void qrot() {
double a[4], b[4], c1[4], c2[4];
aa_vrand( 4, a );
aa_vrand( 4, b );
aa_tf_qnormalize(a);
aa_tf_qnormalize(b);
aa_tf_qrot(a,b,c1);
aa_vecm_qrot(a,b,c2);
aveq( "qrot-equal", 3, c1, c2, .0001 );
aa_tick("qrot non-vec: ");
for( size_t i = 0; i < N; i ++ ) {
aa_tf_qrot(a,b,c1);
}
aa_tock();
aa_tick("qrot vec: ");
for( size_t i = 0; i < N; i ++ ) {
aa_vecm_qrot(a,b,c1);
}
aa_tock();
}
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 qmul() {
double a[4], b[4], c1[4], c2[4];
double va[4], vb[4];
aa_vrand( 4, a );
aa_vrand( 4, b );
aa_tf_qnormalize(a);
aa_tf_qnormalize(b);
aa_vec_d4_st( va, aa_vec_d4_ld(a) );
aa_vec_d4_st( vb, aa_vec_d4_ld(b) );
aveq( "lda", 4, a, va, .000 );
aveq( "ldb", 4, b, vb, .000 );
aa_tf_qmul(a,b,c1);
aa_vecm_qmul(a,b,c2);
aveq( "quat-equal", 4, c1, c2, .0001 );
aa_tick("qmul non-vec: ");
for( size_t i = 0; i < N; i ++ ) {
aa_tf_qmul(a,b,c1);
}
aa_tock();
aa_tick("qmul vec: ");
for( size_t i = 0; i < N; i ++ ) {
aa_vecm_qmul(a,b,c1);
}
aa_tock();
}
void rel_q() {
// random transforms
double q0[4], qrel[4], q1[4];
aa_vrand(4,q0);
aa_vrand(4,q1);
aa_tf_qnormalize(q0);
aa_tf_qnormalize(q1);
aa_tf_qcmul(q0, q1, qrel );
// random velocity, point 0
double dx0[3]={0}, dq0[4];
aa_vrand(3,dx0);
aa_tf_qvel2diff( q0, dx0, dq0 );
// computed velocity, point 1
double dq1[4], dx1[3];
aa_tf_qmul( dq0, qrel, dq1 );
aa_tf_qdiff2vel( q1, dq1, dx1 );
// integrate both velocities
double q0_1[4], q1_1[4];
aa_tf_qsvel( q0, dx0, .1, q0_1 );
aa_tf_qsvel( q1, dx1, .1, q1_1 );
// new relative orientation
double qrel_1[4];
aa_tf_qcmul( q0_1, q1_1, qrel_1 );
// check
aveq("relq", 4, qrel, qrel_1, .000001);
}
void tfmul() {
double q0[4], q1[4];
double T0[12], T1[12];
double Ua[12], Ub[12];
aa_vrand( 4, q0 );
aa_vrand( 4, q1 );
aa_tf_qnormalize(q0);
aa_tf_qnormalize(q1);
aa_tf_quat2rotmat( q0, T0 );
aa_tf_quat2rotmat( q1, T1 );
aa_vrand( 3, T0+9 );
aa_vrand( 3, T1+9 );
// cross
aa_tf_12chain(T0,T1,Ua);
aa_vecm_tfmul(T0,T1,Ub);
aveq( "tfmul-equal", 12, Ua, Ub, .0001 );
aa_tick("tfmul non-vec: ");
for( size_t i = 0; i < N; i ++ ) {
aa_tf_12chain(T0,T1,Ua);
}
aa_tock();
aa_tick("tfmul vec: ");
for( size_t i = 0; i < N; i ++ ) {
aa_vecm_tfmul(T0,T1,Ub);
}
aa_tock();
}
static void slerp() {
double q[4], qy[4], u, du;
double dq1[4], dq2[4], dqy[4];
aa_tf_qurand(q);
u = aa_frand();
du = aa_frand();
aa_vrand(4,dq1);
aa_vrand(4,dq2);
aa_tf_qslerpchaindiff( u, du, q, dq1, q, dq2, qy, dqy );
aveq("chaindiff equiv", 4, q, qy, 1e-6);
}
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);
}
void qvmul(void) {
double q[4], v[4], r1[4], r2[4];
aa_vrand( 3, v );
v[3] = 0;
aa_vrand( 4, q );
aa_tf_qmul_qv( q, v, r1);
aa_tf_qmul( q, v, r2);
aveq( "qmul_qv", 4, r1, r2, 1e-7 );
aa_tf_qmul_vq( v, q, r1);
aa_tf_qmul( v, q, r2);
aveq( "qmul_v", 4, r1, r2, 1e-7 );
}
static void rotmat(double *q) {
//double q[4], R[9], w[3], dR[9], dRw[3];
//aa_tf_qurand( q );
double R[9], w[3], dR[9], dRw[3];
aa_vrand( 3, w );
aa_tf_quat2rotmat(q, R);
aa_tf_rotmat_vel2diff( R, w, dR );
aa_tf_rotmat_diff2vel( R, dR, dRw );
aveq("rotmat-vel", 3, w, dRw, 1e-6 );
}
static void tfmat() {
double v[6], evR[9], ev[12], lneR[3], lne[6];
aa_vrand( 6, v );
aa_tf_tfmat_expv( v, ev );
aa_tf_rotmat_expv( v+3, evR );
aveq( "rotmat-tfmat-exp", 9, evR, ev, 1e-6 );
aa_tf_tfmat_lnv( ev, lne );
aa_tf_rotmat_lnv( evR, lneR );
aveq( "rotmat-exp-ln", 3, v+3, lneR, 1e-6 );
aveq( "tfmat-exp-ln", 6, v, lne, 1e-6 );
}
void cross() {
double a[3], b[3], c1[3], c2[3];
aa_vrand( 3, a );
aa_vrand( 3, b );
// cross
aa_tf_cross(a,b,c1);
aa_vecm_cross(a,b,c2);
aveq( "cross-equal", 3, c1, c2, .0001 );
aa_tick("cross non-vec: ");
for( size_t i = 0; i < N; i ++ ) {
aa_tf_cross(a,b,c1);
}
aa_tock();
aa_tick("cross vec: ");
for( size_t i = 0; i < N; i ++ ) {
aa_vecm_cross(a,b,c1);
}
aa_tock();
}
int main( void ) {
// init
time_t seed = time(NULL);
printf("seed: %ld\n", seed);
srand((unsigned int)seed); // might break in 2038
aa_test_ulimit();
for( size_t i = 0; i < 1000; i++ ) {
/* Random Data */
static const size_t k=2;
double E[2][7], S[2][8], T[2][12], dx[2][6];
for( size_t j = 0; j < k; j ++ ) {
rand_tf(E[j], S[j], T[j]);
aa_vrand(6,dx[j]);
}
//printf("%d\n",i);
/* Run Tests */
rotvec(E[0]);
euler(dx[0]);
euler1(dx[0]);
eulerzyx(E[0]);
chain(E,S,T);
quat(E);
duqu();
rel_q();
rel_d();
slerp();
theta2quat();
rotmat(E[0]);
tfmat();
tfmat_inv(T[0]);
mzlook(dx[0]+0, dx[0]+3, dx[1]+0);
integrate(E[0], S[0], T[0], dx[0]);
tf_conj(E, S);
qdiff(E,dx);
}
return 0;
}
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 );
}
}
static void quat(double E[2][7]) {
double u;
double *q1 = E[0];
double *q2 = E[0];
u = aa_frand();
{
double qg[4], qa[4];
aa_tf_qslerp( u, q1, q2, qg );
aa_tf_qslerpalg( u, q1, q2, qa );
aveq("slerp", 4, qg, qa, .001 );
double dqg[4], dqa[4];
aa_tf_qslerpdiff( u, q1, q2, dqg );
aa_tf_qslerpdiffalg( u, q1, q2, dqa );
aveq("slerpdiff", 4, dqg, dqa, .001 );
}
// mul
{
double Ql[16], Qr[16];
double y0[4], y1[4], y2[4];
aa_tf_qmatrix_l(q1, Ql, 4);
aa_tf_qmatrix_r(q2, Qr, 4);
aa_tf_qmul(q1,q2, y0);
cblas_dgemv( CblasColMajor, CblasNoTrans, 4, 4,
1.0, Ql, 4,
q2, 1,
0, y1, 1 );
cblas_dgemv( CblasColMajor, CblasNoTrans, 4, 4,
1.0, Qr, 4,
q1, 1,
0, y2, 1 );
aveq( "qmul-1", 4, y0, y1, 1e-6 );
aveq( "qmul-2", 4, y0, y2, 1e-6 );
}
// average
{
double qq[8], p[4], s[4];
AA_MEM_CPY( qq, q1, 4 );
AA_MEM_CPY( qq+4, q2, 4 );
double w[2] = {.5,.5};
aa_tf_quat_davenport( 2, w, qq, 4, p );
aa_tf_qslerp( .5, q1, q2, s );
aa_tf_qminimize( p );
aa_tf_qminimize( s );
aveq("davenport-2", 4, p, s, 1e-4 );
}
double R1[9], R2[9], Rr[9], qr[4], qrr[4];
aa_tf_quat2rotmat(q1, R1);
aa_tf_quat2rotmat(q2, R2);
aa_tf_9rel( R1, R2, Rr );
aa_tf_qrel( q1, q2, qr );
aa_tf_rotmat2quat( Rr, qrr );
aa_tf_qminimize( qr );
aa_tf_qminimize( qrr );
aveq("qrel", 4, qr, qrr, .001 );
// minimize
{
double qmin[4], axang[4];
aa_tf_qminimize2( q1, qmin );
test( "quat-minimize", aa_feq( fabs(q1[3]), qmin[3], 0) );
aa_tf_quat2axang( qmin, axang );
test( "quat-minimize-angle", fabs(axang[3]) <= M_PI );
}
// mulc
{
double q1c[4], q2c[4], t1[4], t2[4];
aa_tf_qconj(q1, q1c);
aa_tf_qconj(q2, q2c);
aa_tf_qmul(q1,q2c,t1);
aa_tf_qmulc(q1,q2,t2);
aveq("qmulc", 4, t1, t2, .001 );
aa_tf_qmul(q1c,q2,t1);
aa_tf_qcmul(q1,q2,t2);
aveq("qcmul", 4, t1, t2, .001 );
}
// conj. props
{
// p*q = conj(conj(q) * conj(p))
double c1[4], c2[4], c2c1[4], cc2c1[4], q1q2[4];
aa_tf_qconj(q1,c1);
aa_tf_qconj(q2,c2);
aa_tf_qmul(c2,c1,c2c1);
aa_tf_qmul(q1,q2,q1q2);
aa_tf_qconj(c2c1,cc2c1);
aveq("conjprop", 4, q1q2, cc2c1, .0001);
}
// exp
{
double q1e[4], q1eln[4];
aa_tf_qexp(q1, q1e);
aa_tf_qln(q1e, q1eln);
aveq("exp-log", 4, q1, q1eln, .00001 );
aa_tf_qln(q1, q1eln);
aa_tf_qexp(q1eln, q1e);
aveq("log-exp", 4, q1, q1e, .00001 );
}
// diff
double w[3]={0}, dq[4], wdq[3];
aa_vrand( 3, w );
aa_tf_qvel2diff( q1, w, dq );
aa_tf_qdiff2vel( q1, dq, wdq );
aveq("qveldiff", 3, w, wdq, .000001);
// integrate
double qn_rk1[4], qn_vrk1[4], qn_vrk4[4], qn_vexp[4], qn_dq[4], w0[3] = {0};
double dt = .02;
aa_tf_qrk1( q1, dq, dt, qn_rk1 );
aa_tf_qvelrk1( q1, w, dt, qn_vrk1 );
aa_tf_qvelrk4( q1, w, dt, qn_vrk4 );
aa_tf_qsvel( q1, w, dt, qn_vexp );
aa_tf_qsdiff( q1, dq, dt, qn_dq );
aveq("qvelrk1", 4, qn_rk1, qn_vrk1, .001 );
aveq("qvelrk4", 4, qn_rk1, qn_vrk4, .001 );
aveq("qvelexp", 4, qn_vrk4, qn_vexp, .0001);
aveq("qvelsdiff", 4, qn_vexp, qn_dq, .001 );
aa_tf_qsvel( q1, w0, dt, qn_vexp );
aveq("qvelsvel0", 4, q1, qn_vexp, .000 );
{
double Rb[9], qR[4];
aa_tf_qsvel( q1, w, dt, qn_vexp );
aa_tf_rotmat_svel( R1, w, dt, Rb );
aa_tf_rotmat2quat( Rb, qR );
aa_tf_qminimize( qn_vexp);
aa_tf_qminimize( qR );
aveq("rotmat_svel", 4, qn_vexp, qR, 1e-4 );
}
// vectors
{
double *v0 = E[0] + AA_TF_QUTR_T;
double *v1 = E[1] + AA_TF_QUTR_T;
double q[4], vp[3];
// identify case
aa_tf_vecs2quat( v0, v0, q);
aveq( "vecs2quat-ident", 4, q, aa_tf_quat_ident, 1e-6 );
// regular case
aa_tf_vecs2quat( v0, v1, q);
aa_tf_qrot(q,v0,vp);
// normalize result
{
double n0 = sqrt(v0[0]*v0[0] + v0[1]*v0[1] + v0[2]*v0[2] );
double n1 = sqrt(v1[0]*v1[0] + v1[1]*v1[1] + v1[2]*v1[2] );
double vp1[3];
for( size_t i = 0; i < 3; i ++ ) {
vp1[i] = n0*v1[i] / n1;
}
aveq("vecs2quat", 3, vp, vp1, 1e-6 );
}
// inverted case
double v0n[3] = {-v0[0], -v0[1], -v0[2]};
aa_tf_vecs2quat( v0, v0n, q);
aa_tf_qrot(q,v0,vp);
{
double n0 = sqrt(v0[0]*v0[0] + v0[1]*v0[1] + v0[2]*v0[2] );
double n1 = sqrt(v0n[0]*v0n[0] + v0n[1]*v0n[1] + v0n[2]*v0n[2] );
double vp1[3];
for( size_t i = 0; i < 3; i ++ ) {
vp1[i] = n0*v0n[i] / n1;
}
aveq("vecs2quat-degenerate", 3, vp, vp1, 1e-6 );
}
}
}