netgen/libsrc/geom2d/spline.cpp

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2009-01-13 04:40:13 +05:00
/*
Spline curve for Mesh generator
*/
#include <mystdlib.h>
#include <csg.hpp>
#include <linalg.hpp>
#include <meshing.hpp>
namespace netgen
{
#include "spline.hpp"
/*
template<> void SplineSeg3<2> :: Project (const Point<2> point, Point<2> & point_on_curve, double & t) const
{
double t_old = 0;
t = 0.5;
Point<2> phi;
Vec<2> phip,phipp,phimp;
int i=0;
while(fabs(t-t_old) > 1e-8 && i<10)
{
GetDerivatives(t,phi,phip,phipp);
t_old = t;
phimp = phi-point;
t = min2(max2(t-(phip*phimp)/(phipp*phimp + phip*phip),0.),1.);
i++;
}
if(i<10)
{
point_on_curve = GetPoint(t);
double dist = Dist(point,point_on_curve);
phi = GetPoint(0);
double auxdist = Dist(phi,point);
if(auxdist < dist)
{
t = 0.;
point_on_curve = phi;
dist = auxdist;
}
phi = GetPoint(1);
auxdist = Dist(phi,point);
if(auxdist < dist)
{
t = 1.;
point_on_curve = phi;
dist = auxdist;
}
}
else
{
double t0 = 0;
double t1 = 0.5;
double t2 = 1.;
double d0,d1,d2;
//(*testout) << "2d newtonersatz" << endl;
while(t2-t0 > 1e-8)
{
phi = GetPoint(t0); d0 = Dist(phi,point);
phi = GetPoint(t1); d1 = Dist(phi,point);
phi = GetPoint(t2); d2 = Dist(phi,point);
double a = (2.*d0 - 4.*d1 +2.*d2)/pow(t2-t0,2);
if(a <= 0)
{
if(d0 < d2)
t2 -= 0.3*(t2-t0);
else
t0 += 0.3*(t2-t0);
t1 = 0.5*(t2+t0);
}
else
{
double b = (d1-d0-a*(t1*t1-t0*t0))/(t1-t0);
double auxt1 = -0.5*b/a;
if(auxt1 < t0)
{
t2 -= 0.4*(t2-t0);
t0 = max2(0.,t0-0.1*(t2-t0));
}
else if (auxt1 > t2)
{
t0 += 0.4*(t2-t0);
t2 = min2(1.,t2+0.1*(t2-t0));
}
else
{
t1 = auxt1;
auxt1 = 0.25*(t2-t0);
t0 = max2(0.,t1-auxt1);
t2 = min2(1.,t1+auxt1);
}
t1 = 0.5*(t2+t0);
}
}
phi = GetPoint(t0); d0 = Dist(phi,point);
phi = GetPoint(t1); d1 = Dist(phi,point);
phi = GetPoint(t2); d2 = Dist(phi,point);
double mind = d0;
t = t0;
if(d1 < mind)
{
t = t1;
mind = d1;
}
if(d2 < mind)
{
t = t2;
mind = d2;
}
point_on_curve = GetPoint(t);
}
}
template<> void SplineSeg3<3> :: Project (const Point<3> point, Point<3> & point_on_curve, double & t) const
{
double t_old = -1;
if(proj_latest_t > 0. && proj_latest_t < 1.)
t = proj_latest_t;
else
t = 0.5;
Point<3> phi;
Vec<3> phip,phipp,phimp;
int i=0;
while(fabs(t-t_old) > 1e-8 && t > -0.5 && t < 1.5 && i<10)
{
GetDerivatives(t,phi,phip,phipp);
t_old = t;
phimp = phi-point;
//t = min2(max2(t-(phip*phimp)/(phipp*phimp + phip*phip),0.),1.);
t -= (phip*phimp)/(phipp*phimp + phip*phip);
i++;
}
//if(i<10 && t > 0. && t < 1.)
if(i<10 && t > -0.4 && t < 1.4)
{
if(t < 0)
t = 0.;
if(t > 1)
t = 1.;
point_on_curve = GetPoint(t);
double dist = Dist(point,point_on_curve);
phi = GetPoint(0);
double auxdist = Dist(phi,point);
if(auxdist < dist)
{
t = 0.;
point_on_curve = phi;
dist = auxdist;
}
phi = GetPoint(1);
auxdist = Dist(phi,point);
if(auxdist < dist)
{
t = 1.;
point_on_curve = phi;
dist = auxdist;
}
}
else
{
double t0 = 0;
double t1 = 0.5;
double t2 = 1.;
double d0,d1,d2;
//(*testout) << "newtonersatz" << endl;
while(t2-t0 > 1e-8)
{
phi = GetPoint(t0); d0 = Dist(phi,point);
phi = GetPoint(t1); d1 = Dist(phi,point);
phi = GetPoint(t2); d2 = Dist(phi,point);
double a = (2.*d0 - 4.*d1 +2.*d2)/pow(t2-t0,2);
if(a <= 0)
{
if(d0 < d2)
t2 -= 0.3*(t2-t0);
else
t0 += 0.3*(t2-t0);
t1 = 0.5*(t2+t0);
}
else
{
double b = (d1-d0-a*(t1*t1-t0*t0))/(t1-t0);
double auxt1 = -0.5*b/a;
if(auxt1 < t0)
{
t2 -= 0.4*(t2-t0);
t0 = max2(0.,t0-0.1*(t2-t0));
}
else if (auxt1 > t2)
{
t0 += 0.4*(t2-t0);
t2 = min2(1.,t2+0.1*(t2-t0));
}
else
{
t1 = auxt1;
auxt1 = 0.25*(t2-t0);
t0 = max2(0.,t1-auxt1);
t2 = min2(1.,t1+auxt1);
}
t1 = 0.5*(t2+t0);
}
}
phi = GetPoint(t0); d0 = Dist(phi,point);
phi = GetPoint(t1); d1 = Dist(phi,point);
phi = GetPoint(t2); d2 = Dist(phi,point);
double mind = d0;
t = t0;
if(d1 < mind)
{
t = t1;
mind = d1;
}
if(d2 < mind)
{
t = t2;
mind = d2;
}
point_on_curve = GetPoint(t);
}
//(*testout) << " latest_t " << proj_latest_t << " t " << t << endl;
proj_latest_t = t;
}
*/
void CalcPartition (double l, double h, double r1, double r2,
double ra, double elto0, ARRAY<double> & points)
{
int i, j, n, nel;
double sum, t, dt, fun, fperel, oldf, f;
n = 1000;
points.SetSize (0);
sum = 0;
dt = l / n;
t = 0.5 * dt;
for (i = 1; i <= n; i++)
{
fun = min3 (h/ra, t/elto0 + h/r1, (l-t)/elto0 + h/r2);
sum += dt / fun;
t += dt;
}
nel = int (sum+1);
fperel = sum / nel;
points.Append (0);
i = 1;
oldf = 0;
t = 0.5 * dt;
for (j = 1; j <= n && i < nel; j++)
{
fun = min3 (h/ra, t/elto0 + h/r1, (l-t)/elto0 + h/r2);
f = oldf + dt / fun;
while (f > i * fperel && i < nel)
{
points.Append ( (l/n) * (j-1 + (i * fperel - oldf) / (f - oldf)) );
i++;
}
oldf = f;
t += dt;
}
points.Append (l);
}
template<>
double SplineSeg3<2> :: MaxCurvature(void) const
{
Vec<2> v1 = p1-p2;
Vec<2> v2 = p3-p2;
double l1 = v1.Length();
double l2 = v2.Length();
double cosalpha = (v1*v2)/(l1*l2);
return sqrt(cosalpha + 1.)/(min2(l1,l2)*(1.-cosalpha));
}
template<>
double SplineSeg3<3> :: MaxCurvature(void) const
{
Vec<3> v1 = p1-p2;
Vec<3> v2 = p3-p2;
double l1 = v1.Length();
double l2 = v2.Length();
double cosalpha = v1*v2/(l1*l2);
return sqrt(cosalpha + 1.)/(min2(l1,l2)*(1.-cosalpha));
}
}