main()
{
int i,polish;
fcomplex roots[MP1];
static fcomplex a[MP1] = {{0.0,2.0},
{0.0,0.0},
{-1.0,-2.0},
{0.0,0.0},
{1.0,0.0} };
printf("\nRoots of the polynomial x^4-(1+2i)*x^2+2i\n");
polish=FALSE;
zroots(a,M,roots,polish);
printf("\nUnpolished roots:\n");
printf("%14s %13s %13s\n","root #","real","imag.");
for(i=1;i<=M;i++)
printf("%11d %18.6f %12.6f\n",i,roots[i].r,roots[i].i);
printf("\nCorrupted roots:\n");
for(i=1;i<=M;i++)
roots[i] = RCmul(1+0.01*i,roots[i]);
printf("%14s %13s %13s\n","root #","real","imag.");
for(i=1;i<=M;i++)
printf("%11d %18.6f %12.6f\n",i,roots[i].r,roots[i].i);
polish=TRUE;
zroots(a,M,roots,polish);
printf("\nPolished roots:\n");
printf("%14s %13s %13s\n","root #","real","imag.");
for(i=1;i<=M;i++)
printf("%11d %18.6f %12.6f \n",i,roots[i].r,roots[i].i);
}
void fixrts(float d[], int m)
{
void zroots(fcomplex a[], int m, fcomplex roots[], int polish);
int i,j,polish;
fcomplex a[NMAX],roots[NMAX];
a[m]=ONE;
for (j=m-1;j>=0;j--)
a[j]=Complex(-d[m-j],0.0);
polish=1;
zroots(a,m,roots,polish);
for (j=1;j<=m;j++)
if (Cabs(roots[j]) > 1.0)
roots[j]=Cdiv(ONE,Conjg(roots[j]));
a[0]=Csub(ZERO,roots[1]);
a[1]=ONE;
for (j=2;j<=m;j++) {
a[j]=ONE;
for (i=j;i>=2;i--)
a[i-1]=Csub(a[i-2],Cmul(roots[j],a[i-1]));
a[0]=Csub(ZERO,Cmul(roots[j],a[0]));
}
for (j=0;j<=m-1;j++)
d[m-j] = -a[j].r;
}
int main(void)
{
int i,polish=TRUE;
static float d[NP1]=
{0.0,6.0,-15.0,20.0,-15.0,6.0,0.0};
fcomplex zcoef[NP1],zeros[NP1],z1,z2;
/* finding roots of (z-1.0)^6=1.0 */
/* first write roots */
zcoef[NPOLES]=ONE;
for (i=NPOLES-1;i>=0;i--)
zcoef[i] = Complex(-d[NPOLES-i],0.0);
zroots(zcoef,NPOLES,zeros,polish);
printf("Roots of (z-1.0)^6 = 1.0\n");
printf("%24s %27s \n","Root","(z-1.0)^6");
for (i=1;i<=NPOLES;i++) {
z1=Csub(zeros[i],ONE);
z2=Cmul(z1,z1);
z1=Cmul(z1,z2);
z1=Cmul(z1,z1);
printf("%6d %12.6f %12.6f %12.6f %12.6f\n",
i,zeros[i].r,zeros[i].i,z1.r,z1.i);
}
/* now fix them to lie within unit circle */
fixrts(d,NPOLES);
/* check results */
zcoef[NPOLES]=ONE;
for (i=NPOLES-1;i>=0;i--)
zcoef[i] = Complex(-d[NPOLES-i],0.0);
zroots(zcoef,NPOLES,zeros,polish);
printf("\nRoots reflected in unit circle\n");
printf("%24s %27s \n","Root","(z-1.0)^6");
for (i=1;i<=NPOLES;i++) {
z1=Csub(zeros[i],ONE);
z2=Cmul(z1,z1);
z1=Cmul(z1,z2);
z1=Cmul(z1,z1);
printf("%6d %12.6f %12.6f %12.6f %12.6f\n",
i,zeros[i].r,zeros[i].i,z1.r,z1.i);
}
return 0;
}
int main() {
int i;
double complex a[5];
double complex roots[5];
a[0] = 1.;
a[1] = 1.;
a[2] = 1.;
a[3] = 1.;
a[4] = 1.;
zroots(a, 2, roots, 1);
for(i = 0; i < 2; i++) {
printf("%f %f %f %f\n", creal(roots[i]), cimag(roots[i]),
creal(a[0]+a[1]*roots[i]+a[2]*roots[i]*roots[i]),
cimag(a[0]+a[1]*roots[i]+a[2]*roots[i]*roots[i]));
}
return(0);
}
double curve_segment_distance(double k,double *p1,double *p2,double *p3,
double *p4,double *p,double q1,double q2)
/*******************************************************************************
LAST MODIFIED : 30 August 1996
DESCRIPTION :
Calculates distance potential at a point p from a curve segment defined by
p1-p2, slope p3,p4 with charge(q1,q2) the distance Q(t)-p is minimized by
translating to the origin and solving the minimum sum Q(t)*Q(t) =>
0 = sum Q'(t).Q(t)
==============================================================================*/
{
double at,bt,ct,dist,dt,min_dist,min_t = 0.0,pt1[3],pt2[3],pt3[3],pt4[3],t;
/* intermediate calculations */
double a[3],b[3],c[3],d[3],e[3],f[3],g[3],r[3];
/* coefficients of Q'(t).Q(t) */
double return_code;
fcomplex coeff[6];
/* roots */
fcomplex roots[6];
int real_roots[6];
int i,j,min,n_real_roots;
static double val;
ENTER(curve_segment_distance);
/* default return value */
return_code=0.0;
/* checking arguments */
if (p1&&p2&&p3&&p4&&p)
{
for (i=0;i<6;i++)
{
coeff[i].r=0;
coeff[i].i=0;
roots[i].r=0;
roots[i].i=0;
}
for (i=0;i<3;i++)
{
/* translate to origin */
pt1[i]=p1[i]-p[i];
pt2[i]=p2[i]-p[i];
pt3[i]=p3[i]-p[i] ;
pt4[i]=p4[i]-p[i];
/* Q(t) */
a[i]=-pt1[i]+3*pt2[i]-3*pt3[i]+pt4[i];
b[i]=3*pt1[i]-6*pt2[i]+3*pt3[i];
c[i]=-3*pt1[i]+3*pt2[i];
d[i]=pt1[i];
/* Q'(t) */
e[i]=-3*pt1[i]+9*pt2[i]-9*pt3[i]+3*pt4[i];
f[i]=6*pt1[i]-12*pt2[i]+6*pt3[i];
g[i]=-3*pt1[i]+3*pt2[i];
}
/* calculate coefficients of minimized polynomial */
for (i=0;i<3;i++)
{
coeff[0].r += (GLfloat)d[i]*g[i];
coeff[1].r += (GLfloat)c[i]*g[i]+d[i]*f[i];
coeff[2].r += (GLfloat)b[i]*g[i]+c[i]*f[i]+d[i]*e[i];
coeff[3].r += (GLfloat)a[i]*g[i]+b[i]*f[i]+c[i]*e[i];
coeff[4].r += (GLfloat)a[i]*f[i]+b[i]*e[i];
coeff[5].r += (GLfloat)a[i]*e[i];
}
/* find roots of polynomial */
/* the real root is the t parameter value of the curve pt nearest p */
zroots(coeff,5,roots,1);
min=1;
n_real_roots=0;
/* choose closest to real root if no real root exists*/
for (i=1;i<6;i++)
{
/* printf"Root[%d] = (%lf + %lfi)\n",i,roots[i].r,roots[i].i);*/
if ((roots[i].i*roots[i].i<roots[min].i*roots[min].i)||(roots[i].i == 0))
{
if (roots[i].i == 0)
{
real_roots[n_real_roots]=i;
n_real_roots++;
}
min=i;
}
}
if (n_real_roots == 0)
{
real_roots[n_real_roots]=min;
n_real_roots=1;
}
/* we have our best selection of real roots - now must find */
/* which one is the minimum */
min_dist=0.;
for (i=0;i<n_real_roots;i++)
{
t=(double)roots[real_roots[i]].r;
at=(1-t)*(1-t)*(1-t);
bt=3.0*t*(1-t)*(1-t);
ct=3.0*t*t*(1-t);
dt=t*t*t;
for (j=0;j<3;j++)
{
r[j]=at*pt1[j]+bt*pt2[j]+ct*pt3[j]+dt*pt4[j];
}
dist=norm3(r);
if (dist<min_dist||i==0)
{
min_dist=dist;
min_t=t;
}
}
if ((min_t>=0)&&(min_t<=1.0))
{
if (0!=min_dist)
{
val=k/(min_dist*min_dist)*(q1+min_t*(q2-q1));
return_code=val;
}
else
{
return_code=TEXTURE_LINE_INFINITY;
}
}
else
{
return_code=0.0;
}
}
else
{
display_message(ERROR_MESSAGE,
"curve_segment_distance. Invalid argument(s)");
return_code=0.0;
}
LEAVE;
return (return_code);
} /* curve_segment_distance */
