Table_flottant steps_computation(Table_triplet points, Booleen uniformConf) {
int i;
Table_flottant steps;
steps.nb = points.nb;
ALLOUER(steps.table, steps.nb);
if(uniformConf) {
for(i = 0; i < steps.nb; i++)
steps.table[i] = i * (1.f / (points.nb - 1));
}
else {
double totalDistance = 0;
steps.table[0] = 0.f;
for(i = 1; i < steps.nb; i++) {
totalDistance += distance(points.table[i-1], points.table[i]);
steps.table[i] = totalDistance;
}
for(i = 1; i < steps.nb; i++)
steps.table[i] /= totalDistance;
}
return steps;
}
Grille_flottant duplique_Grille_flottant(Grille_flottant *original)
{
int i,j;
Grille_flottant copie;
ALLOUER(copie.grille,original->nb_lignes);
copie.nb_lignes = original->nb_lignes;
copie.nb_colonnes = original->nb_colonnes;
for (i=0 ; i<original->nb_lignes ; i++)
{
ALLOUER(copie.grille[i],original->nb_colonnes);
for (j=0 ; j<original->nb_colonnes ; j++)
copie.grille[i][j] = original->grille[i][j];
}
return copie;
}
/*
* Allocation des la structure et remplissage des champs pour initialiser
* le tableau des événements avec l'événement ESCAPE (avec une occurrence).
*/
struct shannon_fano* open_shannon_fano()
{
struct shannon_fano* sf;
ALLOUER(sf,1);
sf->nb_evenements = 1;
sf->evenements[0].valeur = VALEUR_ESCAPE;
sf->evenements[0].nb_occurrences = 1;
return sf;
}
Pile* initialiserPile()
{
Pile *p;
ALLOUER(p,1);
p->dernierPile = NULL;
p->nbPile = 0;
p->maxPile = 0;
return p;
}
Grille_flottant produit_matrice(Grille_flottant *a, Grille_flottant *b)
{
int j, i, k ;
Grille_flottant res;
res.nb_lignes = a->nb_lignes;
res.nb_colonnes = b->nb_colonnes;
ALLOUER(res.grille, res.nb_lignes);
for (i=0 ; i < res.nb_lignes ; i++) {
ALLOUER(res.grille[i],res.nb_colonnes);
}
for(i=0; i < a->nb_lignes; ++i){
for(j=0; j < b->nb_colonnes; ++j) {
res.grille[i][j] = 0 ;
for(k=0; k < a->nb_colonnes; ++k)
res.grille[i][j] += a->grille[i][k]*b->grille[k][j] ;
}
}
return res;
}
Table_flottant duplique_Table_flottant(Table_flottant *original)
{
int i;
Table_flottant copie;
ALLOUER(copie.table,original->nb);
copie.nb = original->nb ;
for (i=0 ; i<original->nb ; i++)
copie.table[i] = original->table[i];
return copie;
}
void calcul_surface_bezier(surface_bezier *sb)
{
int i,j;
Grille_quadruplet Ginv;
Grille_triplet courbeU;
courbeU.nb_lignes = sb->G.nb_lignes;
courbeU.nb_colonnes = sb->u;
sb->surface.nb_lignes = sb->u;
sb->surface.nb_colonnes = sb->v;
printf("u %d, v %d \n", sb->u, sb->v);
Ginv.nb_lignes = courbeU.nb_colonnes;
Ginv.nb_colonnes = courbeU.nb_lignes;
ALLOUER(courbeU.grille, courbeU.nb_lignes);
for (i = 0; i < courbeU.nb_lignes; i++)
ALLOUER(courbeU.grille[i], courbeU.nb_colonnes);
ALLOUER(Ginv.grille, Ginv.nb_lignes);
for (i = 0; i < Ginv.nb_lignes; i++)
ALLOUER(Ginv.grille[i], Ginv.nb_colonnes);
ALLOUER(sb->surface.grille, sb->surface.nb_lignes);
for (i = 0; i < sb->surface.nb_lignes; i++)
ALLOUER(sb->surface.grille[i], sb->surface.nb_colonnes);
for (i = 0; i < courbeU.nb_lignes; i++)
{
Casteljau(courbeU.grille[i] ,sb->G.grille[i],
sb->G.nb_colonnes, courbeU.nb_colonnes);
}
for (i = 0; i < Ginv.nb_colonnes; i++)
{
for (j = 0; j < Ginv.nb_lignes; j++)
{
Ginv.grille[j][i].x = courbeU.grille[i][j].x;
Ginv.grille[j][i].y = courbeU.grille[i][j].y;
Ginv.grille[j][i].z = courbeU.grille[i][j].z;
Ginv.grille[j][i].h = 1;
}
}
for (i = 0; i < sb->surface.nb_lignes; i++)
{
Casteljau(sb->surface.grille[i] ,Ginv.grille[i],
Ginv.nb_colonnes, sb->surface.nb_colonnes);
}
for (i = 0; i < Ginv.nb_lignes; i++)
free(Ginv.grille[i]);
free(Ginv.grille);
for (i = 0; i < courbeU.nb_lignes; i++)
free(courbeU.grille[i]);
free(courbeU.grille);
}
Table_quadruplet computeAllPointsNurbs(Table_quadruplet controlPoints, int ptNumber,
int degree, Table_flottant nodalVector) {
int i;
double step = 1.f / (ptNumber - 1);
Table_quadruplet points;
points.nb = ptNumber;
ALLOUER(points.table, ptNumber);
for(i = 0; i < ptNumber; i++)
points.table[i] = computePointNurbs(controlPoints, i * step, degree, nodalVector);
return points;
}
Table_flottant computeNodalVector(int n, int k) {
int i;
Table_flottant tab;
tab.nb = n+k+1;
ALLOUER(tab.table, n+k+1);
for(i = 0; i < k; i++)
tab.table[i] = 0;
for(i = k; i <= n ; i++)
tab.table[i] = (i - k + 1.f)/(n - k + 2.f);
for(i = n+1; i <= n+k; i++)
tab.table[i] = 1;
return tab;
}
Table_flottant produit_matrice_vecteur(Grille_flottant *mat, Table_flottant *v)
{
int i, k ;
Table_flottant res;
res.nb = v->nb;
ALLOUER(res.table, res.nb);
for(i=0; i < mat->nb_lignes; ++i){
res.table[i] = 0 ;
for(k=0; k < mat->nb_colonnes; ++k)
res.table[i] += mat->grille[i][k]*v->table[k] ;
}
return res;
}
Quadruplet computePointNurbs(Table_quadruplet controlPoints, double u, int degree,
Table_flottant nodalVector) {
Quadruplet coords;
int i, j, r;
int k = degree + 1;
double ui, uikj;
double coefi, coefi1;
Quadruplet * temp;
ALLOUER(temp, controlPoints.nb);
for(i = 0; i < nodalVector.nb-1; i++) {
if(u >= nodalVector.table[i] && (u < nodalVector.table[i+1])) {
r = i;
break;
}
}
for(i = 0; i < controlPoints.nb; i++) {
temp[i].x = controlPoints.table[i].x * controlPoints.table[i].h;
temp[i].y = controlPoints.table[i].y * controlPoints.table[i].h;
temp[i].z = controlPoints.table[i].z * controlPoints.table[i].h;
temp[i].h = controlPoints.table[i].h;
}
for(j = 1; j <= degree; j++) {
for(i = r - k + 1 + j; i <= r; i++) {
ui = nodalVector.table[i];
uikj = nodalVector.table[i+k-j];
coefi = (u - ui) / (uikj - ui);
coefi1 = (uikj - u) / (uikj - ui);
temp[i].x = coefi * temp[i].x + coefi1 * temp[i-1].x;
temp[i].y = coefi * temp[i].y + coefi1 * temp[i-1].y;
temp[i].z = coefi * temp[i].z + coefi1 * temp[i-1].z;
temp[i].h = coefi * temp[i].h + coefi1 * temp[i-1].h;
}
}
coords.x = temp[r].x / temp[r].h;
coords.y = temp[r].y / temp[r].h;
coords.z = temp[r].z / temp[r].h;
coords.h = temp[r].h;
free(temp);
return coords;
}
double * matrix_vector_mult(double ** B, double * V, int size) {
int i, j;
double s;
double * mult;
ALLOUER(mult, size);
for(j = 0; j < size; j++)
{
s = 0;
for(i = 0; i < size; i++)
s += B[j][i] * V[i];
mult[j] = s;
}
return mult;
}
static void ac_update_curve_points(struct approximation_curve* ac)
{
int i;
float step;
// Réallocation de la table de points si nécessaire
if (ac->curve_points.nb != ac->curve_point_count)
{
free(ac->curve_points.table);
ac->curve_points.nb = ac->curve_point_count;
ALLOUER(ac->curve_points.table, ac->curve_points.nb);
}
step = 1.f / (ac->curve_point_count - 1);
for (i = 0; i < ac->curve_point_count; ++i)
ac->curve_points.table[i] = casteljau(&ac->curve_polygon, i * step);
}
struct intstream* open_intstream(struct bitstream *bitstream
, enum intstream_type type
, struct shannon_fano *shannon_fano)
{
struct intstream *is ;
ALLOUER(is, 1) ;
is->bitstream = bitstream ;
is->type = type ;
if ( type == Shannon_fano )
{
if ( shannon_fano == NULL )
EXIT ;
is->shannon_fano = shannon_fano ;
}
return(is) ;
}
void Casteljau(Triplet * courbe, Quadruplet *poly, const int nbPoly, const int nbAffiche)
{
int i,j,k;
double u = (double)1/(nbAffiche + 1);
Quadruplet* Quad;
ALLOUER(Quad, nbPoly);//Allocation du tableau de Quad
for(k = 0; k < nbAffiche; ++k)
{
for (j = 0; j < nbPoly; j++)
{
Quad[j] = poly[j];
}
for(j = nbPoly -1; j > 0 ; --j)
{
for(i = 0; i < j ; i++)
{
//Calcul
Quad[i].x = (u * Quad[i+1].x) + (1-u) * Quad[i].x;
Quad[i].y = (u * Quad[i+1].y) + (1-u) * Quad[i].y;
Quad[i].z = (u * Quad[i+1].z) + (1-u) * Quad[i].z;
Quad[i].h = (u * Quad[i+1].h) + (1-u) * Quad[i].h;
}
}
if(Quad[0].h == 0) Quad[0].h = 1;
courbe[k].x = Quad[0].x /Quad[0].h;
courbe[k].y = Quad[0].y /Quad[0].h;
courbe[k].z = Quad[0].z /Quad[0].h;
u += (double)1/(nbAffiche + 1);
}
free(Quad);
}
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;
}
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);
}
int resolution_systeme_lineaire(Grille_flottant *A,
Table_flottant *f,
Table_flottant *x)
{
double s,r;
int i,j,k,n;
Grille_flottant T;
Table_flottant b;
n = A->nb_lignes;
if ( (A->nb_lignes != A->nb_colonnes) || (f->nb != A->nb_lignes) )
return 1;
/* copie de la matrice et du second membre pour triangulation */
T = duplique_Grille_flottant(A);
b = duplique_Table_flottant(f);
/* allocation solution */
ALLOUER(x->table,n);
x->nb = n;
for (k=0 ; k<n ; k++)
{
traite_pivot_max(&T,&b,k);
if ( fabs(T.grille[k][k]) < ZERO)
{
free(x->table);
x->nb = 0;
return(1);
}
for (i=k+1 ; i<n ; i++)
{
s = T.grille[i][k]/T.grille[k][k];
for (j=k+1 ; j<n ; j++)
T.grille[i][j]=T.grille[i][j] - T.grille[k][j]*s;
b.table[i] -= s*b.table[k];
}
}
if (fabs(T.grille[n-1][n -1]) < ZERO)
{
free(x->table);
x->nb = 0;
return(1);
}
x->table[n-1] = b.table[n-1]/T.grille[n-1][n-1];
for (i=n-2 ; i>=0 ; i--)
{
r = 0.0;
for (j=i+1 ; j<n ; j++)
r += (T.grille[i][j])*(x->table[j]);
if (fabs(T.grille[i][i]) < ZERO) return(1);
x->table[i] = (b.table[i] - r)/T.grille[i][i];
}
free(b.table);
for (i=0 ; i<T.nb_lignes ; i++)
free(T.grille[i]);
free(T.grille);
return(0);
}
int main(int argc, char **argv)
{
int c;
int pol,conv;
int option1 = 0, option2 = 0, option3 = 0, option4 = 0;
int nbPoints = 50;
vertex *v;
opterr = 0;
while ((c = getopt(argc, argv, "1i:2o:34n:")) != EOF)
{
switch (c)
{
case '1':
option1 = 1;
break;
case '2':
option2 = 1;
break;
case '3':
option3 = 1;
break;
case '4':
option4 = 1;
break;
case 'n':
if ((sscanf(optarg, "%d", &nbPoints) != 1) || nbPoints <= 0)
nbPoints = 50;
break;
case 'o': /*verifier non null*/
out = optarg;
break;
case 'i': /*verifier non null*/
in = optarg;
break;
case 'h':
case '?':
printf("-1 partie 1 du tp\n");
printf("-2 partie 2 du tp\n");
printf("-3 partie 3 du tp\n");
printf("-ichaine ouvre le fichier \"chaine\" en lecture \n");
printf("-ochaine ouvre le fichier \"chaine\" en écriture \n");
return EXIT_SUCCESS;
break;
default : printf("Shouldn't be here, really...\n");
break;
}
}
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE | GLUT_RGBA);
glutInitWindowPosition(5,5);
glutInitWindowSize(500,500);
glutCreateWindow("fenetre");
definitionFenetre(0, 500, 0, 500, 10);
winInit();
if(option1 && out != NULL)
{
glutDisplayFunc(display);
glutMouseFunc(coordonnesPoint);
ecrireFichier(out, &P);
}
else if(option2 && in != NULL)
{
lireFichier(in, &P);
assert(P.p != NULL);
pol = controlePolygoneSimple();
printf("controlePolygoneSimple : %d\n", pol);
//glutDisplayFunc(displayPolygone);
}
else if(option3 && in != NULL)
{
lireFichier(in, &P);
assert(P.p != NULL);
if(controlePolygoneSimple())
conv = estConvexe();
}
else if(option4 && in != NULL)
{
lireFichier(in, &P);
assert(P.p != NULL);
ALLOUER(v,nbPoints);
selectPoints (v, nbPoints);
if(controlePolygoneSimple() && estConvexe())
positionPointsParRapportPolygone(v, nbPoints);
free(v);
}
glutMainLoop();
clearFenetre();
return EXIT_SUCCESS;
}
