void duqumul() {
double q0[4], q1[4];
double v0[3], v1[3];
double d0[8], d1[8];
double ra[8], rb[8];
aa_vrand( 4, q0 );
aa_vrand( 4, q1 );
aa_tf_qnormalize(q0);
aa_tf_qnormalize(q1);
aa_vrand( 3, v0 );
aa_vrand( 3, v1 );
aa_tf_qv2duqu( q0, v0, d0 );
aa_tf_qv2duqu( q1, v1, d1 );
aa_tf_duqu_mul(q0,q1,ra);
aa_vecm_duqu_mul(q0,q1,rb);
aveq( "duqu_mul-equal", 8, ra, rb, .0001 );
aa_tick("duqu-mul non-vec: ");
for( size_t i = 0; i < N; i ++ ) {
aa_tf_duqu_mul(d0,d1,ra);
}
aa_tock();
aa_tick("duqu-mul vec: ");
for( size_t i = 0; i < N; i ++ ) {
aa_vecm_duqu_mul(q0,q1,rb);
}
aa_tock();
}
void rel_d() {
// random transforms
double q0[4], v0[3], q1[4], v1[4];
aa_vrand(4,q0);
aa_vrand(4,q1);
aa_tf_qnormalize(q0);
aa_tf_qnormalize(q1);
aa_vrand(3,v0);
aa_vrand(3,v1);
// dual quat transforms
double d0[8], drel[8], d1[8], d1p[8];
aa_tf_qv2duqu(q0,v0, d0);
aa_tf_qv2duqu(q1,v1, d1);
// d0 * drel = d1
// drel = conj(d0) * d1
aa_tf_duqu_cmul( d0, d1, drel );
aa_tf_duqu_mul( d0, drel, d1p );
aveq("duqu-relmul", 8, d1, d1p, .001 );
// random velocity
double dx0[6], dd0[8];
aa_vrand(6,dx0);
aa_tf_duqu_vel2diff(d0, dx0, dd0);
// second velocity
// d1 = d0*drel
// d1/dt = d0/dt * drel + d0 * drel/dt, and drel/dt = 0
double dd1[8];
aa_tf_duqu_mul( dd0, drel, dd1 );
// integrate
double d0_1[8], d1_1[8];
double dt = .1;
aa_tf_duqu_sdiff( d0, dd0, dt, d0_1 );
aa_tf_duqu_sdiff( d1, dd1, dt, d1_1 );
aa_tf_duqu_normalize( d0_1 );
aa_tf_duqu_normalize( d1_1 );
// new relative
double drel_1[8];
// drel = d0*inv(d1)
aa_tf_duqu_cmul( d0_1, d1_1, drel_1 );
// twist
double d0_1t[8], d1_1t[8], drel_1t[8];
aa_tf_duqu_svel( d0, dx0, dt, d0_1t );
aa_tf_duqu_sdiff( d1, dd1, dt, d1_1t );
aa_tf_duqu_cmul( d0_1t, d1_1t, drel_1t );
// check
aveq("rel_d", 8, drel, drel_1t, 1e-6);
}
AA_API void
aa_tf_qv_svel( const double q0[AA_RESTRICT 4], const double v0[AA_RESTRICT 3],
const double w[AA_RESTRICT 3], const double dv[AA_RESTRICT 3],
double dt,
double q1[AA_RESTRICT 4], double v1[AA_RESTRICT 3] )
{
double dx[6], S0[8], S1[8];
/* TODO: avoid the memcpy()s */
AA_MEM_CPY( dx+AA_TF_DX_W, w, 3 );
AA_MEM_CPY( dx+AA_TF_DX_V, dv, 3 );
aa_tf_qv2duqu( q0, v0, S0 );
aa_tf_duqu_svel( S0, dx, dt, S1 );
aa_tf_duqu2qv(S1, q1, v1);
}
static void duqu() {
// random tf
aa_tf_tfmat_t T;
aa_tf_duqu_t H;
double E[7];
double S_ident[8] = AA_TF_DUQU_IDENT_INITIALIZER;
double Q_ident[4] = AA_TF_QUAT_IDENT_INITIALIZER;
double v_ident[3] = {0};
double p0[3];
rand_tf( E, H.data, T.data );
aa_vrand( 3, p0 );
{
double A[8], B[8];
aa_vrand(8,A);
aa_vrand(8,B);
// mul
{
double A_L[8*8], B_R[8*8];
double C[8], Cl[8], Cr[8];
aa_tf_duqu_mul(A,B,C);
aa_tf_duqu_matrix_l(A, A_L, 8);
cblas_dgemv( CblasColMajor, CblasNoTrans, 8, 8,
1.0, A_L, 8,
B, 1,
0, Cl, 1 );
aveq( "duqu-mul-L", 8, C, Cl, 1e-6 );
aa_tf_duqu_matrix_r(B, B_R, 8);
cblas_dgemv( CblasColMajor, CblasNoTrans, 8, 8,
1.0, B_R, 8,
A, 1,
0, Cr, 1 );
aveq( "duqu-mul-R", 8, C, Cr, 1e-6 );
}
// add / sub
{
double Ca[8], Cs[8], mB[8];
for( size_t i = 0; i < 8; i ++ ) mB[i] = -B[i];
aa_tf_duqu_add(A,B,Ca);
aa_tf_duqu_sub(A,mB,Cs);
aveq( "duqu-add-sub", 8, Ca, Cs, 1e-6 );
double Cra[4], Crs[4];
double Cda[4], Cds[4];
aa_tf_duqu_sub(A,B,Cs);
aa_tf_qadd(A+AA_TF_DUQU_REAL, B+AA_TF_DUQU_REAL,Cra);
aa_tf_qadd(A+AA_TF_DUQU_DUAL, B+AA_TF_DUQU_DUAL,Cda);
aa_tf_qsub(A+AA_TF_DUQU_REAL, B+AA_TF_DUQU_REAL,Crs);
aa_tf_qsub(A+AA_TF_DUQU_DUAL, B+AA_TF_DUQU_DUAL,Cds);
aveq( "duqu-qadd-real", 4, Cra, Ca+AA_TF_DUQU_REAL, 1e-6);
aveq( "duqu-qadd-dual", 4, Cda, Ca+AA_TF_DUQU_DUAL, 1e-6);
aveq( "duqu-qsub-real", 4, Crs, Cs+AA_TF_DUQU_REAL, 1e-6);
aveq( "duqu-qsub-dual", 4, Cds, Cs+AA_TF_DUQU_DUAL, 1e-6);
}
}
//double q[4], v[3], p0[3];
//aa_vrand( 3, v );
//aa_tf_qurand( q );
//AA_MEM_SET( v, 0, 3 );
// tfmat
//aa_tf_quat2rotmat(q, T.R);
//AA_MEM_CPY( &T.t.x, v, 3 );
// dual quat
//aa_tf_qv2duqu( q, v, H.data );
//aa_tf_qv2duqu( aa_tf_quat_ident, v, H_tran.data );
// check trans
double hv[3];
aa_tf_duqu_trans(H.data, hv);
aveq("duqu-trans", 3, T.v.data, hv, .001 );
//double nreal,ndual;
//aa_tf_duqu_norm( H.data, &nreal, &ndual );
//printf("norm: %f + %f \\epsilon \n", nreal, ndual );
// transform points
double p1H[3], p1qv[3], p1T[3];
aa_tf_12( T.data, p0, p1T );
aa_tf_tf_qv( H.real.data, T.v.data, p0, p1qv );
aa_tf_tf_duqu( H.data, p0, p1H );
aveq( "tf-qv", 3, p1T, p1qv, .001 );
aveq( "tf-duqu", 3, p1T, p1H, .001 );
// conjugate
{
double S_conj[8];
double qv_conj[7], E_conj[7];
double SSc[8], EEc[7];
double Scv[3];
aa_tf_duqu_conj(H.data, S_conj);
aa_tf_qv_conj(H.real.data, T.v.data, qv_conj, qv_conj+4);
aa_tf_qutr_conj(E, E_conj);
aa_tf_duqu_trans(S_conj, Scv);
aveq( "duqu/qutr conj q", 4, S_conj, E_conj, 1e-6 );
aveq( "duqu/qv conj q", 4, S_conj, qv_conj, 1e-6 );
aveq( "duqu/qutr conj v", 3, Scv, E_conj+4, 1e-6 );
aveq( "duqu/qv conj v", 3, Scv, qv_conj+4, 1e-6 );
aa_tf_duqu_mul( H.data, S_conj, SSc );
aa_tf_qv_chain( H.real.data, T.v.data, qv_conj, qv_conj+4, EEc, EEc+4 );
aveq( "duqu conj", 8, SSc, S_ident, 1e-6 );
aveq( "qv conj q", 4, EEc, Q_ident, 1e-6 );
aveq( "qv conj v", 3, EEc+4, v_ident, 1e-6 );
}
// derivative
{
double dx[6], dd[8], dq[4];
aa_vrand(6, dx);
double dt = aa_frand() / 100;
aa_tf_duqu_vel2diff( H.data, dx, dd );
aa_tf_qvel2diff( H.real.data, dx+3, dq );
// back to velocity
double dx1[6];
aa_tf_duqu_diff2vel( H.data, dd, dx1 );
aveq( "duqu-vel invert", 6, dx, dx1, .001 );
// integrate
double H1[8], q1[4], v1[3], H1qv[8];
double H1_sdd[8], H1_sdx[8];
for( size_t i = 0; i < 8; i ++ ) H1[i] = H.data[i] + dd[i]*dt; // some numerical error here...
for( size_t i = 0; i < 3; i ++ ) v1[i] = T.v.data[i] + dx[i]*dt;
aa_tf_duqu_normalize( H1 );
aa_tf_qsvel( H.real.data, dx+3, dt, q1 );
aa_tf_qv2duqu( q1, v1, H1qv );
aveq( "duqu-vel_real", 4, dq, dd, .001 );
aveq( "duqu-vel-int real", 4, H1, H1qv, .001 );
aveq( "duqu-vel-int dual", 4, H1+4, H1qv+4, .001 );
aa_tf_duqu_svel( H.data, dx, dt, H1_sdx );
aa_tf_duqu_sdiff( H.data, dd, dt, H1_sdd );
aveq( "duqu-int vel", 8, H1qv, H1_sdx, .001 );
aveq( "duqu-int diff", 8, H1_sdx, H1_sdd, .0001 );
/* // twist */
double tw[8], dxtw[6];
aa_tf_duqu_vel2twist(H.data, dx, tw );
aa_tf_duqu_twist2vel(H.data, tw, dxtw );
aveq( "duqu twist<->vel", 6, dx, dxtw, 1e-6 );
}
// exponential
{
double expd[8], lnexpd[8];
aa_tf_duqu_exp(H.data, expd );
aa_tf_duqu_ln( expd, lnexpd );
aveq( "duqu-exp-ln", 8, H.data, lnexpd, .001 );
aa_tf_duqu_ln( H.data, lnexpd );
aa_tf_duqu_exp(lnexpd, expd );
aveq( "duqu-ln-exp", 8, H.data, expd, .001 );
}
// Logarithm
{
double HI[8], HIln[8], dxi[6], dx0[6] = {0};
aa_tf_duqu_mulc( H.data, H.data, HI );
aa_tf_duqu_ln(HI, HIln);
aa_tf_duqu_twist2vel(HI, HIln, dxi );
aveq( "duqu ln 0 near", 6, dx0, dxi, .0001 );
aa_tf_duqu_ln(aa_tf_duqu_ident, HIln);
aa_tf_duqu_twist2vel(HI, HIln, dxi );
aveq( "duqu ln 0 exact", 6, dx0, dxi, 0.0 );
}
// Pure translation
{
double S[8], v[3], v1[3];
aa_vrand(3,v);
aa_tf_xyz2duqu( v[0], v[1], v[2], S );
aa_tf_duqu_trans(S, v1);
aveq( "duqu trans orientation", 4, S, aa_tf_quat_ident, 0.0 );
aveq( "duqu trans translation", 3, v, v1, 1e-6 );
}
}
