static void ac_update_curve_polygon(struct approximation_curve* ac)
{
Grille_flottant* m;
Grille_flottant* mt;
Grille_flottant* mmt;
Table_flottant* p;
Table_flottant* a;
Table_flottant* mp;
Table_flottant* params;
// Allocation de la table des points de contrôle de la courbe d'approximation
if (ac->curve_polygon.nb != (ac->degree + 1))
{
free(ac->curve_polygon.table);
ac->curve_polygon.nb = ac->degree + 1;
ALLOUER(ac->curve_polygon.table, ac->curve_polygon.nb);
}
// Paramétrisation de la courbe d'approximation
if (ac->use_uniform_parameterization)
params = ac_uniform_parameterization(&ac->points);
else
params = ac_non_uniform_parameterization(&ac->points);
// Construction de la matrice de Bernstein, de sa transposée et de leur produit
m = matrix_create(ac->degree + 1, ac->points.nb);
ac_bernstein_matrix(m, params);
mt = matrix_transpose(m);
mmt = matrix_product(m, mt);
// Résolution des 3 systèmes d'équations (composantes x, y et z) des points de contrôle recherchés
p = malloc_table_flottant(ac->points.nb);
a = malloc_table_flottant(ac->degree + 1);
mp = malloc_table_flottant(m->nb_lignes);
// X
get_triplets_x_values(&ac->points, p);
matrix_vector_product(m, p, mp);
if (resolution_systeme_lineaire(mmt, mp, a))
EXIT;
set_triplets_x_values(&ac->curve_polygon, a);
// Y
get_triplets_y_values(&ac->points, p);
matrix_vector_product(m, p, mp);
if (resolution_systeme_lineaire(mmt, mp, a))
EXIT;
set_triplets_y_values(&ac->curve_polygon, a);
// Z
get_triplets_z_values(&ac->points, p);
matrix_vector_product(m, p, mp);
if (resolution_systeme_lineaire(mmt, mp, a))
EXIT;
set_triplets_z_values(&ac->curve_polygon, a);
// Libération des ressources
matrix_delete(m);
matrix_delete(mt);
matrix_delete(mmt);
free_table_flottant(a);
free_table_flottant(p);
free_table_flottant(mp);
free_table_flottant(params);
}
Table_quadruplet least_squares_approximation(Table_triplet points,
Booleen uniformConf) {
int i, j;
Table_quadruplet res;
res.nb = points.nb;
ALLOUER(res.table, points.nb);
Table_flottant steps = steps_computation(points, uniformConf);
double ** B;
ALLOUER(B, points.nb);
for(i = 0; i < points.nb; i++)
ALLOUER(B[i], points.nb);
B[0][0] = B[points.nb - 1][points.nb - 1] = 1;
for(i = 1; i < points.nb; i++)
B[0][i] = 0;
for(i = 0; i < points.nb; i++) {
for(j = 1; j < points.nb - 1; j++) {
B[j][i] = bernsteinPolynomial(i, points.nb - 1, steps.table[j]);
}
}
for(i = 0; i < points.nb - 1; i++)
B[points.nb - 1][i] = 0;
double ** BT = transposedMatrix(B, points.nb);
Grille_flottant Aprime;
Aprime.nb_lignes = Aprime.nb_colonnes = points.nb;
Aprime.grille = matrix_matrix_mult(B, BT, points.nb);
for(i = 0; i < points.nb; i++)
free(BT[i]);
free(BT);
double * pointsX, * pointsY, * pointsZ;
ALLOUER(pointsX, points.nb);
ALLOUER(pointsY, points.nb);
ALLOUER(pointsZ, points.nb);
split_x_y_z(points, pointsX, pointsY, pointsZ);
Table_flottant BprimeX, BprimeY, BprimeZ;
BprimeX.nb = BprimeY.nb = BprimeZ.nb = points.nb;
BprimeX.table = matrix_vector_mult(B, pointsX, points.nb);
BprimeY.table = matrix_vector_mult(B, pointsY, points.nb);
BprimeZ.table = matrix_vector_mult(B, pointsZ, points.nb);
free(pointsX); free(pointsY); free(pointsZ);
for(i = 0; i < points.nb; i++)
free(B[i]);
free(B);
Table_flottant resX, resY, resZ;
resX.nb = resY.nb = resZ.nb = points.nb;
ALLOUER(resX.table, points.nb);
ALLOUER(resY.table, points.nb);
ALLOUER(resZ.table, points.nb);
resolution_systeme_lineaire(&Aprime, &BprimeX, &resX);
resolution_systeme_lineaire(&Aprime, &BprimeY, &resY);
resolution_systeme_lineaire(&Aprime, &BprimeZ, &resZ);
for(i = 0; i < points.nb; i++) {
res.table[i].x = resX.table[i];
res.table[i].y = resY.table[i];
res.table[i].z = resZ.table[i];
res.table[i].h = 1;
}
free(BprimeX.table); free(BprimeY.table); free(BprimeZ.table);
free(resX.table); free(resY.table); free(resZ.table);
for(i = 0; i < Aprime.nb_lignes; i++)
free(Aprime.grille[i]);
free(Aprime.grille);
return res;
}
