sum: %d,%d: Angle=%g_deg, AngleLower=%g_deg, AngleUpper=%g_deg\n",
i_1,i_2,Angle*arc_rad2deg,AngleLower*arc_rad2deg,AngleUpper*arc_rad2deg);
/* angular averaging */
cnt = 0;
varcnt = 0;
I1CircleSum = 0.0; I1CircleSumWeight = 0.0;
E1CircleSum = 0.0; E1CircleSumWeight = 0.0;
// Angle .. Angle+NAngle*DAngle
ianglefst = 0;
ianglelst = floor( (AngleUpper - AngleLower) / DAngle + 0.5);
// the reduced angular range is [AngleLower..AngleUpper]
angle = AngleLower + DAngle*0.5;
if (testbit>2)
printf("ang_sum: %d,%d: angle=%g_deg, ianglefst=%d, ianglelst=%d\n",
i_1,i_2,angle*arc_rad2deg,ianglefst,ianglelst);
// average only in range with valid pixels
for (iangle = ianglefst; iangle<ianglelst; iangle++) {
/* averaging range is [AngleFst..AngleLst] */
if ( ( angle < AngleLower ) || ( AngleUpper < angle ) ) {
if (testbit>3)
printf("ang_sum: iangle=%d: angle=%g_deg not in [%g_deg..%g_deg] => continue\n",
iangle,angle*arc_rad2deg,AngleLower*arc_rad2deg,AngleUpper*arc_rad2deg);
angle += DAngle;
continue;
}
W0.s_1 = Radius * cos( angle );
W0.s_2 = Radius * sin( angle );
/* transform saxs-coordinate of unrotated detector (I0params) or Waxs-
projection to saxs-coordinate of rotated detector (I1params) */
W1 = waxs_Transform( &I0params, &I1params, transform, W0 );
if (!W1.status) {
f_11 = INDEX(W1.s_1,Off_11,Ps_11);
f_21 = INDEX(W1.s_2,Off_21,Ps_21);
if ( E0Data ) {
// V0 = V1
if ( Isum2ldwE(I1Data,E1Data,I1Dim_1,I1Dim_2,I1Dummy,I1DDummy,
f_11-0.5, f_21-0.5, f_11+0.5, f_21+0.5,
&I1Sum, &I1Weight, &E1Sum, &E1Weight) ) {
/* then do something with the data */
I1CircleSum += I1Sum;
I1CircleSumWeight += I1Weight;
if ( E1Sum >= 0.0 ) {
E1CircleSum += E1Sum;
E1CircleSumWeight += E1Weight;
varcnt++;
}
cnt++;
} /* if Isum2ldwE ... */
} else {
if ( Isum2ldw(I1Data,I1Dim_1,I1Dim_2,I1Dummy,I1DDummy,
f_11-0.5, f_21-0.5, f_11+0.5, f_21+0.5,
&I1Sum, &I1Weight) ) {
/* then do something with the data */
I1CircleSum += I1Sum;
I1CircleSumWeight += I1Weight;
cnt++;
} /* if Isum2ldw ... */
}
} // if (!W1.status)
angle += DAngle;
} /* for iangle ... */
if (cnt>0) {
pI0Data = ABSPTR(I0Data,I0Dim_1,I0Dim_2,i_1,i_2);
pE0Data = E0Data-I0Data+pI0Data;
/* The following factor adjusts the size of a rectangular pixel with
the size Ps_11*Ps_21 to a circular pixel with height Ps_10
and width Radius*DAngle */
factor = (Radius*DAngle*Ps_10)/(Ps_11*Ps_21);
I1CircleSum *= factor; I1CircleSumWeight *= factor;
E1CircleSum *= factor; E1CircleSumWeight *= factor;
I1Value = I1CircleSum; if (ave) I1Value /= I1CircleSumWeight;
if ( E0Data && ( varcnt==cnt ) ) {
E1Value = E1CircleSum;
if (ave) E1Value /= E1CircleSumWeight*E1CircleSumWeight;
/* Take into account that the data were averaged in a sector */
} else E1Value = -1.0;
if (vsum) {
/* Multiply with number of covered pixels */
factor = I1CircleSumWeight;
I1Value *= I1CircleSumWeight;
if ( E1Value>=0 ) E1Value *= I1CircleSumWeight*I1CircleSumWeight;
}
UPDATE( *pI0Data, I1Value, I0Dummy, I0DDummy );
if ( E0Data && ( E1Value>=0.0 ) ) {
UPDATE( *pE0Data, E1Value, VarDummy, VarDDummy );
}
}
/* end angular averaging */
} /* for i_2 ... */
} /* for i_1 ... */
} /* if ( AngleFst < AngleLst ) */
} /* for range ... */
// REGROUPING END }
if (pstatus) *pstatus = status;
return;
ang_sum_error:
if (pstatus) *pstatus = status;
return;
} /* ang_sum */
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