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#include "cp_types.h"
#include "cp_proto.h"
/* routines for random walk computations, tangency packings only. */
/* ========= euclidean functions =========== */
double G(double x,double y,double z)
/* angle at x */
{
double a;
a=x*(x+y+z);
return ( acos((a-y*z)/(a+y*z)) );
} /* G */
double G1(double x,double y,double z)
/* angle ftn partial. First, convert arguments to s-radii. */
{
double s;
s=x+y+z;
return ((-1.0)*(sqrt(x*y*z)*sqrt(s))*(1.0/s+1.0/x)/((x+y)*(x+z)) );
} /* G1 */
double G2(double x,double y,double z)
/* angle ftn partial. First, convert arguments to s-radii. */
{
return ( (sqrt(x*z)/(sqrt(y)*((x+y)*sqrt(x+y+z)))) );
} /* G2 */
double G3(double x,double y,double z)
/* angle ftn partial. First, convert arguments to s-radii. */
{
return ( (sqrt(x*y)/(sqrt(z)*((x+z)*sqrt(x+y+z)))) );
} /* G3 */
/* ========= hyperbolic functions ========== */
double g(double x,double y,double z)
/* angle function. First, convert arguments to s-radii. */
{
x=1.0/(x*x); y=1.0/(y*y); z=1.0/(z*z);
return (acos( ((x*y+1.0)*(x*z+1.0)-2.0*x*(y*z+1.0)) /
((x*y-1.0)*(x*z-1.0)) ));
} /* g */
double g1(double x,double y,double z)
/* angle ftn partial. First, convert arguments to s-radii. */
{
x=1.0/(x*x); y=1.0/(y*y); z=1.0/(z*z);
return ( (-1.0)*(x*x*y*z-1.0)*sqrt((y-1.0)*(z-1.0)) /
((x*y-1.0)*(x*z-1.0)*sqrt(x*(x-1.0)*(x*y*z-1.0))) );
} /* g1 */
double g2(double x,double y,double z)
/* angle ftn partial. First, convert arguments to s-radii. */
{
x=1.0/(x*x); y=1.0/(y*y); z=1.0/(z*z);
return (sqrt(x*(x-1.0)*(z-1.0)) /
((x*y-1.0)*sqrt((y-1.0)*(x*y*z-1.0))) );
} /* g2 */
double g3(double x,double y,double z)
/* angle ftn partial. First, convert arguments to s-radii. */
{
x=1.0/(x*x); y=1.0/(y*y); z=1.0/(z*z);
return ( sqrt(x*(x-1.0)*(y-1.0)) /
((x*z-1.0)*sqrt((z-1.0)*(x*y*z-1.0))) );
} /* g3 */
double area_div(struct p_data *p,int v)
/* deriv of hyp area. */
{
int k;
double accum=0.0;
struct R_data *pR_ptr;
struct K_data *pK_ptr;
pR_ptr=p->packR_ptr;pK_ptr=p->packK_ptr;
if (p->hes>=0 || v<1 || v>p->nodecount) return 0.0;
for (k=0;k<pK_ptr[v].num;k++)
accum += Av(pR_ptr[v].rad,pR_ptr[pK_ptr[v].flower[k]].rad,
pR_ptr[pK_ptr[v].flower[k+1]].rad);
return accum;
} /* area_div */
double Av(double v,double u,double w)
/* rate of change of area of triangle.*/
{
return ((-1.0)*(g1(v,u,w)+g2(u,v,w)+g3(w,u,v)));
} /* Av */
double dtheta_dlog(struct p_data *p,int v)
/* compute the derivative of the angle_sum theta at vertex v with
respect to the log of the actual hyperbolic radius of v. */
{
double vv,dtdv,h;
vv=p->packR_ptr[v].rad;
if (vv<=0) return 0.0;
vv=1.0/(vv*vv);
h=radius(p,v);
dtdv=node_conductance(p,v)/((1.0-vv)*sqrt(vv));
return (dtdv*2.0*h*exp(2.0*h));
} /* dtheta_dlog */
/* ============= computations ========== */
double twin_conductance(struct p_data *p,int v)
/* conductance to ground in hyp case */
{
double coef,vv;
if (p->hes == 0 || p->hes >0) return 0;
if ((vv=p->packR_ptr[v].rad)<=okerr) return 0.0;
vv=1.0/(vv*vv);
coef=(vv-1.0)*sqrt(vv);
return (area_div(p,v)*coef);
} /* twin_conductance */
double Cvw(double v,double u,double w,double a,int flag,int hes)
/* conductance of edge from v to w. flag: 0=2 nbh, 1=only left
nbh (a), 2=only right nbh (u). */
{
double vv,coef;
if (hes>0) return 0; /* spherical not yet done */
if (hes<0)
{
if (v<=0 || w<=0) return 0;
vv=1.0/(v*v); /* convert to s-radius */
coef=(vv-1.0)*sqrt(vv);
if (flag==1) return (g3(w,a,v)*coef);
if (flag==2) return (g3(w,u,v)*coef);
return ( (g3(w,u,v)+g3(w,a,v))*coef);
}
else
{
coef=v;
if (flag==1) return (G3(w,a,v)*coef);
if (flag==2) return (G3(w,u,v)*coef);
return ( (G3(w,u,v)+G3(w,a,v))*coef );
}
} /* Cvw */
double node_conductance(struct p_data *p,int v)
/* add up edge (and in hyp, twin) conductances */
{
int k;
double accum,coef,vv;
struct R_data *pR_ptr;
struct K_data *pK_ptr;
pR_ptr=p->packR_ptr;pK_ptr=p->packK_ptr;
if (p->hes>0) return 0.0;
if (p->hes==0)
{
accum=0.0;
for (k=1;k<pK_ptr[v].num;k++) /* middle faces */
accum += Cvw(pR_ptr[v].rad,pR_ptr[pK_ptr[v].flower[k-1]].rad,
pR_ptr[pK_ptr[v].flower[k]].rad,
pR_ptr[pK_ptr[v].flower[k+1]].rad,0,p->hes);
accum += Cvw(pR_ptr[v].rad,0.0,pR_ptr[pK_ptr[v].flower[0]].rad,
pR_ptr[pK_ptr[v].flower[1]].rad,1,p->hes); /* first face */
accum += Cvw(pR_ptr[v].rad,
pR_ptr[pK_ptr[v].flower[pK_ptr[v].num-1]].rad,
pR_ptr[pK_ptr[v].flower[pK_ptr[v].num]].rad,
0.0,2,p->hes); /* last face */
return accum;
}
if (p->hes<0)
{
vv=pR_ptr[v].rad;
if (vv<okerr) return 0.0;
vv=1.0/(vv*vv);
coef=(vv-1.0)*sqrt(vv);
accum=area_div(p,v)*coef;
for (k=1;k<pK_ptr[v].num;k++) /* middle faces */
accum += Cvw(pR_ptr[v].rad,pR_ptr[pK_ptr[v].flower[k-1]].rad,
pR_ptr[pK_ptr[v].flower[k]].rad,
pR_ptr[pK_ptr[v].flower[k+1]].rad,0,p->hes);
accum += Cvw(pR_ptr[v].rad,0.0,pR_ptr[pK_ptr[v].flower[0]].rad,
pR_ptr[pK_ptr[v].flower[1]].rad,1,p->hes); /* first face */
accum += Cvw(pR_ptr[v].rad,
pR_ptr[pK_ptr[v].flower[pK_ptr[v].num-1]].rad,
pR_ptr[pK_ptr[v].flower[pK_ptr[v].num]].rad,
0.0,2,p->hes); /* last face */
return accum;
}
return 0.0;
} /* node_conductance */
double edge_conduct(struct p_data *p,int v,int indx)
/* from v to indx neighbor */
{
int w,left_index;
double dum;
struct R_data *pR_ptr;
struct K_data *pK_ptr;
pR_ptr=p->packR_ptr;pK_ptr=p->packK_ptr;
w=pK_ptr[v].flower[indx];
if (pK_ptr[v].bdry_flag && indx==0) /* bdry and upstream ngb */
{
dum=Cvw(pR_ptr[v].rad,0.0,
pR_ptr[w].rad,
pR_ptr[pK_ptr[v].flower[1]].rad,1,p->hes);
return (dum);
}
if (pK_ptr[v].bdry_flag && indx==pK_ptr[v].num) /* bdry, down ngb */
{
dum=Cvw(pR_ptr[v].rad,
pR_ptr[pK_ptr[v].flower[pK_ptr[v].num-1]].rad,
pR_ptr[w].rad,0.0,2,p->hes);
return (dum);
}
if (indx==0) left_index=pK_ptr[v].num-1;
else left_index=indx-1;
dum=Cvw(pR_ptr[v].rad,
pR_ptr[pK_ptr[v].flower[left_index]].rad,
pR_ptr[w].rad,
pR_ptr[pK_ptr[v].flower[indx+1]].rad,0,p->hes);
return (dum);
} /* edge_conduct */
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