void drawCatmullRom(){
glColor3f(0.0f, 1.0f, 0.0f);
glBegin(GL_LINE_STRIP);
for (int i = 0; i < size; i++)
{
for (float t = 0; t <= (points[i + 1].time - points[i].time); t += (points[i + 1].time - points[i].time) / 100)
{
glVertex2f(Hermite(i, t).x, Hermite(i, t).y);
}
}
glEnd();
}
Vector f(float t){
for(int i = 0; i < n; i++){
if(ts[i] <= t && t <= ts[i+1]) return Hermite(cps[i], vs[i], ts[i],
cps[i+1],vs[i+1],ts[i+1],t);
}
return Vector(convertXToNorm(-2.0f),convertYToNorm(-2.0f));
}
// Interpolates between two values using a cubic equation.
// value1: Source value.
// value2: Source value.
// amount: Weighting value.
// Return: Interpolated value.
float CMathHelper::SmoothStep(float value1, float value2, float amount)
{
// It is expected that 0 < amount < 1
// If amount < 0, return value1
// If amount > 1, return value2
float result = Clamp(amount, 0.0f, 1.0f);
result = Hermite(value1, 0.0f, value2, 0.0f, result);
return result;
}
void Call_Hermite ( int n, int m )
{
POLY a[n][m], a1[n][m];
POLY p[n][n], t[n][m];
dcmplx deter, dcmplx_p[n][n], x;
int k;
printf("1 random matrix.\n");
printf("2 input your own matrix.\n");
printf("Please choose the test matrix:");
scanf("%d", &k ); printf("%d\n\n", k );
if(k==1) random_matrix ( n, m, a);
if(k==2) read_matrix( n, m, a );
printf("the original matrix generated :\n");
print(n,m,a);
zero_matrix ( n, m, a1);
I_matrix ( n, p);
copy ( n, m, a, t);
/* Eliminate_Col(n,m,a,p,0,0); */
/* Eliminate_Row(n,m,a,q,0,0); */
Hermite(n, m, a, p);
printf("The hermite form of matrix a is :\n");
print(n,m,a);
/* now begin to test the result */
Multiply ( n, n, m, p, t, a1 );
printf("The calculated hermite form with p*a is:\n");
print(n, m, a1);
printf(" p is:\n");
print(n, n, p);
x=create1(1.1);
evaluate_matrix(n, n, p, dcmplx_p, x);
deter=determinant(n, dcmplx_p);
printf("The determinant of the p is: ");
writeln_dcmplx(deter);
}
//Display
void display (void)
{
glClearColor(rosso_sf,verde_sf,blu_sf,0.0);//rendo variabili i parametri che mi definiscono il colore
glClear(GL_COLOR_BUFFER_BIT);
int i;
glColor3f(0.0,0.0,1.0);
glPointSize(dimpunto);
glBegin(GL_POINTS);//per visualizzare anche i punti dove si clicca di colore blu
for (i=1;i<=last;i++)
glVertex2f(Punti[i].x,Punti[i].y);
glEnd();
glColor3f(rosso_dis,verde_dis,blu_dis);
glBegin(GL_LINE_STRIP); //poligono di controllo
for (i=1;i<=last;i++)
glVertex2f(Punti[i].x,Punti[i].y);
glEnd();
n=last;//setto n al numero di punti disegnato
for(i=1;i<=n;i++)
w[i]=1;//metto tutti i pesi a 1
//scelta parametrizzazione
if (scelta_param==0)
{
Parametrizzazione_Uniforme();
}
else if(scelta_param==1)
{
Parametrizzazione_Corde();
}
//scelta della funzione
glPointSize(2);//la curva la disegno sempre di dimensione 2
if (metodo=='H' && last>1)
{
Hermite();
Disegna_Funzioni_Base();
}
if (metodo=='B' && last>1)
{
if(mod_pesi_bez==1)
w[i_p_b]=val_peso;
Bezier();
if (subd==1)
Subdivision();
if (d_el==1)
Degree_Elevation();
Disegna_fBaseBernstein();
}
if (metodo=='S' && last>3)
{
if(mod_pesi_spline==1)
w[i_p_s]=val_pesos;
Costruisci_Nodi();
Funzioni_Bspline(Nodi);
De_Boor();
}
//glutPostRedisplay();//è per questo che le funzioni base saltellano :)...se non lo metti però quando cambi il metodo non viene cambiato immediatamente ma dopo aver spinto un altro punto
glFlush();
}
void draw() {
if (numcp > 0) {
//kör sugár 5m -> 0.01f
for (int i = 0; i < numcp; i++) {
glColor3f(1, 0, 0);
glBegin(GL_TRIANGLE_FAN);
glVertex2f(cp[i].x, cp[i].y);
for (int j = 0; j < 360; j++) {
//cos/sin (j*pi/180)*sugár+eltolás
glVertex2f(cos(j * 3.14159 / 180.0) * 0.01 + cp[i].x,
sin(j * 3.14159 / 180.0) * 0.01 + cp[i].y);
}
glEnd();
glColor3f(1, 1, 1);
glBegin(GL_LINE_STRIP);
for (int j = 0; j < 360; j++) {
//cos/sin (j*pi/180)*sugár+eltolás
glVertex2f(cos(j * 3.14159 / 180.0) * 0.01 + cp[i].x,
sin(j * 3.14159 / 180.0) * 0.01 + cp[i].y);
}
glVertex2f(cos(0) * 0.01 + cp[i].x, sin(0) * 0.01 + cp[i].y);
glEnd();
}
}
/*
if (numcp > 1) {
glColor3f(0, 0, 1);
glBegin(GL_LINE_STRIP);
for (int i = 0; i < numcp; i++) {
glVertex2f(cp[i].x, cp[i].y);
}
glVertex2f(cp[0].x, cp[0].y);
glEnd();
}
*/
if (numcp > 1) {
glColor3f(1, 1, 1);
glBegin(GL_LINE_STRIP);
Vector v;
for (int i = 0; i < numcp + 1; i++) {
//cout<<i<<"\n"<<flush;
for (float t = ido[i]; t < ido[i + 1]; t += 1.0f) {
v = Hermite(i, t);
if (parabola.isintersecting(v)) { // && !intersected) {
intersectpoint = v;
intersecttime = t;
intersecti = i;
intersected = true;
}
glVertex2f(v.x, v.y);
}
}
glEnd();
if (intersected) {
glColor3f(0, 0.7f, 0);
//glBegin(GL_POINTS);
//glVertex2f(intersectpoint.x, intersectpoint.y);
//glEnd();
glBegin(GL_LINES);
//for (float t = (ido[intersecti] - 100); t < ido[intersecti] + 100; t++) {
v = Hermitederive(intersecti, intersecttime);
v = v * (10/v.Length());
glVertex2f(intersectpoint.x + v.x, intersectpoint.y + v.y);
glVertex2f(intersectpoint.x - v.x, intersectpoint.y - v.y);
//}
glEnd();
}
}
}
double past(int i, int interval, double t, int val)
/* finds past values (val=1) or past derivatives (val=2)*/
{ int j, jn, nq, ip;
double t0, t1, y0, y1, dy0, dy1, res, hh;
double *Yh;
/* error checking */
if ( i >= n_eq)
error("illegal input in lagvalue - var nr too high, %i", i+1);
/* equal to current value... */
if ( interval == indexhist && t == histtime[interval]) {
if (val == 1)
res = histvar [interval * offset + i ];
else
res = histdvar [interval * offset + i ];
/* within last interval - for now: just extrapolate last value */
} else if ( interval == indexhist && interpolMethod == 1) {
if (val == 1) {
t0 = histtime[interval];
y0 = histvar [interval * offset + i ];
dy0 = histdvar [interval * n_eq + i ];
res = y0 + dy0*(t-t0);
}
else
res = histdvar [interval * n_eq + i ];
/* Hermite interpolation */
} else if (interpolMethod == 1) {
j = interval;
jn = nexthist(j);
t0 = histtime[j];
t1 = histtime[jn];
y0 = histvar [j * n_eq + i ];
y1 = histvar [jn * n_eq + i ];
dy0 = histdvar [j * n_eq + i ];
dy1 = histdvar [jn * n_eq + i ];
if (val == 1)
res = Hermite (t0, t1, y0, y1, dy0, dy1, t);
else
res = dHermite (t0, t1, y0, y1, dy0, dy1, t);
/* dense interpolation - livermore solvers */
} else if (interpolMethod == 2) {
j = interval;
jn = nexthist(j);
t0 = histtime[j];
t1 = histtime[jn];
nq = histord [j];
if (nq == 0) {
y0 = histvar [j * offset + i ];
y1 = histvar [jn * offset + i ];
dy0 = histdvar [j * n_eq + i ];
dy1 = histdvar [jn * n_eq + i ];
if (val == 1)
res = Hermite (t0, t1, y0, y1, dy0, dy1, t);
else
res = dHermite (t0, t1, y0, y1, dy0, dy1, t);
} else {
Yh = &histvar [j * offset];
hh = histhh[j];
res = interpolate(i+1, val-1, t0, hh, t, Yh, nq);
}
/* dense interpolation - radau - gets all values (i not used) */
} else {
// if (val == 2)
// error("radau interpol = 2 does not work for lagderiv");
j = interval;
Yh = &histvar [j * offset];
histsave = &histvar [j * offset + 4*n_eq];
ip = i+1;
F77_CALL(contr5alone) (&ip, &n_eq, &t, Yh, &offset, histsave, &res, &val);
}
return(res);
}
ST Cardinal(ST y0, ST y1, ST y2, ST y3, FT c, FT t)
{
const FT m0 = c * (y2 - y0); //Tangent for y1.
const FT m1 = c * (y3 - y1); //Tangent for y2.
return Hermite(m0, y1, y2, m1, t);
}
Vector3 CVector3::Hermite(Vector3 value1, Vector3 tangent1, Vector3 value2, Vector3 tangent2, float amount)
{
Vector3 result;
Hermite(value1, tangent1, value2, tangent2, amount, result);
return result;
}
main()
{
short m;
double abscis[N];
double wt[N];
double left, right;
printf("Table 25.8, k= %1d, n=%1d\n\n", k, N);
Jacobi(N, FLOATk, ZERO, abscis, wt);
for (m=0; m<N; m++) wt[m] /= (k+1);
for (m=0; m<N; m++) printf("%2d %20.18g %20.18g\n", m, abscis[m], wt[m]);
getchar();
printf("\n\n\nTable 25.4, n=9\n\n");
Radau_Jacobi(4, -0.5, ZERO, abscis, wt, &left);
left *= 2;
for (m=0; m<4; m++) abscis[m]= sqrt(abscis[m]);
printf("%2d %20.18g %20.18g\n", 0, ZERO, left);
for (m=0; m<4; m++) printf("%2d %20.18g %20.18g\n", m, abscis[m], wt[m]);
getchar();
printf("\n\n\nTable 25.9, n= %1d\n\n", N);
Laguerre(N, ZERO, abscis, wt);
for (m=0; m<N; m++) printf("%2d %20.18g %20.18g\n", m, abscis[m], wt[m]);
getchar();
printf("\n\n\nTable 25.10, n= %1d\n\n", N);
Hermite(N, ZERO, abscis, wt);
for (m=0; m<N; m++) wt[m] *= SqrtPI;
for (m=0; m<N; m++) printf("%2d %20.18g %20.18g\n", m, abscis[m], wt[m]);
getchar();
printf("\n\n\nSame, n= %1d\n\n", 2*N);
Even_Hermite(2*N, ZERO, abscis, wt);
for (m=0; m<N; m++) wt[m] *= SqrtPI;
for (m=0; m<N; m++) printf("%2d %20.18g %20.18g\n", m, abscis[m], wt[m]);
getchar();
printf("\n\n\nSame, n= %1d\n\n", 9);
Odd_Hermite(9, ZERO, abscis, wt, &left);
left *= SqrtPI;
for (m=0; m<4; m++) wt[m] *= SqrtPI;
printf("%2d %20.18g %20.18g\n", 0, ZERO, left);
for (m=0; m<4; m++) printf("%2d %20.18g %20.18g\n", m, abscis[m], wt[m]);
getchar();
printf("\n\n\nTable 25.6, n= %1d\n\n", N+1);
Lobatto_Jacobi(N-1, ZERO, ZERO, abscis, wt, &left, &right);
for (m=0; m<(N-1); m++) wt[m] *= 2;
left *= 2; right *= 2;
for (m=0; m<(N-1); m++) abscis[m] = (2*abscis[m] - 1);
printf(" %20.18g %20.18g\n", -1.0, left);
for (m=0; m<(N-1); m++)
printf("%2d %20.18g %20.18g\n", m, abscis[m], wt[m]);
printf(" %20.18g %20.18g\n", 1.0, right);
}
