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/*=========================================================================
Program: Insight Segmentation & Registration Toolkit
Module: itkFEMUtility.cxx
Language: C++
Date: $Date$
Version: $Revision$
Copyright (c) Insight Software Consortium. All rights reserved.
See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.
This software is distributed WITHOUT ANY WARRANTY; without even
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE. See the above copyright notices for more information.
=========================================================================*/
// disable debug warnings in MS compiler
#ifdef _MSC_VER
#pragma warning(disable: 4786)
#endif
#include "itkFEMUtility.h"
namespace itk {
namespace fem {
/**
* Numerical integration (Gauss-Legendre formula).
* Integrates function f(x) from x=a to x=b in n points.
*/
double GaussIntegrate::Integrate(double (*f)(double), double a, double b, int n)
{
/**
* This subprogram produces the gauss-legendre numerical
* integral for
* b
* int f(x)*dx
* a
*
* The number of nodes n must satisfy
* 2 <= n <= 20
* The following data statements contain the gauss-legendre
* nodes for the interval [-1,1].
*/
double scale, t, tl, tu, sum;
int i, m, ibase;
/* Begin integration */
scale = (b - a)/two;
if ( (n&1) == 0 )
{
m = n/2;
ibase = m*m;
sum = zero;
}
else
{
m = (n - 1)/2;
ibase = (n*n - 1)/4;
sum = w[ibase+m]*(*f)((a + b)/two);
}
for (i=1; i <= m; i++)
{
t = z[ibase + i - 1];
tl = (a*(one + t) + (one - t)*b)/two;
tu = (a*(one - t) + (one + t)*b)/two;
sum = sum + w[ibase + i - 1]*((*f)(tl) +(*f)(tu));
}
return scale*sum;
}
const double GaussIntegrate::zero = 0.0;
const double GaussIntegrate::one = 1.0;
const double GaussIntegrate::two = 2.0;
const double GaussIntegrate::z[110] = {
0.0, 0.577350269189626, 0.774596669241483, 0.0,
0.861136311594053, 0.339981043584856, 0.906179845938664,
0.538469310105683, 0.0, 0.932469514203152,
0.661209386466265, 0.238619186083197, 0.949107912342759,
0.741531185599394, 0.405845151377397, 0.0,
0.960289856497536, 0.796666477413627, 0.525532409916329,
0.183434642495650, 0.968160239507626, 0.836031107326636,
0.613371432700590, 0.324253423403809, 0.0,
0.973906528517172, 0.865063366688985, 0.679409568299024,
0.433395394129247, 0.148874338981631, 0.978228658146057,
0.887062599768095, 0.730152005574049, 0.519096129206812,
0.269543155952345, 0.0, 0.981560634246719,
0.904117256370475, 0.769902674194305, 0.587317954286617,
0.367831498998180, 0.125233408511469, 0.984183054718588,
0.917598399222978, 0.801578090733310, 0.642349339440340,
0.448492751036447, 0.230458315955135, 0.0,
0.986283808696812, 0.928434883663574, 0.827201315069765,
0.687292904811685, 0.515248636358154, 0.319112368927890,
0.108054948707344, 0.987992518020485, 0.937273392400706,
0.848206583410427, 0.724417731360170, 0.570972172608539,
0.394151347077563, 0.201194093997435, 0.0,
0.989400934991650, 0.944575023073233, 0.865631202387832,
0.755404408355003, 0.617876244402644, 0.458016777657227,
0.281603550779259, 0.0950125098376374,0.990575475314417,
0.950675521768768, 0.880239153726986, 0.781514003896801,
0.657671159216691, 0.512690537086477, 0.351231763453876,
0.178484181495848, 0.0, 0.991565168420931,
0.955823949571398, 0.892602466497556, 0.803704958972523,
0.691687043060353, 0.559770831073948, 0.411751161462843,
0.251886225691506, 0.0847750130417353,0.992406843843584,
0.960208152134830, 0.903155903614818, 0.822714656537143,
0.720966177335229, 0.600545304661681, 0.464570741375961,
0.316564099963630, 0.160358645640225, 0.0,
0.993128599185095, 0.963971927277914, 0.912234428251326,
0.839116971822219, 0.746331906460151, 0.636053680726515,
0.510867001950827, 0.373706088715420, 0.227785851141645,
0.0765265211334973
};
const double GaussIntegrate::w[110] = {
0.0, 1.0, 0.555555555555556, 0.888888888888889,
0.347854845137454, 0.652145154862546, 0.236926885056189,
0.478628670499366, 0.568888888888889, 0.171324492379170,
0.360761573048139, 0.467913934572691, 0.129484966168870,
0.279705391489277, 0.381830050505119, 0.417959183673469,
0.101228536290376, 0.222381034453374, 0.313706645877887,
0.362683783378362, 0.0812743883615744, 0.180648160694857,
0.260610696402935, 0.312347077040003, 0.330239355001260,
0.0666713443086881, 0.149451349150581, 0.219086362515982,
0.269266719309996, 0.295524224714753, 0.0556685671161737,
0.125580369464905, 0.186290210927734, 0.233193764591990,
0.262804544510247, 0.272925086777901, 0.0471753363865118,
0.106939325995318, 0.160078328543346, 0.203167426723066,
0.233492536538355, 0.249147045813403, 0.0404840047653159,
0.0921214998377284, 0.138873510219787, 0.178145980761946,
0.207816047536889, 0.226283180262897, 0.232551553230874,
0.0351194603317519,0.0801580871597602, 0.121518570687903,
0.157203167158194, 0.185538397477938, 0.205198463721296,
0.215263853463158, 0.0307532419961173,0.0703660474881081,
0.107159220467172, 0.139570677926154, 0.166269205816994,
0.186161000015562, 0.198431485327112, 0.202578241925561,
0.0271524594117541,0.0622535239386478,0.0951585116824928,
0.124628971255534, 0.149595988816577, 0.169156519395003,
0.182603415044924, 0.189450610455068, 0.0241483028685479,
0.0554595293739872, 0.0850361483171792,0.111883847193404,
0.135136368468525, 0.154045761076810, 0.168004102156450,
0.176562705366993, 0.179446470356207, 0.0216160135264833,
0.0497145488949698, 0.0764257302548891,0.100942044106287,
0.122555206711478, 0.140642914670651, 0.154684675126265,
0.164276483745833, 0.169142382963144, 0.0194617882297265,
0.0448142267656996,0.0690445427376412,0.0914900216224500,
0.111566645547334, 0.128753962539336, 0.142606702173607,
0.152766042065860, 0.158968843393954, 0.161054449848784,
0.0176140071391521,0.0406014298003869,0.0626720483341091,
0.0832767415767047, 0.101930119817240, 0.118194531961518,
0.131688638449177, 0.142096109318382, 0.149172986472604,
0.152753387130726
};
}} // end namespace itk::fem
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