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This is the
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╚══════╝╚═╝ ╚═════╝ ╚═════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚══════╝®
DEM simulation engine, released by
DCS Computing Gmbh, Linz, Austria
http://www.dcs-computing.com, office@dcs-computing.com
LIGGGHTS® is part of CFDEM®project:
http://www.liggghts.com | http://www.cfdem.com
Core developer and main author:
Christoph Kloss, christoph.kloss@dcs-computing.com
LIGGGHTS® is open-source, distributed under the terms of the GNU Public
License, version 2 or later. It 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. You should have
received a copy of the GNU General Public License along with LIGGGHTS®.
If not, see http://www.gnu.org/licenses . See also top-level README
and LICENSE files.
LIGGGHTS® and CFDEM® are registered trade marks of DCS Computing GmbH,
the producer of the LIGGGHTS® software and the CFDEM®coupling software
See http://www.cfdem.com/terms-trademark-policy for details.
-------------------------------------------------------------------------
Contributing author and copyright for this file:
(if not contributing author is listed, this file has been contributed
by the core developer)
Copyright 2012- DCS Computing GmbH, Linz
Copyright 2009-2012 JKU Linz
------------------------------------------------------------------------- */
#ifndef LMP_MATH_EXTRA_LIGGGHTS_H
#define LMP_MATH_EXTRA_LIGGGHTS_H
#include "pointers.h"
#include <math.h>
#include <stdio.h>
#include <string.h>
#include "error.h"
#include "vector_liggghts.h"
#include "math_extra.h"
#include "random_park.h"
#include "ctype.h"
#define TOLERANCE_ORTHO 1e-10
namespace MathExtraLiggghts {
inline void col_times3(const double m[3][3],const double *v, double *ans);
inline double mdet(const double m[3][3],LAMMPS_NS::Error *error);
//cubic root approx
inline double cbrt_5d(double d);
inline double cbrta_halleyd(const double a, const double R);
inline double halley_cbrt1d(double d);
//exp aproximation
inline double exp_fast(double x);
inline int min(int a,int b);
inline int max(int a,int b);
inline int abs(int a);
inline double min(double a,double b);
inline double max(double a,double b);
inline double min(double a,double b,double c);
inline double max(double a,double b,double c);
inline double min(double a,double b,double c,double d);
inline double min(double *input, int n,int &which);
inline double max(double *input, int n,int &which);
inline double min(int *input, int n,int &which);
inline double max(int *input, int n,int &which);
inline double abs(double a);
inline void matrix_invert_4x4_special(double matrix[4][4]);
inline void transpose3(const double m[3][3], double ans[3][3]);
inline int is_inside_tet(double *pos,double invmatrix[4][4]);
inline void local_coosys_to_cartesian(double * const global, const double * const local, const double * const ex_local, const double * const ey_local, const double * const ez_local);
inline void cartesian_coosys_to_local(double *local,double *global, double *ex_local, double *ey_local, double *ez_local,LAMMPS_NS::Error *error);
inline void cartesian_coosys_to_local_orthogonal(double *local,double *global, double *ex_local, double *ey_local, double *ez_local,LAMMPS_NS::Error *error);
// quaternion operations
inline bool is_unit_quat(const double *q);
inline void quat_normalize(double *q);
inline void qconjugate(const double * const q, double * const qc);
inline void quat_from_vec(const double *v, double *q);
inline void vec_from_quat(const double *q, double * const v);
inline void vec_quat_rotate(const double * const vec, const double * const quat, double *result);
inline void vec_quat_rotate(double * const vec, const double * const quat);
inline void vec_quat_rotate(int * const vec, const double * const quat) { UNUSED(vec); UNUSED(quat); }
inline void vec_quat_rotate(bool * const vec, const double * const quat) { UNUSED(vec); UNUSED(quat); }
inline void quat_diff(double *q_new, double *q_old, double *q_diff);
inline void angmom_from_omega(double *w,
double *ex, double *ey, double *ez,
double *idiag, double *m);
// double comparison, added by P.S.
inline bool compDouble(double const a, double const b, double const prec = 1e-13);
// calculate barycentrc coordinates of p w.r.t node, added by P.S.
inline void calcBaryTriCoords(double *p, double **edgeVec, double *edgeLen, double *bary);
inline void calcBaryTriCoords(double *p, double *edgeVec0, double *edgeVec1, double *edgeVec2, double *edgeLen, double *bary);
inline void random_unit_quat(LAMMPS_NS::RanPark *random,double *quat);
inline bool is_int(char *str);
inline void generateComplementBasis(double *uVec, double *vVec, double *direction);
// template signum function, added by A.A.
template <typename T>
int sgn(T val) {
return (T(0) < val) - (val < T(0));
}
// prime number test, JoKer
inline bool isPrime(int val);
};
/* ----------------------------------------------------------------------
matrix times col vector
------------------------------------------------------------------------- */
void MathExtraLiggghts::col_times3(const double m[3][3],const double *v, double *ans)
{
ans[0] = m[0][0]*v[0]+v[1]*m[1][0]+v[2]*m[2][0];
ans[1] = v[0]*m[0][1]+m[1][1]*v[1]+v[2]*m[2][1];
ans[2] = v[0]*m[0][2]+v[1]*m[1][2]+m[2][2]*v[2];
}
/* ----------------------------------------------------------------------
Matrix determinant
------------------------------------------------------------------------- */
double MathExtraLiggghts::mdet(const double m[3][3],LAMMPS_NS::Error *error)
{
UNUSED(error);
return ( -m[0][2]*m[1][1]*m[2][0] + m[0][1]*m[1][2]*m[2][0] + m[0][2]*m[1][0]*m[2][1] - m[0][0]*m[1][2]*m[2][1] - m[0][1]*m[1][0]*m[2][2] + m[0][0]*m[1][1]*m[2][2] );
}
/* ----------------------------------------------------------------------
Cubic root approx.
------------------------------------------------------------------------- */
inline double MathExtraLiggghts::cbrt_5d(double d)
{
const unsigned int B1 = 715094163;
double t = 0.0;
unsigned int* pt = (unsigned int*) &t;
unsigned int* px = (unsigned int*) &d;
pt[1]=px[1]/3+B1;
return t;
}
inline double MathExtraLiggghts::cbrta_halleyd(const double a, const double R)
{
const double a3 = a*a*a;
const double b= a * (a3 + R + R) / (a3 + a3 + R);
return b;
}
// cube root approximation using 1 iteration of Halley's method (double)
inline double MathExtraLiggghts::halley_cbrt1d(double d)
{
double a = cbrt_5d(d);
return cbrta_halleyd(a, d);
}
/* ----------------------------------------------------------------------
exp approx
------------------------------------------------------------------------- */
inline double MathExtraLiggghts::exp_fast(double x)
{
x = 1.0 + x / 256.0;
x *= x; x *= x; x *= x; x *= x;
x *= x; x *= x; x *= x; x *= x;
return x;
}
/* ----------------------------------------------------------------------
min max stuff
------------------------------------------------------------------------- */
int MathExtraLiggghts::min(int a,int b) { if (a<b) return a; return b;}
int MathExtraLiggghts::max(int a,int b) { if (a>b) return a; return b;}
double MathExtraLiggghts::min(double a,double b) { if (a<b) return a; return b;}
double MathExtraLiggghts::max(double a,double b) { if (a>b) return a; return b;}
double MathExtraLiggghts::min(double a,double b,double c)
{
double ab = MathExtraLiggghts::min(a,b);
if (ab<c) return ab;
return c;
}
double MathExtraLiggghts::max(double a,double b,double c)
{
double ab = MathExtraLiggghts::max(a,b);
if (ab<c) return c;
return ab;
}
double MathExtraLiggghts::min(double a,double b,double c,double d)
{
double ab = MathExtraLiggghts::min(a,b);
double cd = MathExtraLiggghts::min(c,d);
if (ab<cd) return ab;
return cd;
}
double MathExtraLiggghts::min(double *input, int n,int &which)
{
double min = input[0];
which = 0;
for(int i = 1; i < n; i++)
{
if(input[i] < min)
{
which = i;
min = input[i];
}
}
return min;
}
double MathExtraLiggghts::max(double *input, int n,int &which)
{
double max = input[0];
which = 0;
for(int i = 1; i < n; i++)
{
if(input[i] > max)
{
which = i;
max = input[i];
}
}
return max;
}
double MathExtraLiggghts::min(int *input, int n,int &which)
{
double min = input[0];
which = 0;
for(int i = 1; i < n; i++)
{
if(input[i] < min)
{
which = i;
min = input[i];
}
}
return min;
}
double MathExtraLiggghts::max(int *input, int n,int &which)
{
double max = input[0];
which = 0;
for(int i = 1; i < n; i++)
{
if(input[i] > max)
{
which = i;
max = input[i];
}
}
return max;
}
int MathExtraLiggghts::abs(int a) { if (a>0) return a; return -a;}
double MathExtraLiggghts::abs(double a) { if (a>0.) return a; return -a;}
/*----------------------------------------------------------------------
inverts a special 4x4 matrix that looks like this
m11 m12 m13 m14
m21 m22 m23 m24
m31 m32 m33 m34
1 1 1 1
------------------------------------------------------------------------- */
inline void MathExtraLiggghts::matrix_invert_4x4_special(double matrix[4][4])
{
double fac,invfac,v1x,v2x,v3x,v4x,v1y,v2y,v3y,v4y,v1z,v2z,v3z,v4z;
v1x = matrix[0][0]; v1y = matrix[1][0]; v1z = matrix[2][0];
v2x = matrix[0][1]; v2y = matrix[1][1]; v2z = matrix[2][1];
v3x = matrix[0][2]; v3y = matrix[1][2]; v3z = matrix[2][2];
v4x = matrix[0][3]; v4y = matrix[1][3]; v4z = matrix[2][3];
fac = -v1x*v2z*v3y+v1x*v2y*v3z+v2z*v3y*v4x-v2y*v3z*v4x+v1x*v2z*v4y-
v2z*v3x*v4y-v1x*v3z*v4y+v2x*v3z*v4y+v1z*
(v2x*v3y-v3y*v4x+v2y*(-v3x+v4x)-v2x*v4y+v3x*v4y)-
v1x*v2y*v4z+v2y*v3x*v4z+v1x*v3y*v4z-v2x*v3y*v4z+v1y*
(v2z*v3x-v2x*v3z-v2z*v4x+v3z*v4x+v2x*v4z-v3x*v4z);
invfac = 1./fac;
matrix[0][0] = (-v3z*v4y+v2z*(-v3y+v4y)+v2y*(v3z-v4z)+v3y*v4z)*invfac;
matrix[1][0] = (v1z*(v3y-v4y)+v3z*v4y-v3y*v4z+v1y*(-v3z+v4z))*invfac;
matrix[2][0] = (-v2z*v4y+v1z*(-v2y+v4y)+v1y*(v2z-v4z)+v2y*v4z)*invfac;
matrix[3][0] = (v1z*(v2y-v3y)+v2z*v3y-v2y*v3z+v1y*(-v2z+v3z))*invfac;
matrix[0][1] = (v2z*(v3x-v4x)+v3z*v4x-v3x*v4z+v2x*(-v3z+v4z))*invfac;
matrix[1][1] = (-v3z*v4x+v1z*(-v3x+v4x)+v1x*(v3z-v4z)+v3x*v4z)*invfac;
matrix[2][1] = (v1z*(v2x-v4x)+v2z*v4x-v2x*v4z+v1x*(-v2z+v4z))*invfac;
matrix[3][1] = (-v2z*v3x+v1z*(-v2x+v3x)+v1x*(v2z-v3z)+v2x*v3z)*invfac;
matrix[0][2] = (-v3y*v4x+v2y*(-v3x+v4x)+v2x*(v3y-v4y)+v3x*v4y)*invfac;
matrix[1][2] = (v1y*(v3x-v4x)+v3y*v4x-v3x*v4y+v1x*(-v3y+v4y))*invfac;
matrix[2][2] = (-v2y*v4x+v1y*(-v2x+v4x)+v1x*(v2y-v4y)+v2x*v4y)*invfac;
matrix[3][2] = (v1y*(v2x-v3x)+v2y*v3x-v2x*v3y+v1x*(-v2y+v3y))*invfac;
matrix[0][2] = (v2z*v3y*v4x-v2y*v3z*v4x-v2z*v3x*v4y+v2x*v3z*v4y+v2y*v3x*v4z-v2x*v3y*v4z)*invfac;
matrix[1][2] = (-v1z*v3y*v4x+v1y*v3z*v4x+v1z*v3x*v4y-v1x*v3z*v4y-v1y*v3x*v4z+v1x*v3y*v4z)*invfac;
matrix[2][2] = (v1z*v2y*v4x-v1y*v2z*v4x-v1z*v2x*v4y+v1x*v2z*v4y+v1y*v2x*v4z-v1x*v2y*v4z)*invfac;
matrix[3][2] = (-v1z*v2y*v3x+v1y*v2z*v3x+v1z*v2x*v3y-v1x*v2z*v3y-v1y*v2x*v3z+v1x*v2y*v3z)*invfac;
}
/* ----------------------------------------------------------------------
transpose mat1
------------------------------------------------------------------------- */
inline void MathExtraLiggghts::transpose3(const double m[3][3], double ans[3][3])
{
ans[0][0] = m[0][0];
ans[0][1] = m[1][0];
ans[0][2] = m[2][0];
ans[1][0] = m[0][1];
ans[1][1] = m[1][1];
ans[1][2] = m[2][1];
ans[2][0] = m[0][2];
ans[2][1] = m[1][2];
ans[2][2] = m[2][2];
}
/*----------------------------------------------------------------------
checks if a point is inside a tetrader, described by an inverse matrix
This inverse matrix is the the inverse of a special 4x4 matrix that looks like this
m11 m12 m13 m14
m21 m22 m23 m24
m31 m32 m33 m34
1 1 1 1
where m11,m21,m31 is vertex 1 etc.
------------------------------------------------------------------------- */
inline int MathExtraLiggghts::is_inside_tet(double *pos,double invmatrix[4][4])
{
double result[4];
result[0] = invmatrix[0][0] * pos[0] + invmatrix[0][1] * pos[1] + invmatrix[0][2] * pos[2] + invmatrix[0][3];
result[1] = invmatrix[1][0] * pos[0] + invmatrix[1][1] * pos[1] + invmatrix[1][2] * pos[2] + invmatrix[1][3];
result[2] = invmatrix[2][0] * pos[0] + invmatrix[2][1] * pos[1] + invmatrix[2][2] * pos[2] + invmatrix[2][3];
result[3] = invmatrix[3][0] * pos[0] + invmatrix[3][1] * pos[1] + invmatrix[3][2] * pos[2] + invmatrix[3][3];
if(max(result[0],max(result[1],max(result[2],result[3]))) > 1.0) return 0;
return 1;
}
/*----------------------------------------------------------------------
transform from local to global coords
------------------------------------------------------------------------- */
void MathExtraLiggghts::local_coosys_to_cartesian(double * const global, const double * const local, const double * const ex_local, const double * const ey_local, const double * const ez_local)
{
global[0] = local[0]*ex_local[0] + local[1]*ey_local[0] + local[2]*ez_local[0];
global[1] = local[0]*ex_local[1] + local[1]*ey_local[1] + local[2]*ez_local[1];
global[2] = local[0]*ex_local[2] + local[1]*ey_local[2] + local[2]*ez_local[2];
}
/*----------------------------------------------------------------------
transform from global to local coords
------------------------------------------------------------------------- */
void MathExtraLiggghts::cartesian_coosys_to_local(double *local,double *global, double *ex_local, double *ey_local, double *ez_local,LAMMPS_NS::Error *error)
{
UNUSED(error);
double M[3][3] = {{0.,0.,0.},{0.,0.,0.},{0.,0.,0.}};
double Mt[3][3] = {{0.,0.,0.},{0.,0.,0.},{0.,0.,0.}};
// set up the matrix
LAMMPS_NS::vectorCopy3D(ex_local,M[0]);
LAMMPS_NS::vectorCopy3D(ey_local,M[1]);
LAMMPS_NS::vectorCopy3D(ez_local,M[2]);
MathExtraLiggghts::transpose3(M,Mt);
// solve
MathExtra::mldivide3(Mt,global,local);
}
/*----------------------------------------------------------------------
transform from global to local coords
faster for orthogonal matrix
------------------------------------------------------------------------- */
void MathExtraLiggghts::cartesian_coosys_to_local_orthogonal(double *local,double *global, double *ex_local, double *ey_local, double *ez_local,LAMMPS_NS::Error *error)
{
// check if orthogonal
double dot1 = LAMMPS_NS::vectorDot3D(ex_local,ey_local);
double dot2 = LAMMPS_NS::vectorDot3D(ey_local,ez_local);
double dot3 = LAMMPS_NS::vectorDot3D(ez_local,ex_local);
int flag = dot1 > TOLERANCE_ORTHO || dot2 > TOLERANCE_ORTHO || dot3 > TOLERANCE_ORTHO;
if(flag) error->one(FLERR,"Insufficient accuracy: using MathExtraLiggghts::cartesian_coosys_to_local_orthogonal() for non-orthogonal coo-sys");
// solve
local[0] = global[0]*ex_local[0] + global[1]*ex_local[1] + global[2]*ex_local[2];
local[1] = global[0]*ey_local[0] + global[1]*ey_local[1] + global[2]*ey_local[2];
local[2] = global[0]*ez_local[0] + global[1]*ez_local[1] + global[2]*ez_local[2];
}
/* ----------------------------------------------------------------------
conjugate of a quaternion: qc = conjugate of q
assume q is of unit length
------------------------------------------------------------------------- */
void MathExtraLiggghts::qconjugate(const double * const q, double * const qc)
{
qc[0] = q[0];
qc[1] = -q[1];
qc[2] = -q[2];
qc[3] = -q[3];
}
/* ----------------------------------------------------------------------
construct quaternion4 from vector3
------------------------------------------------------------------------- */
void MathExtraLiggghts::quat_from_vec(const double *v, double *q)
{
q[0] = 0.;
q[1] = v[0];
q[2] = v[1];
q[3] = v[2];
}
/* ----------------------------------------------------------------------
construct vector3 from quaternion4
------------------------------------------------------------------------- */
void MathExtraLiggghts::vec_from_quat(const double *q, double * const v)
{
v[0] = q[1];
v[1] = q[2];
v[2] = q[3];
}
/*----------------------------------------------------------------------
rotoate vector by quaternion
------------------------------------------------------------------------- */
void MathExtraLiggghts::vec_quat_rotate(const double * const vec, const double * const quat, double * const result)
{
double vecQ[4], resultQ[4], quatC[4], temp[4];
// construct quaternion (0,vec)
quat_from_vec(vec,vecQ);
// conjugate initial quaternion
qconjugate(quat,quatC);
// rotate by quaternion multiplications
MathExtra::quatquat(quat,vecQ,temp);
MathExtra::quatquat(temp,quatC,resultQ);
// return result
vec_from_quat(resultQ,result);
}
/*----------------------------------------------------------------------
rotoate vector by quaternion
------------------------------------------------------------------------- */
void MathExtraLiggghts::vec_quat_rotate(double * const vec, const double * const quat)
{
double vecQ[4], resultQ[4], quatC[4], temp[4], result[3];
// construct quaternion (0,vec)
quat_from_vec(vec,vecQ);
// conjugate initial quaternion
qconjugate(quat,quatC);
// rotate by quaternion multiplications
MathExtra::quatquat(quat,vecQ,temp);
MathExtra::quatquat(temp,quatC,resultQ);
// return result
vec_from_quat(resultQ,result);
LAMMPS_NS::vectorCopy3D(result,vec);
}
/* ----------------------------------------------------------------------
compute angular momentum from omega, both in space frame
only know Idiag so need to do M = Iw in body frame
ex,ey,ez are column vectors of rotation matrix P
wbody = P_transpose wspace
Mbody = Idiag wbody
Mspace = P Mbody
------------------------------------------------------------------------- */
inline void MathExtraLiggghts::angmom_from_omega(double *w,
double *ex, double *ey, double *ez,
double *idiag, double *m)
{
double mbody[3];
mbody[0] = (w[0]*ex[0] + w[1]*ex[1] + w[2]*ex[2]) * idiag[0];
mbody[1] = (w[0]*ey[0] + w[1]*ey[1] + w[2]*ey[2]) * idiag[1];
mbody[2] = (w[0]*ez[0] + w[1]*ez[1] + w[2]*ez[2]) * idiag[2];
m[0] = mbody[0]*ex[0] + mbody[1]*ey[0] + mbody[2]*ez[0];
m[1] = mbody[0]*ex[1] + mbody[1]*ey[1] + mbody[2]*ez[1];
m[2] = mbody[0]*ex[2] + mbody[1]*ey[2] + mbody[2]*ez[2];
}
/* ----------------------------------------------------------------------
Check if is unit quaternion
------------------------------------------------------------------------- */
inline bool MathExtraLiggghts::is_unit_quat(const double *q)
{
return MathExtraLiggghts::compDouble(LAMMPS_NS::vectorMag4DSquared(q),1.0,1e-6);
}
/* ----------------------------------------------------------------------
normalize a quaternion
------------------------------------------------------------------------- */
inline void MathExtraLiggghts::quat_normalize(double *q)
{
double norm = 1.0 / ::sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
q[0] *= norm;
q[1] *= norm;
q[2] *= norm;
q[3] *= norm;
}
/* ----------------------------------------------------------------------
calculate the quaternion that would rotate q_old into q_new
------------------------------------------------------------------------- */
inline void MathExtraLiggghts::quat_diff(double *q_new, double *q_old, double *q_diff)
{
double q_old_c[4];
// q_diff = q_old^-1 * q_new
qconjugate(q_old,q_old_c);
MathExtra::quatquat(q_old_c,q_new,q_diff);
}
/* -----------------------------------------------------------------------------
* compare two doubles by using their integer representation
* source: http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm
-------------------------------------------------------------------------------*/
bool MathExtraLiggghts::compDouble(double const a, double const b, double const prec)
{
if (a == b)
return true;
if (b == 0)
return a < prec && a > -prec;
double x = (a-b);//b;
return x < prec && x > -prec;
}
/* -----------------------------------------------------------------------------
* calculate barycentric coordinates of a given point (in the triangle plane)
* should work for any point, at least analytics claim this ...
* ap is a vector from node[0] to the point
* edgeVec are assumed to be unit vectors
* source: http://www.blackpawn.com/texts/pointinpoly/default.html
* hints on _which_ barycentric coordinates are computed by this method
* can be found on wikipedia - u_{link} = bary[1] and v_{link} = bary[2]
-------------------------------------------------------------------------------*/
void MathExtraLiggghts::calcBaryTriCoords(double *ap, double **edgeVec, double *edgeLen, double *bary)
{
double a = LAMMPS_NS::vectorDot3D(ap,edgeVec[0]);
double b = LAMMPS_NS::vectorDot3D(ap,edgeVec[2]);
double c = LAMMPS_NS::vectorDot3D(edgeVec[0],edgeVec[2]);
double oneMinCSqr = 1 - c*c;
bary[1] = (a - b*c)/(edgeLen[0] * oneMinCSqr);
bary[2] = (a*c - b)/(edgeLen[2] * oneMinCSqr);
bary[0] = 1. - bary[1] - bary[2];
}
void MathExtraLiggghts::calcBaryTriCoords(double *ap, double *edgeVec0, double *edgeVec1, double *edgeVec2,
double *edgeLen, double *bary)
{
UNUSED(edgeVec1);
double a = LAMMPS_NS::vectorDot3D(ap,edgeVec0);
double b = LAMMPS_NS::vectorDot3D(ap,edgeVec2);
double c = LAMMPS_NS::vectorDot3D(edgeVec0,edgeVec2);
double oneMinCSqr = 1 - c*c;
bary[1] = (a - b*c)/(edgeLen[0] * oneMinCSqr);
bary[2] = (a*c - b)/(edgeLen[2] * oneMinCSqr);
bary[0] = 1. - bary[1] - bary[2];
}
/* ----------------------------------------------------------------------
generate random unit quaternion
from http://planning.cs.uiuc.edu/node198.html
------------------------------------------------------------------------- */
void MathExtraLiggghts::random_unit_quat(LAMMPS_NS::RanPark *random,double *quat)
{
double u1 = random->uniform();
double u2 = random->uniform();
double u3 = random->uniform();
double h1 = ::sqrt(1.-u1);
double h2 = ::sqrt(u1);
quat[0] = h1 * ::sin(2.*M_PI*u2);
quat[1] = h1 * ::cos(2.*M_PI*u2);
quat[2] = h2 * ::sin(2.*M_PI*u3);
quat[3] = h2 * ::cos(2.*M_PI*u3);
}
/* ----------------------------------------------------------------------
check if char * string is int
------------------------------------------------------------------------- */
bool MathExtraLiggghts::is_int(char *str)
{
size_t n = strlen(str);
for (size_t i = 0; i < n; ++i)
if (isdigit(str[i]) == 0)
return false;
return true;
}
/* ----------------------------------------------------------------------
generate complement basis
------------------------------------------------------------------------- */
void MathExtraLiggghts::generateComplementBasis(double *uVec, double *vVec, double *direction)
{
double invLength;
if ( abs(direction[0]) >= abs(direction[1]) )
{
// direction.x or direction.z is the largest magnitude component, swap them
invLength = 1.0/::sqrt ( direction[0]*direction[0]
+direction[2]*direction[2]
);
uVec[0] = -direction[2]*invLength;
uVec[1] = 0.0;
uVec[2] = direction[0]*invLength;
vVec[0] = direction[1]*uVec[2];
vVec[1] = direction[2]*uVec[0]
- direction[0]*uVec[2];
vVec[2] = -direction[1]*uVec[0];
}
else
{
// direction.y or direction.z is the largest magnitude component, swap them
invLength = 1.0/::sqrt ( direction[1]*direction[1]
+direction[2]*direction[2]
);
uVec[0] = 0.0;
uVec[1] = direction[2]*invLength;
uVec[2] = -direction[1]*invLength;
vVec[0] = direction[1]*uVec[2]
- direction[2]*uVec[1];
vVec[1] = -direction[0]*uVec[2];
vVec[2] = direction[0]*uVec[1];
}
}
/* ----------------------------------------------------------------------
check if integer is a prime number (primes are 6k+-1)
------------------------------------------------------------------------- */
bool MathExtraLiggghts::isPrime(int val)
{
if (val < 2)
return false;
else if (val == 2)
return true;
else if (val == 3)
return true;
else if (val % 2 == 0)
return false;
else if (val % 3 == 0)
return false;
// max range is up to square-root
int testTo = static_cast<int>(floor(::sqrt(static_cast<double>(val))));
int test = 5;
int width = 2;
while ( test <= testTo )
{
if (val % test == 0)
return false;
test += width;
width = 6 - width;
}
return true;
}
#endif
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