/********************************************************************** * cbf_airy_disk.c -- functions for airy-disk point spread * * * * ccbf_airy_disk.c version 1 * * * * Kaden Badalian and Herbert J. Bernstein * * CBFlib Version 0.9.5.4 21 June 2015 * * * * Paul Ellis and * * Herbert J. Bernstein (yaya@bernstein-plus-sons.com) * * * * (C) Copyright 2015 Herbert J. Bernstein * * * **********************************************************************/ /********************************************************************** * * * YOU MAY REDISTRIBUTE THE CBFLIB PACKAGE UNDER THE TERMS OF THE GPL * * * * ALTERNATIVELY YOU MAY REDISTRIBUTE THE CBFLIB API UNDER THE TERMS * * OF THE LGPL * * * **********************************************************************/ /*************************** GPL NOTICES ****************************** * * * This program is free software; you can redistribute it and/or * * modify it under the terms of the GNU General Public License as * * published by the Free Software Foundation; either version 2 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 General Public License for more details. * * * * You should have received a copy of the GNU General Public License * * along with this program; if not, write to the Free Software * * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA * * 02111-1307 USA * * * **********************************************************************/ /************************* LGPL NOTICES ******************************* * * * This library 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 2.1 of the License, or (at your option) any later version. * * * * This library 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. 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The CIF and STAR File approaches * * are used increasingly in the structural sciences for data exchange * * and archiving, and are having a significant influence on these * * activities in other fields. * * * * Statement of intent * * * * The IUCr's interest in the STAR File is as a general data * * interchange standard for science, and its interest in the CIF, * * a conformant derivative of the STAR File, is as a concise data * * exchange and archival standard for crystallography and structural * * science. * * * * Protection of the standards * * * * To protect the STAR File and the CIF as standards for * * interchanging and archiving electronic data, the IUCr, on behalf * * of the scientific community, * * * * * holds the copyrights on the standards themselves, * * * * * owns the associated trademarks and service marks, and * * * * * holds a patent on the STAR File. * * * * These intellectual property rights relate solely to the * * interchange formats, not to the data contained therein, nor to * * the software used in the generation, access or manipulation of * * the data. * * * * Promotion of the standards * * * * The sole requirement that the IUCr, in its protective role, * * imposes on software purporting to process STAR File or CIF data * * is that the following conditions be met prior to sale or * * distribution. * * * * * Software claiming to read files written to either the STAR * * File or the CIF standard must be able to extract the pertinent * * data from a file conformant to the STAR File syntax, or the CIF * * syntax, respectively. * * * * * Software claiming to write files in either the STAR File, or * * the CIF, standard must produce files that are conformant to the * * STAR File syntax, or the CIF syntax, respectively. * * * * * Software claiming to read definitions from a specific data * * dictionary approved by the IUCr must be able to extract any * * pertinent definition which is conformant to the dictionary * * definition language (DDL)[3] associated with that dictionary. * * * * The IUCr, through its Committee on CIF Standards, will assist * * any developer to verify that software meets these conformance * * conditions. * * * * Glossary of terms * * * * [1] CIF: is a data file conformant to the file syntax defined * * at http://www.iucr.org/iucr-top/cif/spec/index.html * * * * [2] STAR File: is a data file conformant to the file syntax * * defined at http://www.iucr.org/iucr-top/cif/spec/star/index.html * * * * [3] DDL: is a language used in a data dictionary to define data * * items in terms of "attributes". Dictionaries currently approved * * by the IUCr, and the DDL versions used to construct these * * dictionaries, are listed at * * http://www.iucr.org/iucr-top/cif/spec/ddl/index.html * * * * Last modified: 30 September 2000 * * * * IUCr Policy Copyright (C) 2000 International Union of * * Crystallography * **********************************************************************/ #ifdef __cplusplus extern "C" { #endif #define CBF_AIRY_DISK_C #include "cbf_airy_disk.h" #ifndef CBF_ARGUMENT #define CBF_ARGUMENT 4 #endif const double cbf_airy_unit_disk_partvol_1D[20] = { 1.426420856518437e-4, 0.001836262121580318, 0.00835666373463087, 0.02443516191841331, 0.05536596434951432, 0.1057021433691522, 0.1778607627549379, 0.2710544112372565, 0.3809159889912883, 0.5, 0.6190840110087124, 0.728945588762744, 0.8221392372450625, 0.8942978566308483, 0.9446340356504864, 0.9755648380815874, 0.9916433362653698, 0.9981637378784199, 0.9998573579143488, 1.0}; const double cbf_airy_unit_disk_partvol_2D[20][20] = {/* 0*/{0.00346705051,0.00687093888,0.01015137498,0.01325363,0.01613087439, 0.01874602235,0.0210729779,0.02309722219,0.02481572954,0.0262362476, 0.02737602025,0.028260067814,0.02891916459,0.029387667305,0.029701349023, 0.029895382025,0.030002591544,0.0300520725245,0.0300682266117,0.03007023969885}, /* 1*/{0.00687093888,0.01361651492,0.02011707249,0.02626400701,0.03196440993, 0.03714473227,0.04175325815,0.04576126834,0.04916286917,0.05197355744, 0.05422767792,0.055975001591,0.057276703239,0.058201044041,0.058819066573, 0.059200587596,0.059410730873,0.059507183065,0.059538286112,0.05954200547876}, /* 2*/{0.01015137498,0.02011707249,0.02971988508,0.03879900525,0.04721691669, 0.05486482696,0.06166633187,0.06757913356,0.07259477623,0.0767365049, 0.08005548073,0.082625692379,0.084537978127,0.085893613208,0.086797919453, 0.087354321149,0.0876592067765,0.0877978679698,0.0878416833722,0.0878465959026}, /* 3*/{0.01325363,0.02626400701,0.03879900525,0.05064804234,0.06163112817, 0.07160599402,0.08047289452,0.08817684888,0.0947072748,0.10009515475, 0.104408043237,0.107743362885,0.110220536166,0.111972551582,0.113137566164, 0.113851102023,0.1142393096179,0.1144136536852,0.11446724090183,0.114472794345986}, /* 4*/{0.01613087439,0.03196440993,0.04721691669,0.06163112817,0.07498729427, 0.08711191373,0.09788360577,0.10723583456,0.11515643076,0.12168408346, 0.126902183716,0.130930572083,0.133915863969,0.136021090055,0.137415392204, 0.138264460281,0.1387222899152,0.1389246969786,0.13898485561242,0.138990629865132}, /* 5*/{0.01874602235,0.03714473227,0.05486482696,0.07160599402,0.08711191373, 0.10118048454,0.11367068402,0.12450572989,0.13367247743,0.14121725945, 0.14723861975,0.151877592345,0.155306321045,0.157715888108,0.159304223433, 0.160264900067,0.1607774967045,0.1610000371,0.16106381668609,0.161069618583945}, /* 6*/{0.0210729779,0.04175325815,0.06166633187,0.08047289452,0.09788360577, 0.11367068402,0.1276756668,0.13981295657,0.15006908182,0.158497911592, 0.165212340699,0.170373192337,0.174176246495,0.176838386239,0.17858385588, 0.1796315488013,0.1801840986497,0.1804193515579,0.18048456232083,0.180490364218685}, /* 7*/{0.02309722219,0.04576126834,0.06757913356,0.08817684888,0.10723583456, 0.12450572989,0.13981295657,0.15306459433,0.164247494023,0.173422897088, 0.180717141216,0.186309287366,0.190416682607,0.193279565331,0.195145820046, 0.1962569023884,0.1968357927859,0.19707761724866,0.197143126330647,0.197148928228502}, /* 8*/{0.02481572954,0.04916286917,0.07259477623,0.0947072748,0.11515643076, 0.13367247743,0.15006908182,0.164247494023,0.176195501882,0.185981489282, 0.193744236426,0.199679379223,0.204023640027,0.207038041256,0.2089913123677, 0.210144603992,0.2107384436316,0.21098262459778,0.211048143691914,0.211053945589769}, /* 9*/{0.0262362476,0.05197355744,0.0767365049,0.10009515475,0.12168408346, 0.14121725945,0.158497911592,0.173422897088,0.185981489282,0.196248911791, 0.204375311535,0.210571162955,0.215090304768,0.218211915893,0.2202227339766, 0.2214007134883,0.22200112478044,0.222245696747985,0.222311215842119,0.222317017739974}, /* 10*/{0.02737602025,0.05422767792,0.08005548073,0.104408043237,0.126902183716, 0.14723861975,0.165212340699,0.180717141216,0.193744236426,0.204375311535, 0.212770748181,0.219154088005,0.223794015021,0.2269852484838,0.2290297321883, 0.2302193902632,0.23082150461232,0.231066076579865,0.231131595673999,0.231137397571854}, /* 11*/{0.028260067814,0.055975001591,0.082625692379,0.107743362885,0.130930572083, 0.151877592345,0.170373192337,0.186309287366,0.199679379223,0.210571162955, 0.219154088005,0.225662995349,0.2303791835435,0.2336103704434,0.2356710086544, 0.2368642879497,0.237466520025906,0.237711091993451,0.237776611087585,0.23778241298544}, /* 12*/{0.02891916459,0.057276703239,0.084537978127,0.110220536166,0.133915863969, 0.155306321045,0.174176246495,0.190416682607,0.204023640027,0.215090304768, 0.223794015021,0.2303791835435,0.2351375811481,0.238387513302,0.24045340997332, 0.241647079150478,0.242249311226684,0.242493883194229,0.242559402288363,0.242565204186218}, /* 13*/{0.029387667305,0.058201044041,0.085893613208,0.111972551582,0.136021090055, 0.157715888108,0.176838386239,0.193279565331,0.207038041256,0.218211915893, 0.2269852484838,0.2336103704434,0.238387513302,0.24164333763812,0.243709867436562, 0.24490353661372,0.245505768689926,0.245750340657471,0.245815859751605,0.24582166164946}, /* 14*/{0.029701349023,0.058819066573,0.086797919453,0.113137566164,0.137415392204, 0.159304223433,0.17858385588,0.195145820046,0.2089913123677,0.2202227339766, 0.2290297321883,0.2356710086544,0.24045340997332,0.243709867436562,0.245776397235004, 0.246970066412162,0.247572298488368,0.247816870455913,0.247882389550047,0.247888191447902}, /* 15*/{0.029895382025,0.059200587596,0.087354321149,0.113851102023,0.138264460281, 0.160264900067,0.1796315488013,0.1962569023884,0.210144603992,0.2214007134883, 0.2302193902632,0.2368642879497,0.241647079150478,0.24490353661372,0.246970066412162, 0.24816373558932,0.248765967665526,0.249010539633071,0.249076058727205,0.24908186062506}, /* 16*/{0.030002591544,0.059410730873,0.0876592067765,0.1142393096179,0.1387222899152, 0.1607774967045,0.1801840986497,0.1968357927859,0.2107384436316,0.22200112478044, 0.23082150461232,0.237466520025906,0.242249311226684,0.245505768689926,0.247572298488368, 0.248765967665526,0.249368199741732,0.249612771709277,0.249678290803411,0.249684092701266}, /* 17*/{0.0300520725245,0.059507183065,0.0877978679698,0.1144136536852,0.1389246969786, 0.1610000371,0.1804193515579,0.19707761724866,0.21098262459778,0.222245696747985, 0.231066076579865,0.237711091993451,0.242493883194229,0.245750340657471,0.247816870455913, 0.249010539633071,0.249612771709277,0.249857343676822,0.249922862770956,0.249928664668811}, /* 18*/{0.0300682266117,0.059538286112,0.0878416833722001,0.11446724090183,0.13898485561242, 0.16106381668609,0.18048456232083,0.197143126330647,0.211048143691914,0.222311215842119, 0.231131595673999,0.237776611087585,0.242559402288363,0.245815859751605,0.247882389550047, 0.249076058727205,0.249678290803411,0.249922862770956,0.249988381865091,0.249994183762946}, /* 19*/{0.03007023969885,0.05954200547876,0.0878465959026001,0.114472794345986,0.138990629865132, 0.161069618583945,0.180490364218685,0.197148928228502,0.211053945589769,0.222317017739974, 0.231137397571854,0.23778241298544,0.242565204186218,0.24582166164946,0.247888191447902, 0.24908186062506,0.249684092701266,0.249928664668811,0.249994183762946,0.2499999856608}}; /* compute the value of a normalized Airy disk to the first minimum, with that minimum at r=1, a volume of 1 and a fwhm of 0.8434376803. This is a series approximation good to 8 decimal places. The value is forced to zero outside the unit disk */ int cbf_airy_unit_disk(double x, double y, double *value) { double r,r_2,r_3,r_4,r_5,r_6,r_7,r_8,r_9,r_10,r_11,r_12,r_13,r_14,r_15,r_16; double val; if (!value) return CBF_ARGUMENT; r_2 = x*x+y*y; r = sqrt(r_2); r_3 = r*r_2; r_4 = r_2*r_2; r_5 = r*r_4; r_6 = r_3*r_3; r_7 = r_3*r_4; r_8 = r_4*r_4; r_9 = r_4*r_5; r_10 = r_5*r_5; r_11 = r_5*r_6; r_12 = r_6*r_6; r_13 = r_6*r_7; r_14 = r_7*r_7; r_15 = r_7*r_8; r_16 = r_8*r_8; val = (r>1.)?0.: (-0.0145718909798132 *r_16 +0.1128200913854083 *r_15 -0.3251669103199633 *r_14 +0.3415426671579541 *r_13 +0.03830169403530381 *r_12 +0.3036850720561378 *r_11 -1.622663925343156 *r_10 +0.1035599755468041 *r_9 +3.658218851892756 *r_8 +0.01440953571188533 *r_7 -6.723054067684573 *r_6 +7.828561594404555e-4 *r_5 +7.84111524870691 *r_4 +1.398176146475285e-5 *r_3 -5.12432349713814 *r_2 +5.077977353218757e-8 *r +1.395330318373548); *value = val; return 0; } /* Compute an airy disk for a specified fwhm and volume. */ int cbf_airy_disk(double x, double y, double cenx, double ceny, double volume, double fwhm, double * value) { double scale, xoff, yoff; double val; int error; if (!value || fwhm <= 0. || volume <= 0.) return CBF_ARGUMENT; scale = fwhm/CBF_AIRY_UNIT_DISK_FWHM; xoff = (x-cenx)/scale; yoff = (y-ceny)/scale; error = cbf_airy_unit_disk(xoff,yoff,&val); if (error) return error; *value = val*volume/(scale*scale); return 0; } int cbf_airy_simpsons_rule_step(double xlo, double ylo, double xhi, double yhi, double * value){ double value1,value2,value3,value4,value5,value6, value7,value8,value9,valueAvg,ymid,xmid; int error = 0; ymid = (ylo+yhi)/2.; xmid = (xlo+xhi)/2.; error |= cbf_airy_unit_disk(xlo,ylo,&value1); error |= cbf_airy_unit_disk(xlo,ymid,&value2); error |= cbf_airy_unit_disk(xlo,yhi,&value3); error |= cbf_airy_unit_disk(xmid,ylo,&value4); error |= cbf_airy_unit_disk(xmid,ymid,&value5); error |= cbf_airy_unit_disk(xmid,yhi,&value6); error |= cbf_airy_unit_disk(xhi,ylo,&value7); error |= cbf_airy_unit_disk(xhi,ymid,&value8); error |= cbf_airy_unit_disk(xhi,yhi,&value9); valueAvg = (value1+4.*value2+value3 +4.*value4+16.*value5+4.*value6 +value7+4.*value8+value9)/36.; if (value) *value = valueAvg*(xhi-xlo)*(yhi-ylo); return error; } int cbf_airy_unit_disk_volume(double xlo, double ylo, double xhi, double yhi, int steps, double * volume) { int stepx,stepy; double xstep, ystep; double xlos,ylos,xhis,yhis; double vol; int error=0; if (!volume) return CBF_ARGUMENT; xstep=(xhi-xlo)/((double)steps); ystep=(yhi-ylo)/((double)steps); *volume = 0.; for (stepx = 0; stepx < steps; stepx++) { xlos = xlo + xstep*((double)stepx); xhis = xlos + xstep; for (stepy = 0; stepy < steps; stepy++) { ylos = ylo + ystep*((double)stepy); yhis = ylos + ystep; error|=cbf_airy_simpsons_rule_step(xlos,ylos,xhis,yhis,&vol); *volume += vol; } } return 0; } static int cbf_airy_bin_big(double cutpoint) { if (cutpoint < -0.9) return 0; if (cutpoint >= 1.) return 20; return (int)((cutpoint+1.)*10.); } static double cbf_airy_bin_big_diff(double cutpoint,int bin) { return cutpoint+1. - ((double)(bin))/10.; } static int cbf_airy_bin_small(double cutpoint) { if (cutpoint < -0.95) return -20; if (cutpoint >= 1.) return 20; return -20+(int)((cutpoint+1.)*20.); } static double cbf_airy_bin_small_diff(double cutpoint,int bin) { return cutpoint+1. - ((double)(bin+20))/20.; } static double partvol_1D(int ii) { if (ii <= 0 ) return 0.; if (ii > 20) return 1.; return cbf_airy_unit_disk_partvol_1D[ii-1]; } static double partvol_2D(int ii,int jj) { if (jj < -20) jj = -20; if (jj > 20) jj = 20; if (ii < -20) ii = -20; if (ii > 20) ii = 20; if (ii >= 0 && jj >= 0) { if (ii == 0) { if (jj == 0) return (0.25); return(0.25 + cbf_airy_unit_disk_partvol_2D[19][jj-1]); } if (jj == 0) { return(0.25 + cbf_airy_unit_disk_partvol_2D[ii-1][19]); } return(.25 + cbf_airy_unit_disk_partvol_2D[ii-1][jj-1] + cbf_airy_unit_disk_partvol_2D[ii-1][19] + cbf_airy_unit_disk_partvol_2D[19][jj-1]); } else if (ii < 0 && jj >= 0) { if (jj == 0) { return(0.25 -cbf_airy_unit_disk_partvol_2D[-ii-1][19]); } return((.25-cbf_airy_unit_disk_partvol_2D[-ii-1][19]) + (cbf_airy_unit_disk_partvol_2D[19][jj-1] - cbf_airy_unit_disk_partvol_2D[-ii-1][jj-1])); } else if (ii >= 0 && jj < 0) { if (ii == 0) { return(0.25 -cbf_airy_unit_disk_partvol_2D[19][-jj-1]); } return((.25-cbf_airy_unit_disk_partvol_2D[19][-jj-1]) + (cbf_airy_unit_disk_partvol_2D[ii-1][19] - cbf_airy_unit_disk_partvol_2D[ii-1][-jj-1])); } else return (.25+cbf_airy_unit_disk_partvol_2D[-ii-1][-jj-1] -cbf_airy_unit_disk_partvol_2D[19][-jj-1] -cbf_airy_unit_disk_partvol_2D[-ii-1][19]); } static double partvol_2D_real(int ii, int jj, double xdif, double ydif) { double vol00, vol01, vol10, vol11; double volout; vol00 = partvol_2D(ii,jj); vol01 = partvol_2D(ii+1,jj); vol10 = partvol_2D(ii,jj+1); vol11 = partvol_2D(ii+1,jj+1); volout = vol00 +(vol01-vol00)*xdif*20. +(vol10-vol00)*ydif*20. +(vol11+vol00-vol01-vol10)*xdif*ydif*400; return volout; } int cbf_airy_disk_volume(double xlo, double ylo, double xhi, double yhi, double cenx, double ceny, double volumein, double fwhm, double * volumeout) { double scale, xofflo, yofflo, xoffhi, yoffhi; int icutxlo, icutxhi, icutylo, icutyhi; double diffxlo=0., diffxhi=0., diffylo=0., diffyhi=0.; if (!volumeout || fwhm <= 0.) { return CBF_ARGUMENT; } if (fabs(volumein) < 1.e-38) { *volumeout = 0.; return 0; } scale = fwhm/CBF_AIRY_UNIT_DISK_FWHM; xofflo = (xlo-cenx)/scale; yofflo = (ylo-ceny)/scale; xoffhi = (xhi-cenx)/scale; yoffhi = (yhi-ceny)/scale; if (xofflo <= -1. && yofflo <= -1. && xoffhi >= 1. && yoffhi >= 1. ) { /* return the full volumein */ *volumeout = volumein; return 0; } else if ( xofflo <= -1. && xoffhi >= 1. ) { /* we need to form a slab in the y-direction */ icutylo = cbf_airy_bin_big(yofflo); diffylo = cbf_airy_bin_big_diff(yofflo,icutylo); if (diffylo > 0.1) diffylo = 0.1; icutyhi = cbf_airy_bin_big(yoffhi); diffyhi = cbf_airy_bin_big_diff(yoffhi,icutyhi); if (diffyhi > 0.1) diffyhi = 0.1; *volumeout = volumein* ((partvol_1D(icutyhi)+diffyhi*10.*(partvol_1D(icutyhi+1) -partvol_1D(icutyhi))) -(partvol_1D(icutylo)+diffylo*10.*(partvol_1D(icutylo+1) -partvol_1D(icutylo)))); return 0; } else if ( yofflo <= -1. && yoffhi >= 1. ) { /* we need to form a slab in the x-direction */ icutxlo = cbf_airy_bin_big(xofflo); diffxlo = cbf_airy_bin_big_diff(xofflo,icutxlo); diffxlo = xofflo-1.-((double)icutxlo)/10.; if (diffxlo > 0.1) diffxlo = 0.1; icutxhi = cbf_airy_bin_big(xoffhi); diffxlo = cbf_airy_bin_big_diff(xoffhi,icutxhi); if (diffxhi > 0.1) diffxhi = 0.1; *volumeout = volumein* ((partvol_1D(icutxhi)+diffxhi*10.*(partvol_1D(icutxhi+1) -partvol_1D(icutxhi))) -(partvol_1D(icutxlo)+diffxlo*10.*(partvol_1D(icutxlo+1) -partvol_1D(icutxlo)))); return 0; } else { double v1,v2,v3,v4; icutxlo = cbf_airy_bin_small(xofflo); diffxlo = cbf_airy_bin_small_diff(xofflo,icutxlo); if (diffxlo > 0.05) diffxlo = 0.05; icutxhi = cbf_airy_bin_small(xoffhi); diffxhi = cbf_airy_bin_small_diff(xoffhi,icutxhi); if (diffxhi > 0.05) diffxhi = 0.05; icutylo = cbf_airy_bin_small(yofflo); diffylo = cbf_airy_bin_small_diff(yofflo,icutylo); if (diffylo > 0.05) diffylo = 0.05; icutyhi = cbf_airy_bin_small(yoffhi); diffyhi = cbf_airy_bin_small_diff(yoffhi,icutyhi); if (diffyhi > 0.05) diffyhi = 0.05; v1 = partvol_2D_real(icutxlo,icutylo,diffxlo,diffylo); v2 = partvol_2D_real(icutxhi,icutylo,diffxhi,diffylo); v3 = partvol_2D_real(icutxlo,icutyhi,diffxlo,diffyhi); v4 = partvol_2D_real(icutxhi,icutyhi,diffxhi,diffyhi); *volumeout = volumein*(v1+v4-v2-v3); return 0; } } #ifdef __cplusplus } #endif