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physics.cpp
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physics.cpp
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//
// rigidbody.cpp
// inter_plane
//
// Created by Nobuyuki Umetani on 12/15/13.
// Copyright (c) 2013 Nobuyuki Umetani. All rights reserved.
//
#include <map>
#include "physics.h"
CPhysics::CPhysics()
{
nitr = 30;
damping_ratio = 0.01;
////
n = CVector3D(0,1,0); // normal direction of floor (should be an unit vector)
gravity = CVector3D(0,-10,0); // gravity
////
cont_stiff = 1.0e+4; // contact_stiffness (insensitive)
trans_stiff = 1.0e+4; // joint_translation_stiffness (insensitive)
rot_stiff = 1.0e+9; // joint_rotation_stiffness (insensitive)
scale_force = 0.05; //0.5;
scale_torque = 0.05; //0.5;
irb_draw = -1;
is_draw_deformed = false; //false
is_draw_skeleton = false; //false;
is_draw_force = false; //false;
is_draw_section = true; //true;
is_draw_grid = false; //true;
is_draw_section_moment = false; //false;
is_slit = true;
aDir2D.clear();
aDir2D.push_back(1); aDir2D.push_back(0);
aDir2D.push_back(0); aDir2D.push_back(1);
aDir2D.push_back(0.70710678118); aDir2D.push_back(+0.70710678118);
aDir2D.push_back(0.70710678118); aDir2D.push_back(-0.70710678118);
nHeight = 20;
//max_stress = 50000;
max_stress = 60000000; //this is the value for acrylic, 60MPa (60 * 1,000,000)
}
//main class interface methods to set up problem
void CPhysics::AddPlate(const double p[3], const double t[3], const double n[3], const double b[3], const double thickness, const double rho, const std::vector<double> & pts)
{
CPlate plt;
plt.p = CVector3D(p[0], p[1], p[2]);
plt.t = CVector3D(t[0], t[1], t[2]);
plt.n = CVector3D(n[0], n[1], n[2]);
plt.b = CVector3D(b[0], b[1], b[2]);
plt.thickness = thickness;
plt.rho = rho;
plt.aXY = pts;
aPlate.push_back(plt);
}
void CPhysics::AddRigidBody(const double centre_of_mass[3],
const double mass,
const std::vector<double>& contact_points)
{
CRigidBody rb;
rb.cg = CVector3D(centre_of_mass[0], centre_of_mass[1], centre_of_mass[2] );
rb.m = mass;
const int ncp = (int)contact_points.size()/3;
for(int icp=0;icp<ncp;icp++) {
CVector3D pc(contact_points[icp*3+0],contact_points[icp*3+1],contact_points[icp*3+2]);
rb.aCP.push_back(pc);
}
aRigidBody.push_back(rb);
}
void CPhysics::AddJoint(const double position[3], const double jp0[4], const double jp1[4], const int body_index1, const int body_index2)
{
CJoint j;
j.p = CVector3D(position[0], position[1], position[2]);
j.irb0 = body_index1;
j.irb1 = body_index2;
for (int i=0; i<4; ++i) {
j.jp0[i] = jp0[i];
j.jp1[i] = jp1[i];
}
aJoint.push_back(j);
}
void CPhysics::AddWeightToRigidBody(const double mass_pos[3], const double mass_magnitude[3])
{
if (aRigidBody.empty()) {
return;
}
CRigidBody & c = aRigidBody[aRigidBody.size()-1];
const int exf_size = c.aExForce.size();
c.aExForce.resize(exf_size+1);
std::pair<CVector3D,CVector3D> newWeight;
newWeight.first = CVector3D(mass_pos[0], mass_pos[1], mass_pos[2]);
newWeight.second = CVector3D(mass_magnitude[0], mass_magnitude[1], mass_magnitude[2]);
c.aExForce[exf_size] = newWeight;
}
void CPhysics::ClearProblem(){
aRigidBody.clear();
aJoint.clear();
aPlate.clear();
}
void CPhysics::ReadFile(const char* fname) {
const double rho = 1;
FILE* fp = fopen(fname,"r");
char buff[256];
int nr;
fscanf(fp,"%s %d",buff,&nr);
std::cout << "nrigid: " << nr << std::endl;
aRigidBody.clear();
aPlate.clear();
aJoint.clear();
aRigidBody.resize(nr);
aPlate.resize(nr);
for(int ir=0;ir<nr;ir++){
CRigidBody& rb = aRigidBody[ir];
CPlate& plt = aPlate[ir];
int tmp1;
double d1,d2,d3;
fscanf(fp,"%s %d",buff,&tmp1);
fscanf(fp,"%s %lf %lf %lf",buff,&d1,&d2,&d3); // PlaneP
plt.p = CVector3D(d1,d2,d3);
fscanf(fp,"%s %lf %lf %lf",buff,&d1,&d2,&d3); // PlaneT
plt.t = CVector3D(d1,d2,d3);
fscanf(fp,"%s %lf %lf %lf",buff,&d1,&d2,&d3); // PlaneN
plt.n = CVector3D(d1,d2,d3);
fscanf(fp,"%s %lf %lf %lf",buff,&d1,&d2,&d3); // PlaneB
plt.b = CVector3D(d1,d2,d3);
fscanf(fp,"%s %lf %lf %lf",buff,&d1,&d2,&d3); // CenterofMass3D
rb.cg = CVector3D(d1,d2,d3);
double area,thickness;
fscanf(fp,"%s %lf",buff,&area); // PlaneArea
fscanf(fp,"%s %lf",buff,&thickness); // PlaneThickness
plt.thickness = thickness;
plt.rho = rho;
rb.m = area*thickness*rho;
int ncnt;
fscanf(fp,"%s %d",buff,&ncnt); // PlaneContactPoints
rb.aCP.resize(ncnt);
for(int icnt=0;icnt<ncnt;icnt++){
fscanf(fp,"%lf %lf %lf",&d1,&d2,&d3);
rb.aCP[icnt] = CVector3D(d1,d2,d3);
}
int np;
fscanf(fp,"%s %d",buff,&np); // PlaneBoundary2D
plt.aXY.resize(np*2);
std::cout << "npoint section2d: " << np << std::endl;
for(int ip=0;ip<np;ip++){
fscanf(fp,"%lf %lf",&d1,&d2);
plt.aXY[ip*2+0] = d1;
plt.aXY[ip*2+1] = d2;
}
rb.R.SetIdentity();
rb.u = CVector3D(0,0,0);
rb.aCForce.resize(rb.aCP.size());
}
//////////////////////////////////////////////////////////////////////////////////////////
int nj;
fscanf(fp,"%s %d",buff,&nj); // Joints
aJoint.resize(nj);
for(int ij=0;ij<nj;ij++){
CJoint& j = aJoint[ij];
int tmp1, tmp2;
double d1,d2,d3,d4;
fscanf(fp,"%s %d %d",buff,&tmp1,&tmp2); // JointPlaneIndexes
j.irb0 = tmp1;
j.irb1 = tmp2;
fscanf(fp,"%s %lf %lf %lf",buff,&d1,&d2,&d3); // JointCentre3D
j.p = CVector3D(d1,d2,d3);
fscanf(fp,"%s %lf %lf %lf",buff,&d1,&d2,&d3); // JointAxis3D
fscanf(fp,"%s %lf %lf %lf %lf",buff,&d1,&d2,&d3,&d4); // JointPlane1SlitEndpoints2D
j.jp0[0] = d1;
j.jp0[1] = d2;
j.jp0[2] = d3;
j.jp0[3] = d4;
std::cout << d1 << " " << d2 << " " << d3 << " " << d4 << std::endl;
fscanf(fp,"%s %lf %lf %lf %lf",buff,&d1,&d2,&d3,&d4); // JointPlane1SlitEndpoints2D
j.jp1[0] = d1;
j.jp1[1] = d2;
j.jp1[2] = d3;
j.jp1[3] = d4;
std::cout << d1 << " " << d2 << " " << d3 << " " << d4 << std::endl;
}
//////////////////////////////////////////////////////////////////////////////////////////
int nexf;
fscanf(fp,"%s %d",buff,&nexf); // ExternalForces
for(int iexf=0;iexf<nexf;iexf++){
int irb;
double x0,y0,z0;
double x1,y1,z1;
fscanf(fp,"%d %lf%lf%lf %lf%lf%lf",&irb, &x0,&y0,&z0, &x1,&y1,&z1);
assert( irb < int(aRigidBody.size()) );
int irb_exf = (int)aRigidBody[irb].aExForce.size();
aRigidBody[irb].aExForce.resize(irb_exf+1);
aRigidBody[irb].aExForce[irb_exf].first = CVector3D(x0,y0,z0);
aRigidBody[irb].aExForce[irb_exf].second = CVector3D(x1,y1,z1);
}
fclose(fp);
}
void CPhysics::Solve_InsidePlane()
{
if( aPlate.size() != aRigidBody.size() ) return;
for(int irb=0;irb<int(aRigidBody.size());irb++){
{
CPlate& plt = aPlate[irb];
if( is_slit ){
GetPlateLocalForce(aPlate[irb].alForce,
irb, aRigidBody, aJoint,
plt.p, plt.t, plt.b, plt.n,
plt.aXY_slit);
}
else{
GetPlateLocalForce(aPlate[irb].alForce,
irb, aRigidBody, aJoint,
plt.p, plt.t, plt.b, plt.n,
plt.aXY);
}
}
aPlate[irb].aPS.clear();
if( is_slit ){
AddWeakSection_Inside(aPlate[irb],
aPlate[irb].aXY_slit,
aRigidBody[irb],gravity,
aDir2D,nHeight,max_stress);
// Sampling Around Slit
AddWeakWection_Slit(aPlate[irb],
aPlate[irb].aXY_slit,
aRigidBody[irb],gravity,
aDir2D,nHeight,max_stress);
}
else{
AddWeakSection_Inside(aPlate[irb],
aPlate[irb].aXY,
aRigidBody[irb],gravity,
aDir2D,nHeight,max_stress);
}
}
}
void CPhysics::EdEd_Potential
(double& energy,
CVector3D& dEdu,
CVector3D& dEdw,
const CVector3D& , //cg
const CVector3D& u,
const double mass,
const CVector3D& g // floor normal
)
{
energy = mass*(u*g);
dEdu = mass*g;
dEdw = CVector3D(0,0,0);
}
void CPhysics::EdEddE_Exforce
(double& energy,
CVector3D& dEdu, CVector3D& dEdw,
CMatrix3& ddEddu, CMatrix3& ddEddw, CMatrix3& ddEdudw,
const CVector3D& cg, // the center of gravity
const CVector3D& pex, // external force position
const CVector3D& fex, // external force
const CVector3D& u, // displacement
const CMatrix3& R // rigid rotation
)
{
CVector3D Rv = R * (pex-cg);
CVector3D qex = Rv + cg + u; // current external force position
energy = +qex*fex;
dEdu = +fex;
dEdw = +Rv^fex;
ddEddu = CMatrix3(0.0);
ddEddw = +CMatrix3::Spin(fex)*CMatrix3::Spin(Rv);
ddEdudw = CMatrix3(0.0);
}
void CPhysics::EdEddE_Contact
(double& energy,
CVector3D& dEdu, CVector3D& dEdw,
CMatrix3& ddEddu, CMatrix3& ddEddw, CMatrix3& ddEdudw,
const CVector3D& cg, // the center of gravity
const CVector3D& cp, // contact position
const CVector3D& u, // displacement
const CMatrix3& R, // rigid rotation
const double cont_stiff,
const CVector3D& n // floor normal
)
{
CVector3D Rv = R * (cp-cg);
CVector3D cq = Rv + cg + u;
energy = 0.5*(cq*n)*(cq*n)*cont_stiff;
dEdu = ((cq*n)*cont_stiff)*n;
dEdw = ((cq*n)*cont_stiff)*(Rv^n);
ddEddu = cont_stiff*CMatrix3::OuterProduct(n,n);
ddEddw = cont_stiff*CMatrix3::OuterProduct(Rv^n,Rv^n) + ((cq*n)*cont_stiff)*CMatrix3::Spin(n)*CMatrix3::Spin(Rv);
ddEdudw = cont_stiff*CMatrix3::OuterProduct(Rv^n,n);
}
void CPhysics::EdEddE_ContactFriction
(double& energy,
CVector3D& dEdu, CVector3D& dEdw,
CMatrix3& ddEddu, CMatrix3& ddEddw, CMatrix3& ddEdudw,
const CVector3D& cg, // the center of gravity
const CVector3D& cp, // contact position
const CVector3D& u, // displacement
const CMatrix3& R, // rigid rotation
const double cont_stiff
)
{
CVector3D Rv = R * (cp-cg);
CVector3D cq = Rv + cg + u;
energy = 0.5*(cq-cp)*(cq-cp)*cont_stiff;
dEdu = cont_stiff*(cq-cp);
dEdw = cont_stiff*(Rv^(cq-cp));
ddEddu = cont_stiff*CMatrix3::Identity();
// ddEddw = -cont_stiff*CMatrix3::OuterProduct(Rv,Rv) + cont_stiff*CMatrix3::Spin(Rv)*CMatrix3::Spin(cq-cp);
ddEddw = -cont_stiff*CMatrix3::Spin(Rv)*CMatrix3::Spin(Rv) + cont_stiff*CMatrix3::Spin(cq-cp)*CMatrix3::Spin(Rv);
ddEdudw = cont_stiff*CMatrix3::Spin(Rv);
}
void CPhysics::EdEddE_Joint
(double& energy,
CVector3D& dEdu0, CVector3D& dEdw0, CVector3D& dEdu1, CVector3D& dEdw1,
////
CMatrix3& ddEdu0du0, CMatrix3& ddEdu0dw0, CMatrix3& ddEdu0du1, CMatrix3& ddEdu0dw1, CMatrix3& ddEdw0dw0,
CMatrix3& ddEdw0du1, CMatrix3& ddEdw0dw1, CMatrix3& ddEdu1du1, CMatrix3& ddEdu1dw1, CMatrix3& ddEdw1dw1,
////
const double trans_stiff,
const double rot_stiff,
const CVector3D& pj,
////
const CVector3D& cg0, const CVector3D& u0, const CMatrix3& R0,
const CVector3D& cg1, const CVector3D& u1, const CMatrix3& R1
)
{
CVector3D Rv0 = R0 * (pj-cg0);
CVector3D qj0 = Rv0 + cg0 + u0; // after deformation joint pos relative to rigid body 0
CVector3D Rv1 = R1 * (pj-cg1);
CVector3D qj1 = Rv1 + cg1 + u1; // after deformation joint pos relative to rigid body 1
energy = 0.5*trans_stiff*(qj0 - qj1).DLength();
dEdu0 = trans_stiff*(qj0-qj1);
dEdw0 = trans_stiff*(Rv0^(qj0-qj1));
dEdu1 = trans_stiff*(qj1-qj0);
dEdw1 = trans_stiff*(Rv1^(qj1-qj0));
ddEdu0du0 = trans_stiff*CMatrix3::Identity();
ddEdu0du1 = -trans_stiff*CMatrix3::Identity();
ddEdu0dw0 = +trans_stiff*CMatrix3::Spin(Rv0);
ddEdu0dw1 = -trans_stiff*CMatrix3::Spin(Rv1);
ddEdw0dw0 = -trans_stiff*CMatrix3::Spin(Rv0)*CMatrix3::Spin(Rv0) + trans_stiff*CMatrix3::Spin(qj0-qj1)*CMatrix3::Spin(Rv0);
ddEdw0du1 = +trans_stiff*CMatrix3::Spin(Rv0);
ddEdw0dw1 = +trans_stiff*CMatrix3::Spin(Rv1)*CMatrix3::Spin(Rv0);
ddEdu1du1 = trans_stiff*CMatrix3::Identity();
ddEdu1dw1 = +trans_stiff*CMatrix3::Spin(Rv1);
ddEdw1dw1 = -trans_stiff*CMatrix3::Spin(Rv1)*CMatrix3::Spin(Rv1) + trans_stiff*CMatrix3::Spin(qj1-qj0)*CMatrix3::Spin(Rv1);
CVector3D av(0,0,0);
CMatrix3 davdw0, davdw1;
{
for(unsigned int i=0;i<3;i++){
CVector3D r0( R0.mat[0*3+i], R0.mat[1*3+i], R0.mat[2*3+i] );
CVector3D r1( R1.mat[0*3+i], R1.mat[1*3+i], R1.mat[2*3+i] );
av += (r0^r1);
davdw0 += CMatrix3(r1)*CMatrix3(r0);
davdw1 -= CMatrix3(r0)*CMatrix3(r1);
}
av *= 0.5;
davdw0 *= 0.5;
davdw1 *= 0.5;
}
energy += 0.5*rot_stiff*av.DLength();
CMatrix3 m0,m1,m2;
for(unsigned int i=0;i<3;i++){
CVector3D r0( R0.mat[0*3+i], R0.mat[1*3+i], R0.mat[2*3+i] );
CVector3D r1( R1.mat[0*3+i], R1.mat[1*3+i], R1.mat[2*3+i] );
dEdw0 += 0.5*rot_stiff*r0^(r1^av);
dEdw1 -= 0.5*rot_stiff*r1^(r0^av);
ddEdw0dw0 += 0.5*rot_stiff*( CMatrix3::Spin(r1^av)*CMatrix3::Spin(r0) + CMatrix3::Spin(r0)*CMatrix3::Spin(r1)*davdw0 );
ddEdw1dw1 -= 0.5*rot_stiff*( CMatrix3::Spin(r0^av)*CMatrix3::Spin(r1) + CMatrix3::Spin(r1)*CMatrix3::Spin(r0)*davdw1 );
ddEdw0dw1 -= 0.5*rot_stiff*( CMatrix3::Spin(r1)*CMatrix3::Spin(av)*CMatrix3::Spin(r0)
+ CMatrix3::Spin(r1)*CMatrix3::Spin(r0)*davdw0 );
}
}
CVector3D CPhysics::rand_vec(double s)
{
CVector3D v;
v.x = s*rand()/(RAND_MAX+1.0);
v.y = s*rand()/(RAND_MAX+1.0);
v.z = s*rand()/(RAND_MAX+1.0);
return v;
}
CMatrix3 CPhysics::rand_rot()
{
double s = 3.5;
CVector3D v;
v.x = s*rand()/(RAND_MAX+1.0);
v.y = s*rand()/(RAND_MAX+1.0);
v.z = s*rand()/(RAND_MAX+1.0);
CMatrix3 R; R.SetRotMatrix_Cartesian(v);
return R;
}
void CPhysics::CheckDiff_Contact()
{
double energy = 0.0;
CVector3D dEdu,dEdw;
CMatrix3 ddEddu, ddEddw, ddEdudw;
double epsilon = 1.0e-5;
const double cont_stiff = 1.0e+3;
CVector3D cg = rand_vec(1.0);
CVector3D cp = rand_vec(1.0);
CVector3D u = rand_vec(1.0);
CMatrix3 R = rand_rot();
CVector3D n(0,0,1);
EdEddE_Contact(energy,
dEdu,dEdw, ddEddu,ddEddw,ddEdudw,
cg,cp,u,R,
cont_stiff,n);
for(unsigned int idim=0;idim<3;idim++){
CVector3D dEdu_, dEdw_;
CMatrix3 ddEddu_, ddEddw_, ddEdudw_;
double energy_ = 0.0;
CVector3D u_ = u;
u_[idim] += epsilon;
EdEddE_Contact(energy_, dEdu_,dEdw_, ddEddu_,ddEddw_,ddEdudw_,
cg,cp,u_,R,
cont_stiff,n);
std::cout << "dEdu " << idim << " --> " << (energy_-energy)/epsilon << " " << dEdu[idim] << std::endl;
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEddu " << idim << " " << jdim << " --> " << (dEdu_[jdim]-dEdu[jdim])/epsilon << " " << ddEddu.mat[jdim*3+idim] << std::endl;
}
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEdudw " << idim << " " << jdim << " --> " << (dEdw_[jdim]-dEdw[jdim])/epsilon << " " << ddEdudw.mat[jdim*3+idim] << std::endl;
}
}
for(unsigned int idim=0;idim<3;idim++){
CVector3D dEdu_, dEdw_;
CMatrix3 ddEddu_, ddEddw_, ddEdudw_;
double energy_ = 0.0;
CVector3D w(0,0,0);
w[idim] = epsilon;
CMatrix3 dR; dR.SetRotMatrix_Cartesian(w);
CMatrix3 R_ = dR*R;
EdEddE_Contact(energy_, dEdu_,dEdw_, ddEddu_,ddEddw_,ddEdudw_,
cg,cp,u,R_,
cont_stiff,n);
std::cout << "dEdw " << idim << " --> " << (energy_-energy)/epsilon << " " << dEdw[idim] << std::endl;
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEdudw " << idim << " " << jdim << " --> " << (dEdu_[jdim]-dEdu[jdim])/epsilon << " " << ddEdudw.mat[idim*3+jdim] << std::endl;
}
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEddw " << idim << " " << jdim << " --> " << (dEdw_[jdim]-dEdw[jdim])/epsilon << " " << ddEddw.mat[jdim*3+idim] << std::endl;
}
}
}
void CPhysics::CheckDiff_ContactFriction()
{
double energy = 0.0;
CVector3D dEdu,dEdw;
CMatrix3 ddEddu, ddEddw, ddEdudw;
double epsilon = 1.0e-5;
const double cont_stiff = 1.0e+3;
CVector3D cg = rand_vec(1.0);
CVector3D cp = rand_vec(1.0);
CVector3D u = rand_vec(1.0);
CMatrix3 R = rand_rot();
EdEddE_ContactFriction(energy,
dEdu,dEdw, ddEddu,ddEddw,ddEdudw,
cg,cp,u,R,
cont_stiff);
for(unsigned int idim=0;idim<3;idim++){
CVector3D dEdu_, dEdw_;
CMatrix3 ddEddu_, ddEddw_, ddEdudw_;
double energy_ = 0.0;
CVector3D u_ = u;
u_[idim] += epsilon;
EdEddE_ContactFriction(energy_, dEdu_,dEdw_, ddEddu_,ddEddw_,ddEdudw_,
cg,cp,u_,R,
cont_stiff);
std::cout << "dEdu " << idim << " --> " << (energy_-energy)/epsilon << " " << dEdu[idim] << std::endl;
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEddu " << idim << " " << jdim << " --> " << (dEdu_[jdim]-dEdu[jdim])/epsilon << " " << ddEddu.mat[jdim*3+idim] << std::endl;
}
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEdudw " << idim << " " << jdim << " --> " << (dEdw_[jdim]-dEdw[jdim])/epsilon << " " << ddEdudw.mat[jdim*3+idim] << std::endl;
}
}
for(unsigned int idim=0;idim<3;idim++){
CVector3D dEdu_, dEdw_;
CMatrix3 ddEddu_, ddEddw_, ddEdudw_;
double energy_ = 0.0;
CVector3D w(0,0,0);
w[idim] = epsilon;
CMatrix3 dR; dR.SetRotMatrix_Cartesian(w);
CMatrix3 R_ = dR*R;
EdEddE_ContactFriction(energy_, dEdu_,dEdw_, ddEddu_,ddEddw_,ddEdudw_,
cg,cp,u,R_,
cont_stiff);
std::cout << "dEdw " << idim << " --> " << (energy_-energy)/epsilon << " " << dEdw[idim] << std::endl;
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEdudw " << idim << " " << jdim << " --> " << (dEdu_[jdim]-dEdu[jdim])/epsilon << " " << ddEdudw.mat[idim*3+jdim] << std::endl;
}
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEddw " << idim << " " << jdim << " --> " << (dEdw_[jdim]-dEdw[jdim])/epsilon << " " << ddEddw.mat[jdim*3+idim] << std::endl;
}
}
}
void CPhysics::CheckDiff_Exforce()
{
double energy = 0.0;
CVector3D dEdu,dEdw;
CMatrix3 ddEddu, ddEddw, ddEdudw;
double epsilon = 1.0e-5;
CVector3D cg = rand_vec(1.0);
CVector3D u = rand_vec(1.0);
CVector3D fex = rand_vec(1.0);
CVector3D pex = rand_vec(1.0);
CMatrix3 R = rand_rot();
CVector3D n(0,0,1);
EdEddE_Exforce(energy,
dEdu,dEdw, ddEddu,ddEddw,ddEdudw,
cg,pex,fex,u,R);
for(unsigned int idim=0;idim<3;idim++){
CVector3D dEdu_, dEdw_;
CMatrix3 ddEddu_, ddEddw_, ddEdudw_;
double energy_ = 0.0;
CVector3D u_ = u;
u_[idim] += epsilon;
EdEddE_Exforce(energy_, dEdu_,dEdw_, ddEddu_,ddEddw_,ddEdudw_,
cg,pex,fex,u_,R);
std::cout << "dEdu " << idim << " --> " << (energy_-energy)/epsilon << " " << dEdu[idim] << std::endl;
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEddu " << idim << " " << jdim << " --> " << (dEdu_[jdim]-dEdu[jdim])/epsilon << " " << ddEddu.mat[jdim*3+idim] << std::endl;
}
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEdudw " << idim << " " << jdim << " --> " << (dEdw_[jdim]-dEdw[jdim])/epsilon << " " << ddEdudw.mat[jdim*3+idim] << std::endl;
}
}
for(unsigned int idim=0;idim<3;idim++){
CVector3D dEdu_, dEdw_;
CMatrix3 ddEddu_, ddEddw_, ddEdudw_;
double energy_ = 0.0;
CVector3D w(0,0,0);
w[idim] = epsilon;
CMatrix3 dR; dR.SetRotMatrix_Cartesian(w);
CMatrix3 R_ = dR*R;
EdEddE_Exforce(energy_, dEdu_,dEdw_, ddEddu_,ddEddw_,ddEdudw_,
cg,pex,fex,u,R_);
std::cout << "dEdw " << idim << " --> " << (energy_-energy)/epsilon << " " << dEdw[idim] << std::endl;
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEdudw " << idim << " " << jdim << " --> " << (dEdu_[jdim]-dEdu[jdim])/epsilon << " " << ddEdudw.mat[idim*3+jdim] << std::endl;
}
for(unsigned int jdim=0;jdim<3;jdim++){
std::cout << " ddEddw " << idim << " " << jdim << " --> " << (dEdw_[jdim]-dEdw[jdim])/epsilon << " " << ddEddw.mat[jdim*3+idim] << std::endl;
}
}
}
void CPhysics::CheckDiff_Joint()
{
double energy = 0.0;
CVector3D dEdu0(0,0,0);
CVector3D dEdw0(0,0,0);
CVector3D dEdu1(0,0,0);
CVector3D dEdw1(0,0,0);
CMatrix3 ddEdu0du0;
CMatrix3 ddEdu0dw0;
CMatrix3 ddEdu0du1;
CMatrix3 ddEdu0dw1;
CMatrix3 ddEdw0dw0;
CMatrix3 ddEdw0du1;
CMatrix3 ddEdw0dw1;
CMatrix3 ddEdu1du1;
CMatrix3 ddEdu1dw1;
CMatrix3 ddEdw1dw1;
double epsilon = 1.0e-5;
const double trans_stiff = 1.0e+3;
const double rot_stiff = 1.0e+3;
CVector3D pj = rand_vec(1.0);
////
CVector3D cg0 = rand_vec(1.0);
CVector3D cp0 = rand_vec(1.0);
CVector3D u0 = rand_vec(1.0);
CMatrix3 R0 = rand_rot();
////
CVector3D cg1 = rand_vec(1.0);
CVector3D cp1 = rand_vec(1.0);
CVector3D u1 = rand_vec(1.0);
CMatrix3 R1 = rand_rot();
////
EdEddE_Joint(energy,
dEdu0, dEdw0, dEdu1,dEdw1,
ddEdu0du0, ddEdu0dw0, ddEdu0du1, ddEdu0dw1, ddEdw0dw0, ddEdw0du1, ddEdw0dw1, ddEdu1du1, ddEdu1dw1, ddEdw1dw1,
trans_stiff, rot_stiff, pj,
cg0, u0, R0,
cg1, u1, R1);
for(unsigned int kdim=0;kdim<3;kdim++){
CVector3D dEdu0_, dEdw0_, dEdu1_, dEdw1_;
CMatrix3 ddEdu0du0_, ddEdu0dw0_, ddEdu0du1_, ddEdu0dw1_, ddEdw0dw0_, ddEdw0du1_, ddEdw0dw1_, ddEdu1du1_, ddEdu1dw1_, ddEdw1dw1_;
double energy_ = 0.0;
CVector3D u0_ = u0;
u0_[kdim] += epsilon;
EdEddE_Joint(energy_, dEdu0_,dEdw0_, dEdu1_,dEdw1_,
ddEdu0du0_, ddEdu0dw0_, ddEdu0du1_, ddEdu0dw1_, ddEdw0dw0_, ddEdw0du1_, ddEdw0dw1_, ddEdu1du1_, ddEdu1dw1_, ddEdw1dw1_,
trans_stiff, rot_stiff, pj,
cg0, u0_, R0,
cg1, u1, R1);
std::cout << "dEdu0: " << kdim << " --> " << (energy_-energy)/epsilon << " " << dEdu0[kdim] << std::endl;
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdu0du0 " << kdim << " " << idim << " --> " << (dEdu0_[idim]-dEdu0[idim])/epsilon << " " << ddEdu0du0.mat[idim*3+kdim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdw0du0 " << kdim << " " << idim << " --> " << (dEdw0_[idim]-dEdw0[idim])/epsilon << " " << ddEdu0dw0.mat[idim*3+kdim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << "*ddEdu1du0 " << kdim << " " << idim << " --> " << (dEdu1_[idim]-dEdu1[idim])/epsilon << " " << ddEdu0du1.mat[idim*3+kdim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << "*ddEdw1du0 " << kdim << " " << idim << " --> " << (dEdw1_[idim]-dEdw1[idim])/epsilon << " " << ddEdu0dw1.mat[idim*3+kdim] << std::endl;
}
}
for(unsigned int jdim=0;jdim<3;jdim++){
CVector3D dEdu0_, dEdw0_, dEdu1_, dEdw1_;
CMatrix3 ddEdu0du0_, ddEdu0dw0_, ddEdu0du1_, ddEdu0dw1_, ddEdw0dw0_, ddEdw0du1_, ddEdw0dw1_, ddEdu1du1_, ddEdu1dw1_, ddEdw1dw1_;
double energy_ = 0.0;
CVector3D w(0,0,0);
w[jdim] = epsilon;
CMatrix3 dR; dR.SetRotMatrix_Cartesian(w);
CMatrix3 R0_ = dR*R0;
EdEddE_Joint(energy_, dEdu0_,dEdw0_, dEdu1_,dEdw1_,
ddEdu0du0_, ddEdu0dw0_, ddEdu0du1_, ddEdu0dw1_, ddEdw0dw0_, ddEdw0du1_, ddEdw0dw1_, ddEdu1du1_, ddEdu1dw1_, ddEdw1dw1_,
trans_stiff, rot_stiff, pj,
cg0, u0, R0_,
cg1, u1, R1);
std::cout << "dEdw0: " << jdim << " --> " << (energy_-energy)/epsilon << " " << dEdw0[jdim] << std::endl;
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdu0dw0 " << jdim << " " << idim << " --> " << (dEdu0_[idim]-dEdu0[idim])/epsilon << " " << ddEdu0dw0.mat[jdim*3+idim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdw0dw0 " << jdim << " " << idim << " --> " << (dEdw0_[idim]-dEdw0[idim])/epsilon << " " << ddEdw0dw0.mat[idim*3+jdim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdu1dw0 " << jdim << " " << idim << " --> " << (dEdu1_[idim]-dEdu1[idim])/epsilon << " " << ddEdw0du1.mat[idim*3+jdim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdw1dw0 " << jdim << " " << idim << " --> " << (dEdw1_[idim]-dEdw1[idim])/epsilon << " " << ddEdw0dw1.mat[idim*3+jdim] << std::endl;
}
}
for(unsigned int jdim=0;jdim<3;jdim++){
CVector3D dEdu0_, dEdw0_, dEdu1_, dEdw1_;
CMatrix3 ddEdu0du0_, ddEdu0dw0_, ddEdu0du1_, ddEdu0dw1_, ddEdw0dw0_, ddEdw0du1_, ddEdw0dw1_, ddEdu1du1_, ddEdu1dw1_, ddEdw1dw1_;
double energy_ = 0.0;
CVector3D u1_ = u1;
u1_[jdim] += epsilon;
EdEddE_Joint(energy_, dEdu0_,dEdw0_, dEdu1_,dEdw1_,
ddEdu0du0_, ddEdu0dw0_, ddEdu0du1_, ddEdu0dw1_, ddEdw0dw0_, ddEdw0du1_, ddEdw0dw1_, ddEdu1du1_, ddEdu1dw1_, ddEdw1dw1_,
trans_stiff, rot_stiff, pj,
cg0, u0, R0,
cg1, u1_,R1);
std::cout << "dEdu1: " << jdim << " --> " << (energy_-energy)/epsilon << " " << dEdu1[jdim] << std::endl;
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdu0du1 " << jdim << " " << idim << " --> " << (dEdu0_[idim]-dEdu0[idim])/epsilon << " " << ddEdu0du1.mat[jdim*3+idim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdw0du1 " << jdim << " " << idim << " --> " << (dEdw0_[idim]-dEdw0[idim])/epsilon << " " << ddEdw0du1.mat[jdim*3+idim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdu1du1 " << jdim << " " << idim << " --> " << (dEdu1_[idim]-dEdu1[idim])/epsilon << " " << ddEdu1du1.mat[idim*3+jdim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << "*ddEdw1du1 " << jdim << " " << idim << " --> " << (dEdw1_[idim]-dEdw1[idim])/epsilon << " " << ddEdu1dw1.mat[idim*3+jdim] << std::endl;
}
}
for(unsigned int jdim=0;jdim<3;jdim++){
CVector3D dEdu0_, dEdw0_, dEdu1_, dEdw1_;
CMatrix3 ddEdu0du0_, ddEdu0dw0_, ddEdu0du1_, ddEdu0dw1_, ddEdw0dw0_, ddEdw0du1_, ddEdw0dw1_, ddEdu1du1_, ddEdu1dw1_, ddEdw1dw1_;
double energy_ = 0.0;
CVector3D w(0,0,0);
w[jdim] = epsilon;
CMatrix3 dR; dR.SetRotMatrix_Cartesian(w);
CMatrix3 R1_ = dR*R1;
EdEddE_Joint(energy_, dEdu0_,dEdw0_, dEdu1_,dEdw1_,
ddEdu0du0_, ddEdu0dw0_, ddEdu0du1_, ddEdu0dw1_,
ddEdw0dw0_, ddEdw0du1_, ddEdw0dw1_,
ddEdu1du1_, ddEdu1dw1_,
ddEdw1dw1_,
trans_stiff, rot_stiff, pj,
cg0, u0, R0,
cg1, u1, R1_);
std::cout << "dEdw1: " << jdim << " --> " << (energy_-energy)/epsilon << " " << dEdw1[jdim] << std::endl;
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdu0dw1 " << jdim << " " << idim << " --> " << (dEdu0_[idim]-dEdu0[idim])/epsilon << " " << ddEdu0dw1.mat[jdim*3+idim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdw0dw1 " << jdim << " " << idim << " --> " << (dEdw0_[idim]-dEdw0[idim])/epsilon << " " << ddEdw0dw1.mat[jdim*3+idim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdu1dw1 " << jdim << " " << idim << " --> " << (dEdu1_[idim]-dEdu1[idim])/epsilon << " " << ddEdu1dw1.mat[jdim*3+idim] << std::endl;
}
for(unsigned int idim=0;idim<3;idim++){
std::cout << " ddEdw1dw1 " << jdim << " " << idim << " --> " << (dEdw1_[idim]-dEdw1[idim])/epsilon << " " << ddEdw1dw1.mat[idim*3+jdim] << std::endl;
}
}
}
void CPhysics::AddMatrix(Eigen::MatrixXd& M,
unsigned int i0, unsigned int j0,
const CMatrix3& m,
bool isnt_inverse)
{
if( isnt_inverse ){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
M(i0+idim,j0+jdim) += m.mat[idim*3+jdim];
}
}
}
else{
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
M(i0+idim,j0+jdim) += m.mat[jdim*3+idim];
}
}
}
}
void CPhysics::EdEddE_Total
(double& E,
Eigen::VectorXd& dE,
Eigen::MatrixXd& ddE,
////
const std::vector<CRigidBody>& aRigidBody,
const std::vector<CJoint>& aJoint,
////
const CVector3D n,
const CVector3D gravity,
const double cont_stiff,
const double trans_stiff,
const double rot_stiff,
bool is_friction
)
{
E = 0;
ddE.setConstant(0);
dE.setConstant(0); // u0,w0, u1,w1, ....
////
for(unsigned int irb=0;irb<aRigidBody.size();irb++){
const CRigidBody& rb = aRigidBody[irb];
CVector3D cg = rb.cg;
{
double e = 0;
CVector3D du, dw;
EdEd_Potential(e, du, dw,
cg, rb.u, rb.m,
gravity);
E += e;
for(unsigned int idim=0;idim<3;idim++){
dE[irb*6+0+idim] += du[idim];
dE[irb*6+3+idim] += dw[idim];
}
}
for(unsigned int icp=0;icp<rb.aCP.size();icp++){
CVector3D cp = rb.aCP[icp];
double e = 0;
CVector3D du, dw;
CMatrix3 ddu,ddw,dudw;
if( is_friction ){
EdEddE_ContactFriction(e,
du,dw, ddu,ddw,dudw,
cg,cp,rb.u,rb.R,
cont_stiff);
}
else{
EdEddE_Contact(e,
du,dw, ddu,ddw,dudw,
cg,cp,rb.u,rb.R,
cont_stiff,n);
}
E += e;
for(unsigned int idim=0;idim<3;idim++){
dE[irb*6+0+idim] += du[idim];
dE[irb*6+3+idim] += dw[idim];
}
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
ddE(irb*6+0+idim,irb*6+0+jdim) += ddu.mat[idim*3+jdim];
}
}
AddMatrix(ddE, irb*6+0, irb*6+0, ddu, true );
AddMatrix(ddE, irb*6+0, irb*6+3, dudw, false);
////
AddMatrix(ddE, irb*6+3, irb*6+0, dudw, true );
AddMatrix(ddE, irb*6+3, irb*6+3, ddw, true );
}
for(unsigned int iexf=0;iexf<rb.aExForce.size();iexf++){
CVector3D pex = rb.aExForce[iexf].first;
CVector3D fex = rb.aExForce[iexf].second;
double e = 0;
CVector3D du, dw;
CMatrix3 ddu,ddw,dudw;
EdEddE_Exforce(e,
du,dw, ddu,ddw,dudw,
cg,pex,fex, rb.u,rb.R);
E += e;
for(unsigned int idim=0;idim<3;idim++){
dE[irb*6+0+idim] += du[idim];
dE[irb*6+3+idim] += dw[idim];
}
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
ddE(irb*6+0+idim,irb*6+0+jdim) += ddu.mat[idim*3+jdim];
}
}
AddMatrix(ddE, irb*6+0, irb*6+0, ddu, true );
AddMatrix(ddE, irb*6+0, irb*6+3, dudw, false);
////
AddMatrix(ddE, irb*6+3, irb*6+0, dudw, true );
AddMatrix(ddE, irb*6+3, irb*6+3, ddw, true );
}
}
for(unsigned int ij=0;ij<aJoint.size();ij++){
const CJoint& joint = aJoint[ij];
CVector3D pj = joint.p;
int irb0 = joint.irb0;
int irb1 = joint.irb1;
const CRigidBody& rb0 = aRigidBody[irb0];
const CRigidBody& rb1 = aRigidBody[irb1];
{
double e = 0;
CVector3D du0, dw0, du1, dw1;
CMatrix3 du0du0, du0dw0, du0du1, du0dw1, dw0dw0, dw0du1, dw0dw1, du1du1, du1dw1, dw1dw1;
EdEddE_Joint(e,
du0, dw0, du1, dw1,
du0du0, du0dw0, du0du1, du0dw1, dw0dw0, dw0du1, dw0dw1, du1du1, du1dw1, dw1dw1,
trans_stiff, rot_stiff, pj,
rb0.cg, rb0.u, rb0.R,
rb1.cg, rb1.u, rb1.R);
E += e;
for(unsigned int idim=0;idim<3;idim++){
dE[irb0*6+0+idim] += du0[idim];
dE[irb0*6+3+idim] += dw0[idim];
}
for(unsigned int idim=0;idim<3;idim++){
dE[irb1*6+0+idim] += du1[idim];
dE[irb1*6+3+idim] += dw1[idim];
}
AddMatrix(ddE, irb0*6+0, irb0*6+0, du0du0, true );
AddMatrix(ddE, irb0*6+0, irb0*6+3, du0dw0, false);
AddMatrix(ddE, irb0*6+0, irb1*6+0, du0du1, false);
AddMatrix(ddE, irb0*6+0, irb1*6+3, du0dw1, false);
////
AddMatrix(ddE, irb0*6+3, irb0*6+0, du0dw0, true );
AddMatrix(ddE, irb0*6+3, irb0*6+3, dw0dw0, true );
AddMatrix(ddE, irb0*6+3, irb1*6+0, dw0du1, false);
AddMatrix(ddE, irb0*6+3, irb1*6+3, dw0dw1, false);
////
AddMatrix(ddE, irb1*6+0, irb0*6+0, du0du1, true );
AddMatrix(ddE, irb1*6+0, irb0*6+3, dw0du1, true );
AddMatrix(ddE, irb1*6+0, irb1*6+0, du1du1, true );
AddMatrix(ddE, irb1*6+0, irb1*6+3, du1dw1, false);
////
AddMatrix(ddE, irb1*6+3, irb0*6+0, du0dw1, true );
AddMatrix(ddE, irb1*6+3, irb0*6+3, dw0dw1, true );
AddMatrix(ddE, irb1*6+3, irb1*6+0, du1dw1, true );
AddMatrix(ddE, irb1*6+3, irb1*6+3, dw1dw1, true );
}
}
}
// solve one iteration
void CPhysics::SolveOneIteration()
/*
(
std::vector<CRigidBody>& aRigidBody,
std::vector<CJoint>& aJoint,
////
double damping_ratio,
////
const CVector3D n,
const CVector3D gravity,
const double cont_stiff,
const double trans_stiff,
const double rot_stiff)*/
{
int nDof = (int)aRigidBody.size()*6;
double E = 0;
Eigen::VectorXd dE(nDof);
Eigen::MatrixXd ddE(nDof,nDof);
EdEddE_Total(E,dE,ddE,
aRigidBody,aJoint,
n,gravity,cont_stiff,trans_stiff,rot_stiff,true);
//std::cout << "energy : " << E << std::endl;
/////
Eigen::VectorXd b(nDof);
Eigen::MatrixXd A(nDof,nDof);
b = -dE;
A = ddE;
for(int i=0;i<nDof;i++){
A(i,i) += damping_ratio;
}
Eigen::VectorXd x = A.partialPivLu().solve(b);
for(unsigned int irb=0;irb<aRigidBody.size();irb++){
CRigidBody& rb = aRigidBody[irb];
for(unsigned int idim=0;idim<3;idim++){
rb.u[idim] += x(irb*6+0+idim);
}
{
CVector3D w;
w.x = x(irb*6+3+0);
w.y = x(irb*6+3+1);
w.z = x(irb*6+3+2);
CMatrix3 dR; dR.SetRotMatrix_Cartesian(w);
rb.R = dR*rb.R;
}
}
}
void CPhysics::Solve_InterPlane()
/*
(std::vector<CRigidBody>& aRigidBody,
std::vector<CJoint>& aJoint,
////
double damping_ratio,
int nitr,
////
const CVector3D n,
const CVector3D gravity,
const double cont_stiff,
const double trans_stiff,
const double rot_stiff)
*/
{
for(int itr=0;itr<nitr;itr++){
//SolveOneIteration(aRigidBody, aJoint, damping_ratio, n,gravity,cont_stiff,trans_stiff,rot_stiff);
SolveOneIteration();
}
ComputeForces();
}
void CPhysics::ComputeForces()
/*
(std::vector<CRigidBody>& aRigidBody,
std::vector<CJoint>& aJoint,
////
const CVector3D n,
const double cont_stiff,
const double trans_stiff,