int plane_normal(t_data *data)
{
const t_plane plane = data->scene.planes[data->closest[1]];
const t_ray ray = data->viewray;
if (vec3_dot(plane.normal, ray.dir) < 0)
data->normal = plane.normal;
else
data->normal = vec3_reverse(plane.normal);
data->material = data->scene.materials[
data->scene.planes[data->closest[1]].m];
data->new_start = vec3_add(data->viewray.start,
vec3_mult(data->viewray.dir, data->t));
return (1);
}
// ===========================================================================================
void Quaternion_byAngleAndVector(quat_t *Q, const real_t q_angle, const vec3_t *q_vector)
{
vec3_t rotation_axis;
normRv(&rotation_axis, q_vector);
//real_t f = _sin(q_angle * 0.5);
real_t f, cs;
_sin_cos(q_angle*0.5, &f, &cs);
vec3_copy(&Q->v, &rotation_axis);
vec3_mult(&Q->v, f);
//Q->s = _cos(q_angle*0.5);
Q->s = cs;
quat_mult(Q, 1.0 / quat_norm(Q));
}
void arGetInitRot2_sub(rpp_float &err,
rpp_mat &R,
rpp_vec &t,
const rpp_float cc[2],
const rpp_float fc[2],
const rpp_vec *model,
const rpp_vec *iprts,
const unsigned int model_iprts_size,
const rpp_mat R_init,
const bool estimate_R_init,
const rpp_float epsilon,
const rpp_float tolerance,
const unsigned int max_iterations)
{
vec3_array _model;
vec3_array _iprts;
_model.resize(model_iprts_size);
_iprts.resize(model_iprts_size);
mat33_t K, K_inv;
mat33_eye(K);
K.m[0][0] = (real_t)fc[0];
K.m[1][1] = (real_t)fc[1];
K.m[0][2] = (real_t)cc[0];
K.m[1][2] = (real_t)cc[1];
mat33_inv(K_inv, K);
for(unsigned int i=0; i<model_iprts_size; i++)
{
vec3_t _v,_v2;
vec3_assign(_v,(real_t)model[i][0],(real_t)model[i][1],(real_t)model[i][2]);
_model[i] = _v;
vec3_assign(_v,(real_t)iprts[i][0],(real_t)iprts[i][1],(real_t)iprts[i][2]);
vec3_mult(_v2,K_inv,_v);
_iprts[i] = _v2;
}
options_t options;
options.max_iter = max_iterations;
options.epsilon = (real_t)(epsilon == 0 ? DEFAULT_EPSILON : epsilon);
options.tol = (real_t)(tolerance == 0 ? DEFAULT_TOL : tolerance);
if(estimate_R_init)
mat33_set_all_zeros(options.initR);
else
{
mat33_assign(options.initR,
(real_t)R_init[0][0], (real_t)R_init[0][1], (real_t)R_init[0][2],
(real_t)R_init[1][0], (real_t)R_init[1][1], (real_t)R_init[1][2],
(real_t)R_init[2][0], (real_t)R_init[2][1], (real_t)R_init[2][2]);
}
real_t _err;
mat33_t _R;
vec3_t _t;
arGetInitRot2_sub2(_err,_R,_t,_model,_iprts,options);
for(int j=0; j<3; j++)
{
R[j][0] = (rpp_float)_R.m[j][0];
R[j][1] = (rpp_float)_R.m[j][1];
R[j][2] = (rpp_float)_R.m[j][2];
t[j] = (rpp_float)_t.v[j];
}
err = (rpp_float)_err;
}
void getRotationY_wrtT(double *al_ret, vec3_t *tnew, const vec3_t *v,
const vec3_t *p, const vec3_t *t, const real_t *DB,
const mat33_t *Rz, const int n, int *res_n)
{
int i,j,k;
mat33_t V[n];
for(i=0; i<n; i++)
{
vec3_mul_vec3trans(&V[i], &v[i], &v[i]);
mat33_div(&V[i], vec3trans_mul_vec3(&v[i], &v[i]));
}
mat33_t G, _g1, _g2, _g3;
mat33_array_sum(&_g1, &*V, n);
mat33_eye(&_g2);
mat33_div(&_g1, (real_t)(n));
mat33_sub_mat2(&_g3, &_g2, &_g1);
mat33_inv(&G, &_g3);
mat33_div(&G, (real_t)(n));
mat33_t _opt_t;
mat33_clear(&_opt_t);
for(i=0; i<n; i++)
{
const real_t v11 = V[i].m[0];
const real_t v21 = V[i].m[3];
const real_t v31 = V[i].m[6];
const real_t v12 = V[i].m[1];
const real_t v22 = V[i].m[4];
const real_t v32 = V[i].m[7];
const real_t v13 = V[i].m[2];
const real_t v23 = V[i].m[5];
const real_t v33 = V[i].m[8];
const real_t px = p[i].v[0];
const real_t py = p[i].v[1];
const real_t pz = p[i].v[2];
const real_t r1 = Rz->m[0];
const real_t r2 = Rz->m[1];
const real_t r3 = Rz->m[2];
const real_t r4 = Rz->m[3];
const real_t r5 = Rz->m[4];
const real_t r6 = Rz->m[5];
const real_t r7 = Rz->m[6];
const real_t r8 = Rz->m[7];
const real_t r9 = Rz->m[8];
mat33_t _o;
_o.m[0] = (((v11-(real_t)(1))*r2+v12*r5+v13*r8)*py+(-(v11-(real_t)(1))*r1-v12*r4-v13*r7)*px+(-(v11-(real_t)(1))*r3-v12*r6-v13*r9)*pz);
_o.m[1] = (((real_t)(2)*(v11-(real_t)(1))*r1+(real_t)(2)*v12*r4+(real_t)(2)*v13*r7)*pz+(-(real_t)(2)*(v11-(real_t)(1))*r3-(real_t)(2)*v12*r6-(real_t)(2)*v13*r9)*px);
_o.m[2] = ((v11-(real_t)(1))*r1+v12*r4+v13*r7)*px+((v11-(real_t)(1))*r3+v12*r6+v13*r9)*pz+((v11-(real_t)(1))*r2+v12*r5+v13*r8)*py;
_o.m[3] = ((v21*r2+(v22-(real_t)(1))*r5+v23*r8)*py+(-v21*r1-(v22-(real_t)(1))*r4-v23*r7)*px+(-v21*r3-(v22-(real_t)(1))*r6-v23*r9)*pz);
_o.m[4] = (((real_t)(2)*v21*r1+(real_t)(2)*(v22-(real_t)(1))*r4+(real_t)(2)*v23*r7)*pz+(-(real_t)(2)*v21*r3-(real_t)(2)*(v22-(real_t)(1))*r6-(real_t)(2)*v23*r9)*px);
_o.m[5] = (v21*r1+(v22-(real_t)(1))*r4+v23*r7)*px+(v21*r3+(v22-(real_t)(1))*r6+v23*r9)*pz+(v21*r2+(v22-(real_t)(1))*r5+v23*r8)*py;
_o.m[6] = ((v31*r2+v32*r5+(v33-(real_t)(1))*r8)*py+(-v31*r1-v32*r4-(v33-(real_t)(1))*r7)*px+(-v31*r3-v32*r6-(v33-(real_t)(1))*r9)*pz);
_o.m[7] = (((real_t)(2)*v31*r1+(real_t)(2)*v32*r4+(real_t)(2)*(v33-(real_t)(1))*r7)*pz+(-(real_t)(2)*v31*r3-(real_t)(2)*v32*r6-(real_t)(2)*(v33-(real_t)(1))*r9)*px);
_o.m[8] = (v31*r1+v32*r4+(v33-(real_t)(1))*r7)*px+(v31*r3+v32*r6+(v33-(real_t)(1))*r9)*pz+(v31*r2+v32*r5+(v33-(real_t)(1))*r8)*py;
mat33_add(&_opt_t, &_o);
}
mat33_t opt_t;
mat33_mult_mat2(&opt_t, &G, &_opt_t);
real_t E_2[5] = {0,0,0,0,0};
for(i=0; i<n; i++)
{
const real_t px = p[i].v[0];
const real_t py = p[i].v[1];
const real_t pz = p[i].v[2];
mat33_t Rpi;
mat33_assign(&Rpi, -px, (real_t)(2)*pz,px,py,(real_t)(0),py,-pz,-(real_t)(2)*px,pz);
mat33_t E,_e1,_e2;
mat33_eye(&_e1);
mat33_sub(&_e1, &V[i]);
mat33_mult_mat2(&_e2, Rz, &Rpi);
mat33_add(&_e2, &opt_t);
mat33_mult_mat2(&E,&_e1,&_e2);
vec3_t e2,e1,e0;
mat33_to_col_vec3(&e2,&e1,&e0,&E);
vec3_t _E2_0,_E2_1,_E2_2,_E2_3,_E2_4;
vec3_copy(&_E2_0,&e2);
vec3_mult_vec(&_E2_0,&e2);
vec3_copy(&_E2_1,&e1);
vec3_mult_vec(&_E2_1,&e2);
vec3_mult(&_E2_1,2.0);
vec3_copy(&_E2_2,&e0);
vec3_mult_vec(&_E2_2,&e2);
vec3_mult(&_E2_2,2.0);
vec3_t _e1_sq;
vec3_copy(&_e1_sq,&e1);
vec3_mult_vec(&_e1_sq,&e1);
vec3_add_vec(&_E2_2,&_e1_sq);
vec3_copy(&_E2_3,&e0);
vec3_mult_vec(&_E2_3,&e1);
vec3_mult(&_E2_3,2.0);
vec3_copy(&_E2_4,&e0);
vec3_mult_vec(&_E2_4,&e0);
E_2[0] += vec3_sum(&_E2_0);
E_2[1] += vec3_sum(&_E2_1);
E_2[2] += vec3_sum(&_E2_2);
E_2[3] += vec3_sum(&_E2_3);
E_2[4] += vec3_sum(&_E2_4);
}
//scalar_array _a;
//_a.resize(5);
double _a[5];
_a[4] = -E_2[1];
_a[3] = (real_t)(4)*E_2[0] - (real_t)(2)*E_2[2];
_a[2] = -(real_t)(3)*E_2[3] + (real_t)(3)*E_2[1];
_a[1] = -(real_t)(4)*E_2[4] + (real_t)(2)*E_2[2];
_a[0] = E_2[3];
double at_sol[5];
int num_sol = solve_polynomial(&*at_sol, &*_a, 5);
double e[num_sol];
scalar_array_clear(&*e, num_sol);
double at[num_sol];
if(COMPLICATED_ERROR_CMP)
{
// get the error in a complicate way
scalar_array_clear(&*e, num_sol);
scalar_array_add(&*e, _a[0], num_sol);
//at.clear();
//at.assign(at_sol.begin(),at_sol.end());
memcpy(&*at, &*at_sol, num_sol*sizeof(double));
scalar_array_mult(&*at, _a[1], num_sol);
scalar_array_add_vec(&*e, &*at, num_sol);
for(j=2; j<=4; j++)
{
//at.clear();
//at.assign(at_sol.begin(),at_sol.end());
memcpy(&*at, &*at_sol, num_sol*sizeof(double));
scalar_array_pow(&*at, (real_t)(j), num_sol);
scalar_array_mult(&*at, _a[j], num_sol);
scalar_array_add_vec(&*e, &*at, num_sol);
}
}
else
{
// Or in a fast one
scalar_array_add(&*e, _a[4], num_sol);
for(j=3;j>0;j--)
{
// multiply with at & add a_
for(k=0;k<num_sol;k++)
{
e[k] = e[k]*at_sol[k] + _a[j] ;
}
}
}
memcpy(&*at, &*at_sol, num_sol*sizeof(double));
// get the angle al
//scalar_array sa(at.begin(),at.end());
double sa[num_sol];
memcpy(&*sa, &*at, num_sol*sizeof(double));
scalar_array_mult(&*sa, 2.0, num_sol);
//scalar_array _ca1(at.begin(),at.end());
double _ca1[num_sol];
memcpy(&*_ca1, &*at, num_sol*sizeof(double));
scalar_array_pow(&*_ca1,2.0, num_sol);
scalar_array_add(&*_ca1,1.0, num_sol);
//scalar_array ca(at.begin(),at.end());
double ca[num_sol];
memcpy(&*ca, &*at, num_sol*sizeof(double));
scalar_array_pow(&*ca,2, num_sol);
scalar_array_negate(&*ca, num_sol);
scalar_array_add(&*ca,1.0, num_sol);
scalar_array_div_vec(&*ca, &*_ca1, num_sol);
scalar_array_div_vec(&*sa, &*_ca1, num_sol);
double al[num_sol];
scalar_array_atan2(&*al, &*sa, &*ca, num_sol);
// check the sign of the derivative
scalar_array_mult(&*al, (real_t)(180./CONST_PI), num_sol);
double _c_tMaxMin[num_sol];
//_c_tMaxMin.resize(at.size());
scalar_array_clear(&*_c_tMaxMin, num_sol);
scalar_array_add(&*_c_tMaxMin, _a[1], num_sol);
double _at[num_sol];
//_at.clear();
//_at.assign(at.begin(),at.end());
memcpy(&*_at, &*at, num_sol*sizeof(double));
scalar_array_mult(&*_at, _a[2], num_sol);
scalar_array_mult(&*_at, 2.0, num_sol);
scalar_array_add_vec(&*_c_tMaxMin, &*_at, num_sol);
for(j=3; j<=4; j++)
{
memcpy(&*_at, &*at, num_sol*sizeof(double));
scalar_array_pow(&*_at, (real_t)(j)-(real_t)(1.0), num_sol);
scalar_array_mult(&*_at, _a[j], num_sol);
scalar_array_mult(&*_at, (real_t)(j), num_sol);
scalar_array_add_vec(&*_c_tMaxMin, &*_at, num_sol);
}
double tMaxMin[num_sol];
double al_[num_sol];
int al_idx = 0, a;
memcpy(&*tMaxMin, &*_c_tMaxMin, num_sol*sizeof(double));
for(i=0; i<num_sol; i++)
{
if(tMaxMin[i] > 0) al_[al_idx++] = al[i];
}
for(a=0; a<al_idx; a++)
{
vec3_t rpy;
vec3_assign(&rpy, (real_t)0, (real_t)(al_[a] * CONST_PI / (real_t)(180)), (real_t)(0));
mat33_t R, Ry_;
rpyMat(&Ry_, &rpy);
mat33_mult_mat2(&R, Rz, &Ry_);
vec3_t t_opt;
vec3_clear(&t_opt);
for(i=0; i<n; i++)
{
mat33_t _m1, _eye3;
mat33_eye(&_eye3);
mat33_copy(&_m1, &V[i]);
mat33_sub(&_m1, &_eye3);
vec3_t _v1, _v2;
vec3_mult_mat(&_v1, &R, &p[i]);
vec3_mult_mat(&_v2, &_m1, &_v1);
vec3_add_vec(&t_opt, &_v2);
}
vec3_t t_opt_;
vec3_mult_mat(&t_opt_, &G, &t_opt);
tnew[a] = t_opt_;
}
memcpy(al_ret, &*al_, al_idx*sizeof(double));
*res_n = al_idx;
}
void objpose(mat33_t *R, vec3_t *t, int *it, real_t *obj_err, real_t *img_err,
bool calc_img_err, const vec3_t *_P, const vec3_t *Qp, const options_t options, const int n)
{
int i, j;
//vec3_array P(_P.begin(),_P.end());
vec3_t P[n];
memcpy(&*P, _P, n*sizeof(vec3_t));
//const int n = (unsigned int) P.size();
vec3_t pbar;
vec3_array_sum(&pbar, &*P, n);
vec3_div(&pbar, (real_t)(n));
vec3_array_sub(&*P, &pbar, n);
//vec3_array Q(Qp.begin(),Qp.end());
vec3_t Q[n];
memcpy(&*Q, Qp, n*sizeof(vec3_t));
vec3_t ones;
ones.v[0] = 1;
ones.v[1] = 1;
ones.v[2] = 1;
const bool mask_z[3] = {0,0,1};
vec3_array_set(&*Q, &ones, mask_z, n);
//mat33_array F;
//F.resize(n);
mat33_t F[n];
vec3_t V;
for(i=0; i<n; i++)
{
V.v[0] = Q[i].v[0] / Q[i].v[2];
V.v[1] = Q[i].v[1] / Q[i].v[2];
V.v[2] = 1.0;
mat33_t _m;
vec3_mul_vec3trans(&_m, &V, &V);
mat33_div(&_m, vec3trans_mul_vec3(&V,&V));
F[i] = _m;
}
mat33_t tFactor;
mat33_t _m1,_m2,_m3;
mat33_eye(&_m1);
mat33_array_sum(&_m2, &*F, n);
mat33_div(&_m2, (real_t)(n));
mat33_sub_mat2(&_m3, &_m1, &_m2);
mat33_inv(&tFactor, &_m3);
mat33_div(&tFactor, (real_t)(n));
*it = 0;
int initR_approximate = mat33_all_zeros(&options.initR);
mat33_t Ri;
vec3_t ti;
//vec3_array Qi;
//Qi.resize(n);
vec3_t Qi[n];
real_t old_err = 0.0, new_err = 0.0;
// ----------------------------------------------------------------------------------------
if(initR_approximate == 0)
{
mat33_copy(&Ri, &options.initR);
vec3_t _sum;
vec3_t _v1, _v2;
mat33_t _m1,_m2;
vec3_clear(&_sum);
for(j=0; j<n; j++)
{
mat33_eye(&_m1);
mat33_sub_mat2(&_m2, &F[j], &_m1);
vec3_mult_mat(&_v1, &Ri, &P[j]);
vec3_mult_mat(&_v2, &_m2, &_v1);
vec3_add_vec(&_sum, &_v2);
}
vec3_mult_mat(&ti,&tFactor,&_sum);
xform(&*Qi, &*P, &Ri, &ti, n);
old_err = 0;
vec3_t _v;
for(j=0; j<n; j++)
{
mat33_eye(&_m1);
mat33_sub_mat2(&_m2, &F[j], &_m1);
vec3_mult_mat(&_v, &_m2, &Qi[j]);
old_err += vec3_dot(&_v, &_v);
}
// ----------------------------------------------------------------------------------------
}
else
{
abskernel(&Ri, &ti, &*Qi, &old_err, &*P, &*Q, &*F, &tFactor, n);
*it = 1;
}
// ----------------------------------------------------------------------------------------
abskernel(&Ri, &ti, &*Qi, &new_err, &*P, &*Qi, &*F, &tFactor, n);
*it = *it + 1;
while((_abs((old_err-new_err)/old_err) > options.tol) && (new_err > options.epsilon) &&
(options.max_iter == 0 || *it < options.max_iter))
{
old_err = new_err;
abskernel(&Ri, &ti, &*Qi, &new_err, &*P, &*Qi, &*F, &tFactor, n);
*it = *it + 1;
}
mat33_copy(R, &Ri);
vec3_copy(t, &ti);
*obj_err = _sqrt(new_err/(real_t)(n));
if(calc_img_err == 1)
{
//vec3_array Qproj;
//Qproj.resize(n);
vec3_t Qproj[n];
xformproj(&*Qproj, &*P, &Ri, &ti, n);
*img_err = 0;
vec3_t _v;
for(j=0; j<n; j++)
{
vec3_sub_vec2(&_v, &Qproj[j], &Qp[j]);
*img_err += vec3_dot(&_v, &_v);
}
*img_err = _sqrt(*img_err/(real_t)(n));
}
if(t->v[2] < 0)
{
mat33_mult(R, -1.0);
vec3_mult(t, -1.0);
}
vec3_t _ts;
vec3_mult_mat(&_ts, &Ri, &pbar);
vec3_sub_vec(t, &_ts);
}
Vec3 vec3_reflect(Vec3* vIncidentVector, Vec3* vNormalVector) {
return Vec3_diff(*vIncidentVector, vec3_mult(*vNormalVector, 2.0f * vec3_dot(vNormalVector, vIncidentVector)));
}