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Commit 68e02e80 authored by Rossen Apostolov's avatar Rossen Apostolov
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Combined the Ewald and PME routines into a single one and added calculation of vdW interactions.

parent 351f6455
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Showing with 1327 additions and 388 deletions
platforms/reference/src/SimTKReference/pme.cpp → platforms/reference/src/SimTKReference/PME.cpp
View file @ 68e02e80
......@@ -33,7 +33,7 @@
#include <stdio.h>
#include <stdlib.h>
#include "pme.h"
#include "PME.h"
#include "fftpack.h"
......
platforms/reference/src/SimTKReference/ReferenceLJCoulombIxn.cpp
View file @ 68e02e80
......@@ -31,8 +31,7 @@
#include "../SimTKUtilities/SimTKOpenMMUtilities.h"
#include "ReferenceLJCoulombIxn.h"
#include "ReferenceForce.h"
#include "pme.h"
#include "PME.h"
// In case we're using some primitive version of Visual Studio this will
// make sure that erf() and erfc() are defined.
......@@ -233,40 +232,80 @@ int ReferenceLJCoulombIxn::calculateEwaldIxn( int numberOfAtoms, RealOpenMM** at
#include "../SimTKUtilities/RealTypeSimTk.h"
typedef std::complex<RealOpenMM> d_complex;
int kmax = std::max(numRx, std::max(numRy,numRz));
static const RealOpenMM epsilon = 1.0;
static const RealOpenMM one = 1.0;
static const RealOpenMM six = 6.0;
static const RealOpenMM twelve = 12.0;
int kmax = std::max(numRx, std::max(numRy,numRz));
RealOpenMM factorEwald = -1 / (4*alphaEwald*alphaEwald);
RealOpenMM SQRT_PI = sqrt(PI);
RealOpenMM TWO_PI = 2.0 * PI;
static const RealOpenMM epsilon = 1.0;
static const RealOpenMM one = 1.0;
RealOpenMM recipCoeff = (RealOpenMM)(4*PI/(periodicBoxSize[0] * periodicBoxSize[1] * periodicBoxSize[2]) /epsilon);
RealOpenMM selfEwaldEnergy = 0.0;
RealOpenMM realSpaceEwaldEnergy = 0.0;
RealOpenMM recipEnergy = 0.0;
RealOpenMM vdwEnergy = 0.0;
// **************************************************************************************
// SELF ENERGY
// **************************************************************************************
for( int atomID = 0; atomID < numberOfAtoms; atomID++ ){
selfEwaldEnergy = selfEwaldEnergy + atomParameters[atomID][QIndex]*atomParameters[atomID][QIndex];
selfEwaldEnergy = atomParameters[atomID][QIndex]*atomParameters[atomID][QIndex] * alphaEwald/SQRT_PI;
if( totalEnergy )
*totalEnergy -= selfEwaldEnergy;
if( energyByAtom ){
energyByAtom[atomID] -= selfEwaldEnergy;
}
}
selfEwaldEnergy = selfEwaldEnergy * alphaEwald/SQRT_PI ;
// **************************************************************************************
// RECIPROCAL SPACE EWALD ENERGY AND FORCES
// **************************************************************************************
// setup reciprocal box
// PME
if (pme) {
pme_t pmedata; /* abstract handle for PME data */
int ngrid[3];
RealOpenMM virial[3][3];
/* PME grid dimensions.
* We typically want to set this as the spacing rather than absolute dimensions, but
* to be able to reproduce results from other programs (e.g. Gromacs) we need to be
* able to set exact grid dimenisions occasionally.
*/
ngrid[0] = 16;
ngrid[1] = 16;
ngrid[2] = 16;
pme_init(&pmedata,alphaEwald,numberOfAtoms,ngrid,4,1);
pme_exec(pmedata,atomCoordinates,forces,atomParameters,periodicBoxSize,&recipEnergy,virial);
if( totalEnergy )
*totalEnergy += recipEnergy;
if( energyByAtom )
for(int n = 0; n < numberOfAtoms; n++)
energyByAtom[n] += recipEnergy;
}
// Ewald method
else if (ewald) {
// setup reciprocal box
RealOpenMM recipBoxSize[3] = { TWO_PI / periodicBoxSize[0], TWO_PI / periodicBoxSize[1], TWO_PI / periodicBoxSize[2]};
// setup K-vectors
// setup K-vectors
#define EIR(x, y, z) eir[(x)*numberOfAtoms*3+(y)*3+z]
vector<d_complex> eir(kmax*numberOfAtoms*3);
......@@ -292,7 +331,8 @@ int ReferenceLJCoulombIxn::calculateEwaldIxn( int numberOfAtoms, RealOpenMM** at
EIR(j, i, m) = EIR(j-1, i, m) * EIR(1, i, m);
}
// calculate reciprocal space energy and forces
// calculate reciprocal space energy and forces
int lowry = 0;
int lowrz = 1;
......@@ -335,231 +375,92 @@ int ReferenceLJCoulombIxn::calculateEwaldIxn( int numberOfAtoms, RealOpenMM** at
ss += tab_qxyz[n].imag();
}
RealOpenMM kz = rz * recipBoxSize[2];
RealOpenMM k2 = kx * kx + ky * ky + kz * kz;
RealOpenMM ak = exp(k2*factorEwald) / k2;
recipEnergy += ak * ( cs * cs + ss * ss);
for(int n = 0; n < numberOfAtoms; n++) {
RealOpenMM force = ak * (cs * tab_qxyz[n].imag() - ss * tab_qxyz[n].real());
forces[n][0] += 2 * recipCoeff * force * kx ;
forces[n][1] += 2 * recipCoeff * force * ky ;
forces[n][2] += 2 * recipCoeff * force * kz ;
}
lowrz = 1 - numRz;
}
lowry = 1 - numRy;
}
}
recipEnergy *= recipCoeff;
// **************************************************************************************
// SHORT-RANGE ENERGY AND FORCES
// **************************************************************************************
RealOpenMM deltaR[2][ReferenceForce::LastDeltaRIndex];
recipEnergy = recipCoeff * ak * ( cs * cs + ss * ss);
for( int atomID1 = 0; atomID1 < numberOfAtoms; atomID1++ ){
for( int atomID2 = atomID1 + 1; atomID2 < numberOfAtoms; atomID2++ ){
if( totalEnergy )
*totalEnergy += recipEnergy;
ReferenceForce::getDeltaRPeriodic( atomCoordinates[atomID2], atomCoordinates[atomID1], periodicBoxSize, deltaR[0] );
RealOpenMM r = deltaR[0][ReferenceForce::RIndex];
RealOpenMM r2 = deltaR[0][ReferenceForce::R2Index];
RealOpenMM inverseR = one/(deltaR[0][ReferenceForce::RIndex]);
if( energyByAtom )
for(int n = 0; n < numberOfAtoms; n++)
energyByAtom[n] += recipEnergy;
realSpaceEwaldEnergy =
(RealOpenMM)(realSpaceEwaldEnergy + atomParameters[atomID1][QIndex]*atomParameters[atomID2][QIndex]*inverseR*erfc(alphaEwald*r));
lowrz = 1 - numRz;
}
lowry = 1 - numRy;
}
// allocate and initialize exclusion array
vector<int> exclusionIndices(numberOfAtoms);
for( int ii = 0; ii < numberOfAtoms; ii++ ){
exclusionIndices[ii] = -1;
}
for( int ii = 0; ii < numberOfAtoms; ii++ ){
// set exclusions
for( int jj = 1; jj <= exclusions[ii][0]; jj++ ){
exclusionIndices[exclusions[ii][jj]] = ii;
}
// loop over atom pairs
else {
std::stringstream message;
message << " Wrong method for Ewald summation, Aborting" << std::endl;
SimTKOpenMMLog::printError( message );
}
for( int jj = ii+1; jj < numberOfAtoms; jj++ ){
// **************************************************************************************
// SHORT-RANGE ENERGY AND FORCES
// **************************************************************************************
if( exclusionIndices[jj] != ii ){
for (int i = 0; i < (int) neighborList->size(); i++) {
OpenMM::AtomPair pair = (*neighborList)[i];
int ii = pair.first;
int jj = pair.second;
RealOpenMM deltaR[2][ReferenceForce::LastDeltaRIndex];
ReferenceForce::getDeltaRPeriodic( atomCoordinates[jj], atomCoordinates[ii], periodicBoxSize, deltaR[0] );
RealOpenMM r = deltaR[0][ReferenceForce::RIndex];
RealOpenMM r2 = deltaR[0][ReferenceForce::R2Index];
RealOpenMM inverseR = one/(deltaR[0][ReferenceForce::RIndex]);
RealOpenMM alphaR = alphaEwald * r;
realSpaceEwaldEnergy =
(RealOpenMM)(realSpaceEwaldEnergy + atomParameters[ii][QIndex]*atomParameters[jj][QIndex]*inverseR*erfc(alphaR));
RealOpenMM dEdR = atomParameters[ii][QIndex] * atomParameters[jj][QIndex] * inverseR * inverseR * inverseR;
dEdR = (RealOpenMM)(dEdR * (erfc(alphaR) + 2 * alphaR * exp ( - alphaR * alphaR) / SQRT_PI ));
RealOpenMM sig = atomParameters[ii][SigIndex] + atomParameters[jj][SigIndex];
RealOpenMM sig2 = inverseR*sig;
sig2 *= sig2;
RealOpenMM sig6 = sig2*sig2*sig2;
RealOpenMM eps = atomParameters[ii][EpsIndex]*atomParameters[jj][EpsIndex];
dEdR += eps*( twelve*sig6 - six )*sig6;
// accumulate forces
for( int kk = 0; kk < 3; kk++ ){
RealOpenMM force = dEdR*deltaR[0][kk];
forces[ii][kk] += force;
forces[jj][kk] -= force;
}
}
}
}
// ***********************************************************************
if( totalEnergy ) {
*totalEnergy += recipEnergy + realSpaceEwaldEnergy - selfEwaldEnergy;
}
return ReferenceForce::DefaultReturn;
}
/**---------------------------------------------------------------------------------------
Calculate PME ixn
@param numberOfAtoms number of atoms
@param atomCoordinates atom coordinates
@param atomParameters atom parameters atomParameters[atomIndex][paramterIndex]
@param exclusions atom exclusion indices exclusions[atomIndex][atomToExcludeIndex]
exclusions[atomIndex][0] = number of exclusions
exclusions[atomIndex][1-no.] = atom indices of atoms to excluded from
interacting w/ atom atomIndex
@param fixedParameters non atom parameters (not currently used)
@param forces force array (forces added)
@param energyByAtom atom energy
@param totalEnergy total energy
@return ReferenceForce::DefaultReturn
--------------------------------------------------------------------------------------- */
int ReferenceLJCoulombIxn::calculatePMEIxn( int numberOfAtoms, RealOpenMM** atomCoordinates,
RealOpenMM** atomParameters, int** exclusions,
RealOpenMM* fixedParameters, RealOpenMM** forces,
RealOpenMM* energyByAtom, RealOpenMM* totalEnergy) const {
RealOpenMM SQRT_PI = sqrt(PI);
static const RealOpenMM one = 1.0;
RealOpenMM selfEwaldEnergy = 0.0;
RealOpenMM realSpaceEwaldEnergy = 0.0;
RealOpenMM recipEnergy = 0.0;
// **************************************************************************************
// SELF ENERGY
// **************************************************************************************
for( int atomID = 0; atomID < numberOfAtoms; atomID++ ){
selfEwaldEnergy = selfEwaldEnergy + atomParameters[atomID][QIndex]*atomParameters[atomID][QIndex];
}
selfEwaldEnergy = selfEwaldEnergy * alphaEwald/SQRT_PI ;
// **************************************************************************************
// RECIPROCAL SPACE EWALD ENERGY AND FORCES
// **************************************************************************************
pme_t pmedata; /* abstract handle for PME data */
int ngrid[3];
RealOpenMM virial[3][3];
/* PME grid dimensions.
* We typically want to set this as the spacing rather than absolute dimensions, but
* to be able to reproduce results from other programs (e.g. Gromacs) we need to be
* able to set exact grid dimenisions occasionally.
*/
ngrid[0] = 16;
ngrid[1] = 16;
ngrid[2] = 16;
pme_init(&pmedata,alphaEwald,numberOfAtoms,ngrid,4,1);
pme_exec(pmedata,atomCoordinates,forces,atomParameters,periodicBoxSize,&recipEnergy,virial);
// **************************************************************************************
// SHORT-RANGE ENERGY AND FORCES
// **************************************************************************************
RealOpenMM deltaR[2][ReferenceForce::LastDeltaRIndex];
for( int atomID1 = 0; atomID1 < numberOfAtoms; atomID1++ ){
for( int atomID2 = atomID1 + 1; atomID2 < numberOfAtoms; atomID2++ ){
ReferenceForce::getDeltaRPeriodic( atomCoordinates[atomID2], atomCoordinates[atomID1], periodicBoxSize, deltaR[0] );
RealOpenMM r = deltaR[0][ReferenceForce::RIndex];
RealOpenMM r2 = deltaR[0][ReferenceForce::R2Index];
RealOpenMM inverseR = one/(deltaR[0][ReferenceForce::RIndex]);
realSpaceEwaldEnergy =
(RealOpenMM)(realSpaceEwaldEnergy + atomParameters[atomID1][QIndex]*atomParameters[atomID2][QIndex]*inverseR*erfc(alphaEwald*r));
}
}
// allocate and initialize exclusion array
vector<int> exclusionIndices(numberOfAtoms);
for( int ii = 0; ii < numberOfAtoms; ii++ ){
exclusionIndices[ii] = -1;
}
// accumulate energies
for( int ii = 0; ii < numberOfAtoms; ii++ ){
realSpaceEwaldEnergy = atomParameters[ii][QIndex]*atomParameters[jj][QIndex]*inverseR*erfc(alphaR);
vdwEnergy = eps*(sig6-one)*sig6;
// set exclusions
if( totalEnergy )
*totalEnergy += realSpaceEwaldEnergy + vdwEnergy;
for( int jj = 1; jj <= exclusions[ii][0]; jj++ ){
exclusionIndices[exclusions[ii][jj]] = ii;
if( energyByAtom ){
energyByAtom[ii] += realSpaceEwaldEnergy + vdwEnergy;
energyByAtom[jj] += realSpaceEwaldEnergy + vdwEnergy;
}
// loop over atom pairs
for( int jj = ii+1; jj < numberOfAtoms; jj++ ){
if( exclusionIndices[jj] != ii ){
ReferenceForce::getDeltaRPeriodic( atomCoordinates[jj], atomCoordinates[ii], periodicBoxSize, deltaR[0] );
RealOpenMM r = deltaR[0][ReferenceForce::RIndex];
RealOpenMM r2 = deltaR[0][ReferenceForce::R2Index];
RealOpenMM inverseR = one/(deltaR[0][ReferenceForce::RIndex]);
RealOpenMM alphaR = alphaEwald * r;
realSpaceEwaldEnergy =
(RealOpenMM)(realSpaceEwaldEnergy + atomParameters[ii][QIndex]*atomParameters[jj][QIndex]*inverseR*erfc(alphaR));
RealOpenMM dEdR = atomParameters[ii][QIndex] * atomParameters[jj][QIndex] * inverseR * inverseR * inverseR;
dEdR = (RealOpenMM)(dEdR * (erfc(alphaR) + 2 * alphaR * exp ( - alphaR * alphaR) / SQRT_PI ));
for( int kk = 0; kk < 3; kk++ ){
RealOpenMM force = dEdR*deltaR[0][kk];
forces[ii][kk] += force;
forces[jj][kk] -= force;
}
}
}
}
// ***********************************************************************
if( totalEnergy ) {
*totalEnergy += recipEnergy + realSpaceEwaldEnergy - selfEwaldEnergy;
}
return ReferenceForce::DefaultReturn;
}
......@@ -590,10 +491,8 @@ int ReferenceLJCoulombIxn::calculatePairIxn( int numberOfAtoms, RealOpenMM** ato
RealOpenMM* fixedParameters, RealOpenMM** forces,
RealOpenMM* energyByAtom, RealOpenMM* totalEnergy ) const {
if (ewald)
if (ewald || pme)
return calculateEwaldIxn(numberOfAtoms, atomCoordinates, atomParameters, exclusions, fixedParameters, forces, energyByAtom, totalEnergy);
if (pme)
return calculatePMEIxn(numberOfAtoms, atomCoordinates, atomParameters, exclusions, fixedParameters, forces, energyByAtom, totalEnergy);
if (cutoff) {
for (int i = 0; i < (int) neighborList->size(); i++) {
OpenMM::AtomPair pair = (*neighborList)[i];
......
platforms/reference/tests/TestReferenceEwald.cpp
View file @ 68e02e80
......@@ -49,6 +49,41 @@ using namespace std;
const double TOL = 1e-5;
void testLargeSystem() {
ReferencePlatform platform;
System system;
for (int i = 0; i < 500; i++)
system.addParticle(22.99);
for (int i = 0; i < 500; i++)
system.addParticle(35.45);
VerletIntegrator integrator(0.01);
NonbondedForce* nonbonded = new NonbondedForce();
for (int i = 0; i < 500; i++)
nonbonded->addParticle(1.0, 1.0,0.0);
// nonbonded->addParticle(1.0, 0.33284,0.0115897);
for (int i = 0; i < 500; i++)
nonbonded->addParticle(-1.0, 1.0,0.0);
// nonbonded->addParticle(-1.0, 0.440104,0.4184);
nonbonded->setNonbondedMethod(NonbondedForce::PME);
const double cutoff = 1.0;
nonbonded->setCutoffDistance(cutoff);
nonbonded->setPeriodicBoxVectors(Vec3(2.82, 0, 0), Vec3(0, 2.82, 0), Vec3(0, 0, 2.82));
nonbonded->setEwaldErrorTolerance(TOL);
system.addForce(nonbonded);
Context context(system, integrator, platform);
vector<Vec3> positions(1000);
#include "nacl_crystal.dat"
context.setPositions(positions);
State state = context.getState(State::Forces | State::Energy);
const vector<Vec3>& forces = state.getForces();
// cout << "force 0: " << forces[0] << endl;
// cout << "force 1: " << forces[1] << endl;
cout << "PotentialEnergy: " << state.getPotentialEnergy() << endl;
ASSERT_EQUAL_TOL(-430355, state.getPotentialEnergy(), 100*TOL);
// ASSERT_EQUAL_VEC(Vec3(-123.711, 64.1877, -302.716), forces[0], 10*TOL);
// ASSERT_EQUAL_VEC(Vec3(123.711, -64.1877, 302.716), forces[1], 10*TOL);
}
void testEwald() {
ReferencePlatform platform;
System system;
......@@ -58,6 +93,9 @@ void testEwald() {
NonbondedForce* nonbonded = new NonbondedForce();
nonbonded->addParticle(1.0, 1, 0);
nonbonded->addParticle(-1.0, 1, 0);
// Sodium Chloride
// nonbonded->addParticle(1.0, 0.33284,0.0115897);
// nonbonded->addParticle(-1.0, 0.440104,0.4184);
nonbonded->setNonbondedMethod(NonbondedForce::Ewald);
const double cutoff = 2.0;
nonbonded->setCutoffDistance(cutoff);
......@@ -71,9 +109,9 @@ void testEwald() {
context.setPositions(positions);
State state = context.getState(State::Forces | State::Energy);
const vector<Vec3>& forces = state.getForces();
cout << "force 0: " << forces[0] << endl;
cout << "force 1: " << forces[1] << endl;
cout << "PotentialEnergy: " << state.getPotentialEnergy() << endl;
// cout << "force 0: " << forces[0] << endl;
// cout << "force 1: " << forces[1] << endl;
// cout << "PotentialEnergy: " << state.getPotentialEnergy() << endl;
ASSERT_EQUAL_VEC(Vec3(-123.711, 64.1877, -302.716), forces[0], 10*TOL);
ASSERT_EQUAL_VEC(Vec3(123.711, -64.1877, 302.716), forces[1], 10*TOL);
}
......@@ -101,48 +139,7 @@ void testPME() {
system.addForce(nonbonded);
Context context(system, integrator, platform);
vector<Vec3> positions(42);
positions[0] = Vec3( 0.23,0.628,0.113);
positions[1] = Vec3(0.137,0.626, 0.15);
positions[2] = Vec3(0.231,0.589,0.021);
positions[3] = Vec3(-0.307,-0.351,0.703);
positions[4] = Vec3(-0.364,-0.367,0.784);
positions[5] = Vec3(-0.366,-0.341,0.623);
positions[6] = Vec3(-0.569,-0.634,-0.439);
positions[7] = Vec3(-0.532,-0.707,-0.497);
positions[8] = Vec3(-0.517,-0.629,-0.354);
positions[9] = Vec3(-0.871, 0.41,-0.62);
positions[10] = Vec3(-0.948,0.444,-0.566);
positions[11] = Vec3(-0.905,0.359,-0.699);
positions[12] = Vec3(0.249,-0.077,-0.621);
positions[13] = Vec3(0.306,-0.142,-0.571);
positions[14] = Vec3(0.233,-0.11,-0.714);
positions[15] = Vec3(0.561,0.222,-0.715);
positions[16] = Vec3(0.599,0.138,-0.678);
positions[17] = Vec3(0.473,0.241,-0.671);
positions[18] = Vec3(-0.515,-0.803,-0.628);
positions[19] = Vec3(-0.491,-0.866,-0.702);
positions[20] = Vec3(-0.605,-0.763,-0.646);
positions[21] = Vec3(-0.021,0.175,-0.899);
positions[22] = Vec3(0.018, 0.09,-0.935);
positions[23] = Vec3(-0.119,0.177,-0.918);
positions[24] = Vec3(-0.422,0.856,-0.464);
positions[25] = Vec3(-0.479,0.908,-0.527);
positions[26] = Vec3(-0.326,0.868,-0.488);
positions[27] = Vec3(-0.369,-0.095,-0.903);
positions[28] = Vec3(-0.336,-0.031,-0.972);
positions[29] = Vec3(-0.303,-0.101,-0.828);
positions[30] = Vec3(0.594,0.745,0.652);
positions[31] = Vec3(0.644, 0.83,0.633);
positions[32] = Vec3(0.506,0.747,0.604);
positions[33] = Vec3(-0.157,-0.375,-0.758);
positions[34] = Vec3(-0.25, -0.4,-0.785);
positions[35] = Vec3(-0.131,-0.425,-0.676);
positions[36] = Vec3(0.618,-0.295,-0.578);
positions[37] = Vec3(0.613,-0.213,-0.521);
positions[38] = Vec3(0.707,-0.298,-0.623);
positions[39] = Vec3(0.039,-0.785, 0.3);
positions[40] = Vec3(0.138,-0.796,0.291);
positions[41] = Vec3(-0.001,-0.871,0.332);
#include "water.dat"
context.setPositions(positions);
State state = context.getState(State::Forces | State::Energy);
const vector<Vec3>& forces = state.getForces();
......@@ -156,6 +153,7 @@ positions[41] = Vec3(-0.001,-0.871,0.332);
int main() {
try {
testLargeSystem();
testEwald();
testPME();
}
......
platforms/reference/tests/nacl_crystal.dat 0 → 100644
View file @ 68e02e80
This diff is collapsed.
platforms/reference/tests/water.dat 0 → 100644
View file @ 68e02e80
positions[0] = Vec3( 0.23,0.628,0.113);
positions[1] = Vec3(0.137,0.626, 0.15);
positions[2] = Vec3(0.231,0.589,0.021);
positions[3] = Vec3(-0.307,-0.351,0.703);
positions[4] = Vec3(-0.364,-0.367,0.784);
positions[5] = Vec3(-0.366,-0.341,0.623);
positions[6] = Vec3(-0.569,-0.634,-0.439);
positions[7] = Vec3(-0.532,-0.707,-0.497);
positions[8] = Vec3(-0.517,-0.629,-0.354);
positions[9] = Vec3(-0.871, 0.41,-0.62);
positions[10] = Vec3(-0.948,0.444,-0.566);
positions[11] = Vec3(-0.905,0.359,-0.699);
positions[12] = Vec3(0.249,-0.077,-0.621);
positions[13] = Vec3(0.306,-0.142,-0.571);
positions[14] = Vec3(0.233,-0.11,-0.714);
positions[15] = Vec3(0.561,0.222,-0.715);
positions[16] = Vec3(0.599,0.138,-0.678);
positions[17] = Vec3(0.473,0.241,-0.671);
positions[18] = Vec3(-0.515,-0.803,-0.628);
positions[19] = Vec3(-0.491,-0.866,-0.702);
positions[20] = Vec3(-0.605,-0.763,-0.646);
positions[21] = Vec3(-0.021,0.175,-0.899);
positions[22] = Vec3(0.018, 0.09,-0.935);
positions[23] = Vec3(-0.119,0.177,-0.918);
positions[24] = Vec3(-0.422,0.856,-0.464);
positions[25] = Vec3(-0.479,0.908,-0.527);
positions[26] = Vec3(-0.326,0.868,-0.488);
positions[27] = Vec3(-0.369,-0.095,-0.903);
positions[28] = Vec3(-0.336,-0.031,-0.972);
positions[29] = Vec3(-0.303,-0.101,-0.828);
positions[30] = Vec3(0.594,0.745,0.652);
positions[31] = Vec3(0.644, 0.83,0.633);
positions[32] = Vec3(0.506,0.747,0.604);
positions[33] = Vec3(-0.157,-0.375,-0.758);
positions[34] = Vec3(-0.25, -0.4,-0.785);
positions[35] = Vec3(-0.131,-0.425,-0.676);
positions[36] = Vec3(0.618,-0.295,-0.578);
positions[37] = Vec3(0.613,-0.213,-0.521);
positions[38] = Vec3(0.707,-0.298,-0.623);
positions[39] = Vec3(0.039,-0.785, 0.3);
positions[40] = Vec3(0.138,-0.796,0.291);
positions[41] = Vec3(-0.001,-0.871,0.332);
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