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Body.h
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#ifndef Body3D_h
#define Body3D_h
#include <math.h>
#include <cstdlib>
#include <stdio.h>
#include "fastmath.h"
#include "Vec3.h"
#include "Mat3.h"
#include "quaternion.h"
template<typename T>
struct PoseQ{
union{
struct{
Vec3T <T> pos;
Quat4T<T> rot;
};
T array[7];
};
};
template<typename T>
struct BodyQ{
double mass;
PoseQ<T> pose;
PoseQ<T> vel;
PoseQ<T> force;
};
// ========================
// CLASS : KinematicBody
// ========================
class KinematicBody{ public:
Vec3d lpos = (Vec3d){0.0,0.0,0.0};
Mat3d lrot = (Mat3d){ 1.0,0.0,0.0, 0.0,1.0,0.0, 0.0,0.0,1.0};
inline void globalPosT( const Vec3d& pos0, const Mat3d& rot0, Vec3d& gpos ){ rot0.dot_to ( lpos, gpos ); gpos.add( pos0 ); }
inline void globalRot ( const Mat3d& rot0, Mat3d& grot ){ grot.set_mmul ( lrot, rot0 ); }
inline void globalPos ( const Vec3d& pos0, const Mat3d& rot0, Vec3d& gpos ){ rot0.dot_to_T ( lpos, gpos ); gpos.add( pos0 ); }
inline void globalRotT( const Mat3d& rot0, Mat3d& grot ){ grot.set_mmul_NT( lrot, rot0 ); }
//inline void globalRot( const Mat3d& rot0, Mat3d& grot ){ grot.set_mmul_NT( lrot, rot0 ); }
};
// ========================
// CLASS : PointBody
// ========================
template<typename T>
class Particle3D{ public:
double age;
Vec3T<T> pos;
Vec3T<T> vel;
inline void move(T dt, const Vec3T<T>& accel ){
age += dt;
vel.add_mul( accel, dt );
pos.add_mul( vel, dt );
}
inline void getOldPos(double dt, Vec3d& op) const { op.set_add_mul(pos,vel,-dt); }
};
typedef Particle3D<float> Particle3f;
typedef Particle3D<double> Particle3d;
class PointBody{ public:
// parameters
double mass = 1.0;
// auxiliary parameters
double invMass = 1.0;
// State variables
Vec3d pos = (Vec3d){0.0,0.0,0.0};
Vec3d vel = (Vec3d){0.0,0.0,0.0};
// auxiliary variables
Vec3d force = (Vec3d){0.0,0.0,0.0};
// ==== function declarations
virtual void evalForce();
virtual void move(double dt);
//virtual void render();
// ==== inline functions
inline void setMass( double mass_ ){
mass = mass_;
invMass = 1 / mass;
};
inline void move_PointBody( double dt ){
vel.add_mul( force, dt*invMass );
pos.add_mul( vel, dt );
//printf( "dt: %f force: ",dt ); printVec( force ); printf( " vel: " ); printVec( vel ); printf( " pos: " ); printVec( pos ); printf( "\n" );
};
inline void clean_temp( ){ force.set(0.0); }
};
// ========================
// RigidBody Functions
// ========================
inline void pointBodyDynamicsStep( double invMass, double dt, const Vec3d& force, Vec3d& vel, Vec3d& pos ){
vel.add_mul( force, dt*invMass );
pos.add_mul( vel, dt );
//printf( "dt: %f force: ",dt ); printVec( force ); printf( " vel: " ); printVec( vel ); printf( " pos: " ); printVec( pos ); printf( "\n" );
};
inline void rigidBodyRotationDynamicsStep_mat( const Mat3d& invIbody, double dt, const Vec3d& torq, Vec3d& L, Mat3d& rotMat, Vec3d& omega ){
L .add_mul( torq, dt );
rotMat.dot_to_T ( L, omega );
invIbody.dot_to ( omega, omega );
rotMat.dot_to ( omega, omega );
//rotMat.dot_to ( L, omega );
//invIbody.dot_to ( omega, omega );
//rotMat.dot_to_T ( omega, omega );
double r2omega = omega.norm2();
if( r2omega > 1e-12 ){ // TODO - more efficient would be do this for |L| instead of |omega|
double romega = sqrt(r2omega);
double dphi = dt*romega;
rotMat.rotate_csa( cos(dphi), sin(dphi), omega*(1/romega) );
}
//return omega;
};
inline void rigidBodyRotationDynamicsStep_mat_taylor( const Mat3d& invIbody, double dt, const Vec3d& torq, Vec3d& L, Mat3d& rotMat, Vec3d& omega ){
L .add_mul ( torq, dt );
rotMat.dot_to_T ( L, omega );
//omega .mul ( invIbody ); // we don't need invI !!!!
invIbody.dot_to ( omega, omega );
rotMat.dot_to ( omega, omega );
rotMat.drotate_omega6(omega*dt);
//return omega;
};
inline void rigidBodyRotationDynamicsStep_quat( const Mat3d& invIbody, double dt, const Vec3d& torq, Vec3d& L, Quat4d& qrot, Mat3d& rotMat, Vec3d& omega ){
qrot .toMatrix_unitary_T( rotMat );
L .add_mul ( torq, dt );
rotMat.dot_to_T ( L, omega );
//omega .mul ( invIbody );
invIbody.dot_to ( omega, omega );
rotMat.dot_to ( omega, omega );
qrot.dRot_taylor2( dt, omega );
//return omega;
};
inline void rigidBodyRotationDynamicsStep_mat_diag( const Vec3d& invIbody, double dt, const Vec3d& torq, Vec3d& L, Mat3d& rotMat, Vec3d& omega ){
L .add_mul ( torq, dt );
rotMat.dot_to_T( L, omega );
omega.mul ( invIbody );
rotMat.dot_to ( omega, omega );
double r2omega = omega.norm2();
if( r2omega > 1e-12 ){ // TODO - more efficient would be do this for |L| instead of |omega|
double romega = sqrt(r2omega);
double dphi = dt*romega;
rotMat.rotate_csa( cos(dphi), sin(dphi), omega*(1/romega) );
}
//return omega;
};
inline void rigidBodyRotationDynamicsStep_mat_diag_taylor( const Vec3d& invIbody, double dt, const Vec3d& torq, Vec3d& L, Mat3d& rotMat, Vec3d& omega ){
L .add_mul ( torq, dt );
rotMat.dot_to_T( L, omega );
omega .mul ( invIbody );
//omega .mul ( invIbody ); // we don't need invI !!!!
rotMat.dot_to ( omega, omega );
rotMat.drotate_omega6(omega);
//return omega;
};
inline void rigidBodyRotationDynamicsStep_quat__diag_taylor( const Vec3d& invIbody, double dt, const Vec3d& torq, Vec3d& L, Quat4d& qrot, Mat3d& rotMat, Vec3d& omega ){
qrot .toMatrix_unitary_T( rotMat );
L .add_mul ( torq, dt );
rotMat.dot_to_T ( L, omega );
omega .mul ( invIbody );
rotMat.dot_to ( omega, omega );
qrot.dRot_taylor2( dt, omega );
//return omega;
};
// ========================
// CLASS : RigidBody
// ========================
class RigidBody : public PointBody { public:
// parameters
// Mat3d Ibody = Mat3dIdentity;
// auxiliary parameters
Mat3d invIbody = Mat3dIdentity;
//Vec3d invIbody = Vec3dOne; // TODO: maybe we will need full tensor of inertia at some point?
// State variables
//Quat4d qrot = Quat4dOne;
Vec3d L = Vec3dZero;
// auxiliary variables
Mat3d rotMat = Mat3dIdentity;
//Mat3d invI = Mat3dIdentity;
Vec3d omega = Vec3dZero;
Vec3d torq = Vec3dZero;
int shape = 0; // displayList
// ==== function declarations
void from_mass_points( int n, double* amass, Vec3d* apos );
void init( );
//void apply_anchor( double k, const Vec3d& lpos, const Vec3d& gpos0 );
virtual void move( double dt );
//virtual void render();
// ==== inline functions
inline void clean_temp( ){ force.set(0.0); torq.set(0.0); }
/*
inline void update_aux( ){
//double qr2 = qrot.norm2();
//if( (qr2 > 1.000001d) || (qr2 < 0.999999d) ){
// qrot.mul(1/sqrt(qr2));
//}
//qrot.toMatrix ( rotMat );
rotMat.orthogonalize_taylor3(2,1,0);
Mat3d tmp;
tmp.set_mmul_NT( invIbody, rotMat ); invI.set_mmul( rotMat, tmp );
//tmp.set_mmul( invIbody, rotMat ); invI.set_mmul_TN( rotMat, tmp );
//tmp.set_mmul( invIbody, rotMat ); invI.set_mmul_NT( rotMat, tmp );
};
*/
inline void move_RigidBody( double dt ){
/*
// postion
vel.add_mul( force, dt*invMass );
pos.add_mul( vel, dt );
// rotation
//update_aux(); // MUST BE HERE, otherwise invI is not initialized in the first step !!!
L .add_mul ( torq, dt ); // we have to use angular momentum as state variable, omega is not conserved
invI.dot_to ( L, omega );
//invI.dot_to_T ( L, omega );
//qrot.dRot_exact ( dt, omega );
qrot.dRot_taylor2( dt, omega );
update_aux();
//printf("force (%3.3f,%3.3f,%3.3f) vel (%3.3f,%3.3f,%3.3f) pos (%3.3f,%3.3f,%3.3f)\n", force.x,force.y,force.z, vel.x,vel.y,vel.z, pos.x, pos.y, pos.z );
//printf("L (%3.3f,%3.3f,%3.3f) omega (%3.3f,%3.3f,%3.3f) qrot (%3.3f,%3.3f,%3.3f,%3.3f)\n", L.x,L.y,L.z, omega.x,omega.y,omega.z, qrot.x, qrot.y, qrot.z, qrot.w );
*/
pointBodyDynamicsStep( invMass, dt, force, vel, pos );
// --- Fast
//rotMat.orthogonalize_taylor3(2,1,0);
//rigidBodyRotationDynamicsStep_mat_taylor( invIbody, dt, torq, L, rotMat, omega );
// --- Stable
rotMat.orthogonalize(2,1,0);
rigidBodyRotationDynamicsStep_mat( invIbody, dt, torq, L, rotMat, omega );
//rigidBodyRotationDynamicsStep_quat( {invIbody.xx,invIbody.yy,invIbody.zz}, dt, torq, L, qrot, rotMat, omega );
};
inline void glob2loc( const Vec3d& gp, Vec3d& lp ) const{
Vec3d tmp; tmp.set_sub(gp,pos);
rotMat.dot_to( tmp, lp );
//rotMat.dot_to_T( tmp, lp );
};
inline void loc2glob( const Vec3d& lp, Vec3d& gp ) const {
rotMat.dot_to_T( lp, gp );
//rotMat.dot_to( lp, gp );
gp.add(pos);
};
inline void velOfPoint( const Vec3d& lp, Vec3d& gv, Vec3d& gdp ) const {
rotMat.dot_to_T( lp, gdp );
gv.set_cross ( omega, gdp );
gv.add(vel);
//gp.add(pos);
}
inline void apply_force( const Vec3d& dforce, const Vec3d& gdpos ){
torq .add_cross( gdpos, dforce );
//torq .add_cross( dforce, gdpos );
force.add( dforce );
};
inline void apply_anchor( double k, const Vec3d& lpos, const Vec3d& gpos0 ){
Vec3d sforce, gdpos;
rotMat.dot_to_T( lpos, gdpos );
//rotMat.dot_to( lpos, gdpos );
sforce.set (( gdpos + pos - gpos0 )*(-k) );
apply_force ( sforce, gdpos );
//drawLine( gpos0, gdpos + pos );
};
/*
inline void checkStateNormal(){
// check if rotation is normalized
double qr2 = qrot.norm2();
double dqr2 = qr2-1;
if( (dqr2*dqr2) > 0.0001 ){ qrot.mul( 1/sqrt(qr2) ); }
}
*/
inline void initInertiaOne(){
setMass( 1.0 );
//invIbody = Vec3dOne;
//Ibody.a.set(1,0,0);
//Ibody.b.set(0,1,0);
//Ibody.c.set(0,0,1);
//Ibody.invert_to( invIbody );
invIbody.a.set(1,0,0);
invIbody.b.set(0,1,0);
invIbody.c.set(0,0,1);
//qrot.setOne();
//qrot.toMatrix ( rotMat );
//update_aux();
};
inline void setPose( const Vec3d& pos_, const Vec3d& dir, const Vec3d& up ){
//w->kind = kind; w->id = warriorCount; warriorCount++;
//initOne();
pos.set ( pos_ );
rotMat.a.set ( dir );
rotMat.b.set ( up );
rotMat.c.set_cross( dir, up );
//qrot.fromMatrix ( rotMat );
//printf( "pos (%g,%g,%g) qrot (%g,%g,%g,%g)\n", pos.x, pos.x, pos.x, qrot.x,qrot.y,qrot.z,qrot.w );
//update_aux();
}
/*
inline void initSpherical( double mass, double I ){
setMass( mass );
//invIbody.set(1/I);
//Ibody.a.set(1/I,0,0);
//Ibody.b.set(0,1/I,0);
//Ibody.c.set(0,0,1/I);
//Ibody.invert_to( invIbody );
invIbody.a.set(1/I,0,0);
invIbody.b.set(0,1/I,0);
invIbody.c.set(0,0,1/I);
//qrot.setOne();
//qrot.toMatrix( rotMat );
//qrot.toMatrix_T( rotMat );
//update_aux();
};
*/
inline void setInertia_box( double m, const Vec3d& halfSpan ){
// https://en.wikipedia.org/wiki/List_of_moments_of_inertia
setMass( m );
double xx = m*halfSpan.x*halfSpan.x;
double yy = m*halfSpan.y*halfSpan.y;
double zz = m*halfSpan.z*halfSpan.z;
invIbody.a.set( 3/(yy+zz), 0, 0 );
invIbody.b.set( 0, 3/(xx+zz), 0 );
invIbody.c.set( 0, 0, 3/(yy+xx) );
}
};
// ===============================
// CLASS : SpringConstrain
// ===============================
class SpringConstrain{ public:
Vec3d p1,p2;
RigidBody *b1=NULL,*b2=NULL;
double kPull,kPush,L0;
// ==== functiopn declarations
inline void getPoints( Vec3d& gp1, Vec3d& gp2 ){
b1->loc2glob(p1,gp1);
if(b2){ b2->loc2glob(p2,gp2); }else{gp2.set(p2);}
}
inline Vec3d getForce( const Vec3d& gp1, const Vec3d& gp2 ){
Vec3d dp; dp.set_sub(gp2, gp1);
double r = dp.norm();
//printf("(%3.3f,%3.3f,%3.3f) %f \n", dp.x, dp.y, dp.z, r);
if( r > L0){
dp.mul( kPull*(r-L0)/(r+1e-16) );
}else{
dp.mul( kPush*(L0-r)/(r+1e-16) );
}
//printf("(%3.3f,%3.3f,%3.3f) \n", dp.x, dp.y, dp.z);
return dp;
}
inline Vec3d apply(){
Vec3d gp1,gp2;
getPoints( gp1, gp2 );
Vec3d f = getForce( gp1, gp2 );
b1 ->apply_force( f , gp1-b1->pos );
if(b2)b2->apply_force( f*-1, gp2-b2->pos );
return f;
};
//void render();
//SpringConstrain( double k_, RigidBody* b1_, RigidBody* b2_, const Vec3d& p1_, const Vec3d& p2_ );
SpringConstrain( double kPull_, double kPush_, double L0_, RigidBody* b1_, RigidBody* b2_, const Vec3d& p1_, const Vec3d& p2_ );
};
#endif // #ifndef Body_h