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utils.c
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/*************************************************************************************************************
The MIT License
Copyright (C) 2006-2019 David Dubbeldam, Sofia Calero, Thijs Vlugt, Donald E. Ellis, and Randall Q. Snurr.
D.Dubbeldam@uva.nl http://www.uva.nl/profiel/d/u/d.dubbeldam/d.dubbeldam.html
scaldia@upo.es http://www.upo.es/raspa/
t.j.h.vlugt@tudelft.nl http://homepage.tudelft.nl/v9k6y
don-ellis@northwestern.edu http://dvworld.northwestern.edu/
snurr@northwestern.edu http://zeolites.cqe.northwestern.edu/
Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation
files (the "Software"), to deal in the Software without
restriction, including without limitation the rights to use,
copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following
conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.
**************************************************************************************************************/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <string.h>
#include <ctype.h>
#include <sys/time.h>
#include "molecule.h"
#include "utils.h"
#include "integrate.h"
#include "simulation.h"
#include "framework.h"
#include "framework_energy.h"
#include "framework_force.h"
#include "internal_force.h"
#include "recrossing.h"
#ifdef HAVE_FFTW3
#include <fftw3.h>
#endif
long Factorial(int n)
{
int c;
long result = 1;
for (c = 1; c <= n; c++)
result = result * c;
return result;
}
void BubbleSort(int list[], int n)
{
long c, d, t;
for (c = 0 ; c < ( n - 1 ); c++)
{
for (d = 0 ; d < n - c - 1; d++)
{
if (list[d] > list[d+1])
{
/* Swapping */
t = list[d];
list[d] = list[d+1];
list[d+1] = t;
}
}
}
}
int isInArrayOfSize(int value,int n,int *array)
{
int i;
for(i=0;i<n;i++)
{
if(value==array[i]) return TRUE;
}
return FALSE;
}
double get_wall_time(void)
{
struct timeval time;
if (gettimeofday(&time,NULL)) return 0;
return (double)time.tv_sec + (double)time.tv_usec * .000001;
}
double get_cpu_time(void)
{
return (double)clock() / CLOCKS_PER_SEC;
}
REAL Smoothing(REAL theta)
{
REAL on,off;
on=170.0*DEG2RAD;
off=180.0*DEG2RAD;
if(theta<on) return 1.0;
return SQR(off-theta)*(off+2.0*theta-3.0*on)/CUBE(off-on);
}
REAL SmoothingDerivative(REAL theta)
{
REAL on,off;
on=170.0*DEG2RAD;
off=180.0*DEG2RAD;
if(theta<on) return 0.0;
return 6.0*(off-theta)*(on-theta)/CUBE(off-on);
}
REAL Exp(REAL x)
{
return (REAL)exp(x);
}
REAL MExp(REAL x)
{
return (REAL)exp(-x);
}
REAL Exp2(REAL x)
{
return (REAL)exp(2.0*x);
}
REAL MExp2(REAL x)
{
return (REAL)exp(-2.0*x);
}
REAL Identity(REAL x)
{
return (REAL)x;
}
REAL ExpRM(REAL x)
{
return (REAL)(exp(2.0*x)*exp(-x));
}
// Rotate a point 'p' about the line through 'origin' parallel to 'dir' by an angle 'theta'
VECTOR RotateAboutArbitraryLine(VECTOR p, VECTOR origin, VECTOR dir,REAL theta)
{
VECTOR vec;
REAL r;
// normalize the direction vector
r=SQR(dir.x)+SQR(dir.y)+SQR(dir.z);
dir.x/=r;
dir.y/=r;
dir.z/=r;
vec.x=origin.x*(SQR(dir.y)+SQR(dir.z))+
dir.x*(-origin.y*dir.y-origin.z*dir.z+dir.x*p.x+dir.y*p.y+dir.z*p.z)+
((p.x-origin.x)*(SQR(dir.y)+SQR(dir.z))+dir.x*(origin.y*dir.y+origin.z*dir.z-dir.y*p.y-dir.z*p.z))*cos(theta)+
(origin.y*dir.z-origin.z*dir.y-dir.z*p.y+dir.y*p.z)*sin(theta);
vec.y=origin.y*(SQR(dir.x)+SQR(dir.z))+
dir.y*(-origin.x*dir.x-origin.z*dir.z+dir.x*p.x+dir.y*p.y+dir.z*p.z)+
((p.y-origin.y)*(SQR(dir.x)+SQR(dir.z))+dir.y*(origin.x*dir.x+origin.z*dir.z-dir.x*p.x-dir.z*p.z))*cos(theta)+
(-origin.x*dir.z+origin.z*dir.x+dir.z*p.x-dir.x*p.z)*sin(theta);
vec.z=origin.z*(SQR(dir.x)+SQR(dir.y))+
dir.z*(-origin.x*dir.x-origin.y*dir.y+dir.x*p.x+dir.y*p.y+dir.z*p.z)+
((p.z-origin.z)*(SQR(dir.x)+SQR(dir.y))+dir.z*(origin.x*dir.x+origin.y*dir.y-dir.x*p.x-dir.y*p.y))*cos(theta)+
(origin.x*dir.y-origin.y*dir.x-dir.y*p.x+dir.x*p.y)*sin(theta);
return vec;
}
// Rotate a point 'p' about the the bondvector of two beads by an angle 'theta'
VECTOR RotateAboutBondVector(VECTOR p, VECTOR first_bead, VECTOR second_bead, REAL theta)
{
VECTOR vec,dir;
REAL r;
dir.x=second_bead.x-first_bead.x;
dir.y=second_bead.y-first_bead.y;
dir.z=second_bead.z-first_bead.z;
// normalize the direction vector
r=SQR(dir.x)+SQR(dir.y)+SQR(dir.z);
dir.x/=r;
dir.y/=r;
dir.z/=r;
vec.x=first_bead.x*(SQR(dir.y)+SQR(dir.z))+
dir.x*(-first_bead.y*dir.y-first_bead.z*dir.z+dir.x*p.x+dir.y*p.y+dir.z*p.z)+
((p.x-first_bead.x)*(SQR(dir.y)+SQR(dir.z))+dir.x*(first_bead.y*dir.y+first_bead.z*dir.z-dir.y*p.y-dir.z*p.z))*cos(theta)+
(first_bead.y*dir.z-first_bead.z*dir.y-dir.z*p.y+dir.y*p.z)*sin(theta);
vec.y=first_bead.y*(SQR(dir.x)+SQR(dir.z))+
dir.y*(-first_bead.x*dir.x-first_bead.z*dir.z+dir.x*p.x+dir.y*p.y+dir.z*p.z)+
((p.y-first_bead.y)*(SQR(dir.x)+SQR(dir.z))+dir.y*(first_bead.x*dir.x+first_bead.z*dir.z-dir.x*p.x-dir.z*p.z))*cos(theta)+
(-first_bead.x*dir.z+first_bead.z*dir.x+dir.z*p.x-dir.x*p.z)*sin(theta);
vec.z=first_bead.z*(SQR(dir.x)+SQR(dir.y))+
dir.z*(-first_bead.x*dir.x-first_bead.y*dir.y+dir.x*p.x+dir.y*p.y+dir.z*p.z)+
((p.z-first_bead.z)*(SQR(dir.x)+SQR(dir.y))+dir.z*(first_bead.x*dir.x+first_bead.y*dir.y-dir.x*p.x-dir.y*p.y))*cos(theta)+
(first_bead.x*dir.y-first_bead.y*dir.x-dir.y*p.x+dir.x*p.y)*sin(theta);
return vec;
}
void ConvertStringToLowercase(char *buffer)
{
int i;
for(i=0;i<strlen(buffer);i++)
buffer[i]=(char)tolower(buffer[i]);
}
void ConvertStringToUppercase(char *buffer)
{
int i;
for(i=0;i<strlen(buffer);i++)
buffer[i]=(char)toupper(buffer[i]);
}
#if defined (__LP64__) || defined (__64BIT__) || defined (_LP64) || (__WORDSIZE == 64)
/*
http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/VERSIONS/C-LANG/mt19937-64.c
A C-program for MT19937-64 (2004/9/29 version).
Coded by Takuji Nishimura and Makoto Matsumoto.
This is a 64-bit version of Mersenne Twister pseudorandom number
generator.
Before using, initialize the state by using init_genrand64(seed)
Copyright (C) 2004, Makoto Matsumoto and Takuji Nishimura,
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The names of its contributors may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
References:
T. Nishimura, ``Tables of 64-bit Mersenne Twisters''
ACM Transactions on Modeling and
Computer Simulation 10. (2000) 348--357.
M. Matsumoto and T. Nishimura,
``Mersenne Twister: a 623-dimensionally equidistributed
uniform pseudorandom number generator''
ACM Transactions on Modeling and
Computer Simulation 8. (Jan. 1998) 3--30.
Any feedback is very welcome.
http://www.math.hiroshima-u.ac.jp/~m-mat/MT/emt.html
email: m-mat @ math.sci.hiroshima-u.ac.jp (remove spaces)
*/
#define NN 312
#define MM 156
#define MATRIX_A 0xB5026F5AA96619E9ULL
#define UM 0xFFFFFFFF80000000ULL /* Most significant 33 bits */
#define LM 0x7FFFFFFFULL /* Least significant 31 bits */
/* The array for the state vector */
/* mti==NN+1 means mt[NN] is not initialized */
static unsigned long long mt[NN];
static unsigned long long mag01[2]={0ULL,MATRIX_A};
static int mti=NN+1;
static unsigned long long mt_bak[NN];
static unsigned long long mag01_bak[2];
static int mti_bak;
/* initializes mt[NN] with a seed */
void InitializeRandomNumberGenerator(unsigned long long seed)
{
mt[0]=seed;
for(mti=1;mti<NN;mti++)
mt[mti]=(6364136223846793005ULL*(mt[mti-1]^(mt[mti-1]>>62))+mti);
}
/* generates a random number on [0, 2^64-1]-interval */
unsigned long long genrand64_int64(void)
{
int i;
unsigned long long x;
if(mti>=NN)
{ /* generate NN words at one time */
/* if init_genrand64() has not been called, */
/* a default initial seed is used */
if(mti==NN+1)
InitializeRandomNumberGenerator(5489ULL);
for(i=0;i<NN-MM;i++)
{
x=(mt[i]&UM)|(mt[i+1]&LM);
mt[i]=mt[i+MM]^(x>>1)^mag01[(int)(x&1ULL)];
}
for(;i<NN-1;i++)
{
x=(mt[i]&UM)|(mt[i+1]&LM);
mt[i]=mt[i+(MM-NN)]^(x>>1)^mag01[(int)(x&1ULL)];
}
x=(mt[NN-1]&UM)|(mt[0]&LM);
mt[NN-1]=mt[MM-1]^(x>>1)^mag01[(int)(x&1ULL)];
mti=0;
}
x=mt[mti++];
x^=(x>>29)&0x5555555555555555ULL;
x^=(x<<17)&0x71D67FFFEDA60000ULL;
x^=(x<<37)&0xFFF7EEE000000000ULL;
x^=(x>>43);
return x;
}
/* generates a random number on [0, 2^63-1]-interval */
long long RandomInteger(void)
{
return (long long)(genrand64_int64()>>1);
}
/* generates a random number on [0,1]-real-interval */
double RandomNumber(void)
{
return (genrand64_int64()>>11)*(1.0/9007199254740991.0);
}
/* generates a random number on [0,1)-real-interval */
double RandomNumber2(void)
{
return (genrand64_int64()>>11)*(1.0/9007199254740992.0);
}
/* generates a random number on (0,1)-real-interval */
double RandomNumber3(void)
{
return ((genrand64_int64()>>12)+0.5)*(1.0/4503599627370496.0);
}
void StoreRandomNumberStatus(void)
{
int i;
for(i=0;i<NN;i++)
mt_bak[i]=mt[i];
mti_bak=mti;
mag01_bak[0]=mag01[0];
mag01_bak[1]=mag01[1];
}
void RetrieveRandomNumberStatus(void)
{
int i;
for(i=0;i<NN;i++)
mt[i]=mt_bak[i];
mti=mti_bak;
mag01[0]=mag01_bak[0];
mag01[1]=mag01_bak[1];
}
static int versionNumber=1;
void WriteRestartUtils(FILE *FilePtr)
{
REAL Check;
fwrite(&versionNumber,sizeof(int),1,FilePtr);
fwrite(mt,NN,sizeof(unsigned long long),FilePtr);
fwrite(&mti,1,sizeof(int),FilePtr);
fwrite(mag01,1,sizeof(unsigned long long[2]),FilePtr);
Check=123456789.0;
fwrite(&Check,1,sizeof(REAL),FilePtr);
}
void ReadRestartUtils(FILE *FilePtr)
{
REAL Check;
int readversionNumber=0;
fread(&readversionNumber,sizeof(int),1,FilePtr);
if(readversionNumber > versionNumber)
{
fprintf(stderr,"Upgrade to last version of RASPA to read binary restart-file");
exit(-1);
}
fread(mt,NN,sizeof(unsigned long long),FilePtr);
fread(&mti,1,sizeof(int),FilePtr);
fread(mag01,1,sizeof(unsigned long long[2]),FilePtr);
fread(&Check,1,sizeof(REAL),FilePtr);
if(fabs(Check-123456789.0)>1e-10)
{
fprintf(stderr, "Error in binary restart-file (ReadRestartUtils)\n");
ContinueAfterCrash=FALSE;
}
}
#undef NN
#undef MM
#undef MATRIX_A
#undef UM
#undef LM
#else
/*
A C-program for MT19937, with initialization improved 2002/1/26.
Coded by Takuji Nishimura and Makoto Matsumoto.
Before using, initialize the state by using init_genrand(seed)
Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The names of its contributors may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
Any feedback is very welcome.
http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
*/
/* Period parameters */
#define N 624
#define M 397
#define MATRIX_A 0x9908b0dfUL /* constant vector a */
#define UPPER_MASK 0x80000000UL /* most significant w-r bits */
#define LOWER_MASK 0x7fffffffUL /* least significant r bits */
static unsigned long mt[N]; /* the array for the state vector */
static int mti=N+1; /* mti==N+1 means mt[N] is not initialized */
static unsigned long mag01[2]={0x0UL, MATRIX_A}; /* mag01[x] = x * MATRIX_A for x=0,1 */
static unsigned long mt_bak[N];
static int mti_bak;
static unsigned long mag01_bak[2];
/* initializes mt[N] with a seed */
void InitializeRandomNumberGenerator(unsigned long s)
{
mt[0]=s&0xffffffffUL;
for(mti=1;mti<N;mti++)
{
mt[mti]=(1812433253UL*(mt[mti-1]^(mt[mti-1]>>30))+mti);
/* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
/* In the previous versions, MSBs of the seed affect */
/* only MSBs of the array mt[]. */
/* 2002/01/09 modified by Makoto Matsumoto */
mt[mti]&=0xffffffffUL;
/* for >32 bit machines */
}
}
/* generates a random number on [0,0xffffffff]-interval */
unsigned long genrand_int32(void)
{
unsigned long y;
/* mag01[x] = x * MATRIX_A for x=0,1 */
if(mti>=N)
{ /* generate N words at one time */
int kk;
if(mti==N+1) /* if init_genrand() has not been called, */
InitializeRandomNumberGenerator(5489UL); /* a default initial seed is used */
for(kk=0;kk<N-M;kk++)
{
y=(mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
mt[kk]=mt[kk+M]^(y>>1)^mag01[y&0x1UL];
}
for(;kk<N-1;kk++)
{
y=(mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
mt[kk]=mt[kk+(M-N)]^(y>>1)^mag01[y&0x1UL];
}
y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
mt[N-1]=mt[M-1]^(y>>1)^mag01[y&0x1UL];
mti=0;
}
y = mt[mti++];
/* Tempering */
y^=(y>>11);
y^=(y<<7)&0x9d2c5680UL;
y^=(y<<15)&0xefc60000UL;
y^=(y>>18);
return y;
}
/* generates a random number on [0,0x7fffffff]-interval */
long RandomInteger(void)
{
return (long)(genrand_int32()>>1);
}
/* generates a random number on [0,1]-real-interval */
double RandomNumber(void)
{
return genrand_int32()*(1.0/4294967295.0);
/* divided by 2^32-1 */
}
/* generates a random number on [0,1)-real-interval */
double RandomNumber2(void)
{
return genrand_int32()*(1.0/4294967296.0);
/* divided by 2^32 */
}
/* generates a random number on (0,1)-real-interval */
double RandomNumber3(void)
{
return (((double)genrand_int32())+0.5)*(1.0/4294967296.0);
/* divided by 2^32 */
}
/* generates a random number on [0,1) with 53-bit resolution*/
double RandomNumber4(void)
{
unsigned long a=genrand_int32()>>5,b=genrand_int32()>>6;
return(a*67108864.0+b)*(1.0/9007199254740992.0);
}
void StoreRandomNumberStatus(void)
{
int i;
for(i=0;i<N;i++)
mt_bak[i]=mt[i];
mti_bak=mti;
mag01_bak[0]=mag01[0];
mag01_bak[1]=mag01[1];
}
void RetrieveRandomNumberStatus(void)
{
int i;
for(i=0;i<N;i++)
mt[i]=mt_bak[i];
mti=mti_bak;
mag01[0]=mag01_bak[0];
mag01[1]=mag01_bak[1];
}
void WriteRestartUtils(FILE *FilePtr)
{
fwrite(mt,N,sizeof(unsigned long),FilePtr);
fwrite(&mti,1,sizeof(int),FilePtr);
fwrite(mag01,1,sizeof(unsigned long[2]),FilePtr);
}
void ReadRestartUtils(FILE *FilePtr)
{
fread(mt,N,sizeof(unsigned long),FilePtr);
fread(&mti,1,sizeof(int),FilePtr);
fread(mag01,1,sizeof(unsigned long[2]),FilePtr);
}
#undef N 624
#undef M 397
#undef MATRIX_A
#undef UPPER_MASK
#undef LOWER_MASK
#endif
// The polar form of the Box-Muller transformation, See Knuth v2, 3rd ed, p122
REAL RandomGaussianNumber(void)
{
REAL ran1,ran2,r2;
do
{
ran1=2.0*RandomNumber()-1.0;
ran2=2.0*RandomNumber()-1.0;
r2=SQR(ran1)+SQR(ran2);
}
while((r2>1.0)||(r2==0.0));
return ran2*sqrt(-2.0*log(r2)/r2);
}
REAL RandomGaussianNumberMeanVariance(REAL mean,REAL sigma)
{
REAL ran1,ran2,r2;
do
{
ran1=2.0*RandomNumber()-1.0;
ran2=2.0*RandomNumber()-1.0;
r2=SQR(ran1)+SQR(ran2);
}
while((r2>1.0)||(r2==0.0));
return mean+sigma*ran2*sqrt(-2.0*log(r2)/r2);
}
// G. Marsaglia
// "Choosing a Point from the Surface of a Sphere"
// Ann. Math. Stat., Volume 43, page 645-646, 1972
VECTOR RandomNumberOnUnitSphere(void)
{
REAL ran1,ran2,ranh,ransq;
VECTOR v;
do
{
ran1=2.0*RandomNumber()-1.0;
ran2=2.0*RandomNumber()-1.0;
ransq=SQR(ran1)+SQR(ran2);
}
while(ransq>=1.0);
ranh=2.0*sqrt(1.0-ransq);
v.x=ran1*ranh;
v.y=ran2*ranh;
v.z=1.0-2.0*ransq;
return v;
}
VECTOR RandomNumberOnCone(VECTOR v,REAL theta)
{
REAL xprev,yprev,zprev,ran1,cosin;
cosin=cos(theta);
ran1=1.0/sqrt(SQR(v.x)+SQR(v.y)+SQR(v.z));
xprev=v.x*ran1;
yprev=v.y*ran1;
zprev=v.z*ran1;
v=RandomNumberOnUnitSphere();
ran1=v.x*xprev+v.y*yprev+v.z*zprev;
v.x=v.x-ran1*xprev;
v.y=v.y-ran1*yprev;
v.z=v.z-ran1*zprev;
ran1=sqrt((1.0-cosin*cosin)/(SQR(v.x)+SQR(v.y)+SQR(v.z)));
v.x=v.x*ran1+cosin*xprev;
v.y=v.y*ran1+cosin*yprev;
v.z=v.z*ran1+cosin*zprev;
ran1=1.0/sqrt(SQR(v.x)+SQR(v.y)+SQR(v.z));
v.x=v.x*ran1;
v.y=v.y*ran1;
v.z=v.z*ran1;
return v;
}
// Calculates the matrix from the rotation of source a to image b
// a and b are untouched by this procedure. At the end of this
// procedure, the matrix b is recovered by:
// b[0]=a[0]*rot[0][0]+a[1]*rot[0][1]+a[2]*rot[0][2]
// b[1]=a[0]*rot[1][0]+a[1]*rot[1][1]+a[2]*rot[1][2]
// b[2]=a[0]*rot[2][0]+a[1]*rot[2][1]+a[2]*rot[2][2]
// a=source vector
// b=target vector
// rot=rotation matrix
// note:
// 1) no need to normalize a and b
// 2) beware of the singularity when a==b !!!!
void CalculateRotationMatrix(VECTOR a,VECTOR b,REAL_MATRIX3x3 *rot)
{
REAL x,y,z,w,s,c,nn;
nn=(a.x*b.x+a.y*b.y+a.z*b.z)/sqrt((a.x*a.x+a.y*a.y+
a.z*a.z)*(b.x*b.x+b.y*b.y+b.z*b.z));
if(nn>0.999999)
{
rot->ax=1.0; rot->bx=0.0; rot->cx=0.0;
rot->ay=0.0; rot->by=1.0; rot->cy=0.0;
rot->az=0.0; rot->bz=0.0; rot->cz=1.0;
}
else if (nn<-0.999999)
{
rot->ax=-1.0; rot->bx=0.0; rot->cx=0.0;
rot->ay=0.0; rot->by=-1.0; rot->cy=0.0;
rot->az=0.0; rot->bz=0.0; rot->cz=-1.0;
}
else
{
x=a.z*b.y-a.y*b.z;
y=a.x*b.z-a.z*b.x;
z=a.y*b.x-a.x*b.y;
s=1.0/sqrt(x*x+y*y+z*z);
x=x*s;
y=y*s;
z=z*s;
c=(a.x*b.x+a.y*b.y+a.z*b.z)/sqrt((a.x*a.x+a.y*a.y+
a.z*a.z)*(b.x*b.x+b.y*b.y+b.z*b.z));
w=1.0-c;
s=sqrt(1.0-c*c);
rot->ax=x*x*w+c; rot->bx=x*y*w+z*s; rot->cx=x*z*w-y*s;
rot->ay=x*y*w-z*s; rot->by=y*y*w+c; rot->cy=y*z*w+x*s;
rot->az=x*z*w+y*s; rot->bz=y*z*w-x*s; rot->cz=z*z*w+c;
}
}
VECTOR Perpendicular(VECTOR a,VECTOR b)
{
VECTOR v,fac;
int choise;
fac.x=fabs(b.y*a.z-a.y*b.z);
fac.y=fabs(b.x*a.z-a.x*b.z);
fac.z=fabs(b.y*a.x-a.y*b.x);
choise=1;
if(fac.y>fac.x)
{
choise=2;
fac.x=fac.y;
}
if(fac.z>fac.x) choise=3;
if(choise==1)
{
v.x=1.0;
v.y=(a.x*b.z-b.x*a.z)/(b.y*a.z-a.y*b.z);
v.z=(b.x*a.y-a.x*b.y)/(b.y*a.z-a.y*b.z);
}
else if (choise==2)
{
v.x=(a.y*b.z-b.y*a.z)/(b.x*a.z-a.x*b.z);
v.y=1.0;
v.z=(b.y*a.x-a.y*b.x)/(b.x*a.z-a.x*b.z);
}
else
{
v.x=(b.z*a.y-a.z*b.y)/(b.y*a.x-a.y*b.x);
v.y=(a.z*b.x-b.z*a.x)/(b.y*a.x-a.y*b.x);
v.z=1.0;
}
fac.x=1.0/sqrt(SQR(v.x)+SQR(v.y)+SQR(v.z));
v.x*=fac.x;
v.y*=fac.x;
v.z*=fac.x;
return v;
}
// Random-rotation matrix Shoemake's method
void RandomArrayRotationMatrix(VECTOR *Cord,int n)
{
int i;
REAL R[3][3];
POINT p;
REAL R1,R2;
REAL X0,Y1,Y2;
REAL U0,U1,U2,U3;
REAL COEFI,COEFUU,COEFE;
X0=RandomNumber();
Y1=2.0*M_PI*RandomNumber();
Y2=2.0*M_PI*RandomNumber();
R1=sqrt(1.0-X0);
R2=sqrt(X0);
U0=cos(Y2)*R2;
U1=sin(Y1)*R1;
U2=cos(Y1)*R1;
U3=sin(Y2)*R2;
COEFI=2.0*U0*U0-1.0;
COEFUU=2.0;
COEFE=2.0*U0;
R[0][0]=COEFI+COEFUU*U1*U1;
R[1][1]=COEFI+COEFUU*U2*U2;
R[2][2]=COEFI+COEFUU*U3*U3;
R[1][2]=COEFUU*U2*U3-COEFE*U1;
R[2][0]=COEFUU*U3*U1-COEFE*U2;
R[0][1]=COEFUU*U1*U2-COEFE*U3;
R[2][1]=COEFUU*U3*U2+COEFE*U1;
R[0][2]=COEFUU*U1*U3+COEFE*U2;
R[1][0]=COEFUU*U2*U1+COEFE*U3;
for(i=0;i<n;i++)
{
p.x=Cord[i].x*R[0][0]+Cord[i].y*R[0][1]+Cord[i].z*R[0][2];
p.y=Cord[i].x*R[1][0]+Cord[i].y*R[1][1]+Cord[i].z*R[1][2];
p.z=Cord[i].x*R[2][0]+Cord[i].y*R[2][1]+Cord[i].z*R[2][2];
Cord[i]=p;
}
}
void RotationAroundXAxis(VECTOR *Cord,int n,REAL theta)
{
int i;
REAL w,s,c,rot[3][3];
c=cos(theta);
s=sin(theta);
rot[0][0]=1.0; rot[1][0]=0.0; rot[2][0]=0.0;
rot[0][1]=0.0; rot[1][1]=c; rot[2][1]=-s;
rot[0][2]=0.0; rot[1][2]=s; rot[2][2]=c;
for(i=0;i<n;i++)
{
w=Cord[i].x*rot[0][0]+Cord[i].y*rot[0][1]+Cord[i].z*rot[0][2];
s=Cord[i].x*rot[1][0]+Cord[i].y*rot[1][1]+Cord[i].z*rot[1][2];
c=Cord[i].x*rot[2][0]+Cord[i].y*rot[2][1]+Cord[i].z*rot[2][2];
Cord[i].x=w;
Cord[i].y=s;
Cord[i].z=c;
}
}
void RotationAroundYAxis(VECTOR *Cord,int n,REAL theta)
{
int i;
REAL w,s,c,rot[3][3];
c=cos(theta);
s=sin(theta);
rot[0][0]=c; rot[1][0]=0; rot[2][0]=s;
rot[0][1]=0; rot[1][1]=1.0; rot[2][1]=0;
rot[0][2]=-s; rot[1][2]=0; rot[2][2]=c;
for(i=0;i<n;i++)
{
w=Cord[i].x*rot[0][0]+Cord[i].y*rot[0][1]+Cord[i].z*rot[0][2];
s=Cord[i].x*rot[1][0]+Cord[i].y*rot[1][1]+Cord[i].z*rot[1][2];
c=Cord[i].x*rot[2][0]+Cord[i].y*rot[2][1]+Cord[i].z*rot[2][2];
Cord[i].x=w;
Cord[i].y=s;
Cord[i].z=c;
}
}
void RotationAroundZAxis(VECTOR *Cord,int n,REAL theta)
{
int i;
REAL w,s,c,rot[3][3];
c=cos(theta);
s=sin(theta);
rot[0][0]=c; rot[1][0]=-s; rot[2][0]=0;
rot[0][1]=s; rot[1][1]=c; rot[2][1]=0;
rot[0][2]=0; rot[1][2]=0; rot[2][2]=1.0;
for(i=0;i<n;i++)
{
w=Cord[i].x*rot[0][0]+Cord[i].y*rot[0][1]+Cord[i].z*rot[0][2];
s=Cord[i].x*rot[1][0]+Cord[i].y*rot[1][1]+Cord[i].z*rot[1][2];
c=Cord[i].x*rot[2][0]+Cord[i].y*rot[2][1]+Cord[i].z*rot[2][2];
Cord[i].x=w;
Cord[i].y=s;
Cord[i].z=c;
}
}
void RotationAroundXYZAxis(VECTOR v,VECTOR *Cord,int n,REAL theta)
{
int i;
REAL w,s,c,rot[3][3];
c=cos(theta);
w=1.0-c;
s=sqrt(1.0-c*c);
if(theta<0.0) s=-s;
rot[0][0]=(v.x)*(v.x)*w+c;
rot[0][1]=(v.x)*(v.y)*w+(v.z)*s;
rot[0][2]=(v.x)*(v.z)*w-(v.y)*s;
rot[1][0]=(v.x)*(v.y)*w-(v.z)*s;
rot[1][1]=(v.y)*(v.y)*w+c;
rot[1][2]=(v.y)*(v.z)*w+(v.x)*s;
rot[2][0]=(v.x)*(v.z)*w+(v.y)*s;
rot[2][1]=(v.y)*(v.z)*w-(v.x)*s;
rot[2][2]=(v.z)*(v.z)*w+c;
for(i=0;i<n;i++)
{
w=Cord[i].x*rot[0][0]+Cord[i].y*rot[0][1]+Cord[i].z*rot[0][2];
s=Cord[i].x*rot[1][0]+Cord[i].y*rot[1][1]+Cord[i].z*rot[1][2];
c=Cord[i].x*rot[2][0]+Cord[i].y*rot[2][1]+Cord[i].z*rot[2][2];
Cord[i].x=w;
Cord[i].y=s;
Cord[i].z=c;
}
}
// by Glenn Murray: 'Rotation About an Arbitrary Axis in 3 Dimensions'
// http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/
// tested with: http://twist-and-shout.appspot.com
void RotationArrayAroundXYZAxisAtPoint(POINT origin,VECTOR v,POINT *Cord,int n,REAL theta)
{
int i;
REAL s,c;
VECTOR p;
c=cos(theta);
s=sin(theta);
for(i=0;i<n;i++)
{
p=Cord[i];
Cord[i].x=(origin.x*(SQR(v.y)+SQR(v.z))-v.x*(origin.y*v.y+origin.z*v.z-v.x*p.x-v.y*p.y-v.z*p.z))*(1.0-c)+p.x*c+(-origin.z*v.y+origin.y*v.z-v.z*p.y+v.y*p.z)*s;
Cord[i].y=(origin.y*(SQR(v.x)+SQR(v.z))-v.y*(origin.x*v.x+origin.z*v.z-v.x*p.x-v.y*p.y-v.z*p.z))*(1.0-c)+p.y*c+( origin.z*v.x-origin.x*v.z+v.z*p.x-v.x*p.z)*s;
Cord[i].z=(origin.z*(SQR(v.x)+SQR(v.y))-v.z*(origin.x*v.x+origin.y*v.y-v.x*p.x-v.y*p.y-v.z*p.z))*(1.0-c)+p.z*c+(-origin.y*v.x+origin.x*v.y-v.y*p.x+v.x*p.y)*s;
}
}
VECTOR RotationAroundXYZAxisAtPoint(POINT origin,VECTOR v,POINT p,REAL theta)
{
REAL s,c;