mirror of
https://github.com/NGSolve/netgen.git
synced 2024-12-27 06:10:34 +05:00
342 lines
7.4 KiB
C++
342 lines
7.4 KiB
C++
/*
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Spline curve for Mesh generator
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*/
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#include <mystdlib.h>
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#include <csg.hpp>
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#include <linalg.hpp>
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#include <meshing.hpp>
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namespace netgen
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{
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#include "spline.hpp"
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// just for testing (JS)
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template <int D>
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void ProjectTrivial (const SplineSeg3<D> & seg,
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const Point<D> point, Point<D> & point_on_curve, double & t)
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{
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double mindist = -1;
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for (int i = 0; i <= 1000; i++)
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{
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double ht = double(i)/1000;
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Point<D> p = seg.GetPoint(ht);
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double dist = Dist2 (p, point);
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if (i == 0 || dist < mindist)
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{
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mindist = dist;
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t = ht;
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}
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}
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point_on_curve = seg.GetPoint(t);
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}
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template<int D>
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void SplineSeg3<D> :: Project (const Point<D> point, Point<D> & point_on_curve, double & t) const
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{
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double t_old = -1;
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if(proj_latest_t > 0. && proj_latest_t < 1.)
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t = proj_latest_t;
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else
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t = 0.5;
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Point<D> phi;
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Vec<D> phip,phipp,phimp;
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int i=0;
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while(t > -0.5 && t < 1.5 && i<20 && fabs(t-t_old) > 1e-15 )
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{
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GetDerivatives(t,phi,phip,phipp);
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t_old = t;
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phimp = phi-point;
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//t = min2(max2(t-(phip*phimp)/(phipp*phimp + phip*phip),0.),1.);
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t -= (phip*phimp)/(phipp*phimp + phip*phip);
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i++;
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}
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//if(i<10 && t > 0. && t < 1.)
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if(i<20 && t > -0.4 && t < 1.4)
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{
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if(t < 0)
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{
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t = 0.;
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}
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if(t > 1)
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{
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t = 1.;
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}
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point_on_curve = SplineSeg3<D>::GetPoint(t);
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double dist = Dist(point,point_on_curve);
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phi = SplineSeg3<D> ::GetPoint(0);
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double auxdist = Dist(phi,point);
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if(auxdist < dist)
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{
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t = 0.;
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point_on_curve = phi;
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dist = auxdist;
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}
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phi = SplineSeg3<D> ::GetPoint(1);
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auxdist = Dist(phi,point);
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if(auxdist < dist)
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{
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t = 1.;
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point_on_curve = phi;
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dist = auxdist;
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}
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}
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else
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{
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double t0 = 0;
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double t1 = 0.5;
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double t2 = 1.;
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double d0,d1,d2;
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//(*testout) << "newtonersatz" << endl;
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while(t2-t0 > 1e-8)
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{
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phi = SplineSeg3<D> ::GetPoint(t0); d0 = Dist(phi,point);
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phi = SplineSeg3<D> ::GetPoint(t1); d1 = Dist(phi,point);
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phi = SplineSeg3<D> ::GetPoint(t2); d2 = Dist(phi,point);
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double a = (2.*d0 - 4.*d1 +2.*d2)/pow(t2-t0,2);
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if(a <= 0)
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{
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if(d0 < d2)
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t2 -= 0.3*(t2-t0);
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else
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t0 += 0.3*(t2-t0);
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t1 = 0.5*(t2+t0);
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}
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else
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{
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double b = (d1-d0-a*(t1*t1-t0*t0))/(t1-t0);
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double auxt1 = -0.5*b/a;
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if(auxt1 < t0)
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{
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t2 -= 0.4*(t2-t0);
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t0 = max2(0.,t0-0.1*(t2-t0));
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}
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else if (auxt1 > t2)
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{
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t0 += 0.4*(t2-t0);
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t2 = min2(1.,t2+0.1*(t2-t0));
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}
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else
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{
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t1 = auxt1;
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auxt1 = 0.25*(t2-t0);
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t0 = max2(0.,t1-auxt1);
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t2 = min2(1.,t1+auxt1);
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}
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t1 = 0.5*(t2+t0);
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}
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}
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phi = SplineSeg3<D> ::GetPoint(t0); d0 = Dist(phi,point);
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phi = SplineSeg3<D> ::GetPoint(t1); d1 = Dist(phi,point);
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phi = SplineSeg3<D> ::GetPoint(t2); d2 = Dist(phi,point);
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double mind = d0;
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t = t0;
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if(d1 < mind)
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{
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t = t1;
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mind = d1;
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}
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if(d2 < mind)
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{
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t = t2;
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mind = d2;
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}
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point_on_curve = SplineSeg3<D> ::GetPoint(t);
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}
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//(*testout) << " latest_t " << proj_latest_t << " t " << t << endl;
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proj_latest_t = t;
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/*
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// test it by trivial sampling
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double ht;
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Point<D> hp;
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ProjectTrivial (*this, point, hp, ht);
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if (fabs (t-ht) > 1e-3)
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{
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// if (Dist2 (point, hp) < Dist2 (point, point_on_curve))
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cout << "project is wrong" << endl;
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cout << "t = " << t << ", ht = " << ht << endl;
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cout << "dist org = " << Dist(point, point_on_curve) << endl;
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cout << "dist trivial = " << Dist(point, hp) << endl;
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}
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*/
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}
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template<int D>
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void SplineSeg3<D> :: GetDerivatives (const double t,
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Point<D> & point,
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Vec<D> & first,
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Vec<D> & second) const
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{
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Vec<D> v1(p1), v2(p2), v3(p3);
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double b1 = (1.-t)*(1.-t);
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double b2 = sqrt(2.)*t*(1.-t);
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double b3 = t*t;
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double w = b1+b2+b3;
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b1 *= 1./w; b2 *= 1./w; b3 *= 1./w;
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double b1p = 2.*(t-1.);
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double b2p = sqrt(2.)*(1.-2.*t);
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double b3p = 2.*t;
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const double wp = b1p+b2p+b3p;
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const double fac1 = wp/w;
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b1p *= 1./w; b2p *= 1./w; b3p *= 1./w;
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const double b1pp = 2.;
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const double b2pp = -2.*sqrt(2.);
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const double b3pp = 2.;
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const double wpp = b1pp+b2pp+b3pp;
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const double fac2 = (wpp*w-2.*wp*wp)/(w*w);
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for(int i=0; i<D; i++)
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point(i) = b1*p1(i) + b2*p2(i) + b3*p3(i);
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first = (b1p - b1*fac1) * v1 +
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(b2p - b2*fac1) * v2 +
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(b3p - b3*fac1) * v3;
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/*
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second = (b1pp/w - b1p*fac1 - b1*fac2) * v1 +
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(b2pp/w - b2p*fac1 - b2*fac2) * v2 +
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(b3pp/w - b3p*fac1 - b3*fac2) * v3;
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*/
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// JS: 2 was missing
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second = (b1pp/w - 2*b1p*fac1 - b1*fac2) * v1 +
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(b2pp/w - 2*b2p*fac1 - b2*fac2) * v2 +
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(b3pp/w - 2*b3p*fac1 - b3*fac2) * v3;
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}
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template class SplineSeg3<2>;
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template class SplineSeg3<3>;
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void CalcPartition (double l, double h, double h1, double h2,
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double hcurve, double elto0, Array<double> & points)
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{
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cout << "calcpart, h = " << h << ", h1 = " << h1 << ", h2 = " << h2 << ", hcurve = " << hcurve << endl;
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int i, j, n, nel;
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double sum, t, dt, fun, fperel, oldf, f;
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n = 1000;
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points.SetSize (0);
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sum = 0;
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dt = l / n;
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t = 0.5 * dt;
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for (i = 1; i <= n; i++)
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{
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fun = min3 (hcurve, t/elto0 + h1, (l-t)/elto0 + h2);
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sum += dt / fun;
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t += dt;
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}
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nel = int (sum+1);
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fperel = sum / nel;
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points.Append (0);
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i = 1;
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oldf = 0;
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t = 0.5 * dt;
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for (j = 1; j <= n && i < nel; j++)
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{
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fun = min3 (hcurve, t/elto0 + h1, (l-t)/elto0 + h2);
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f = oldf + dt / fun;
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while (f > i * fperel && i < nel)
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{
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points.Append ( (l/n) * (j-1 + (i * fperel - oldf) / (f - oldf)) );
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i++;
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}
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oldf = f;
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t += dt;
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}
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points.Append (l);
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}
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template<>
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double SplineSeg3<2> :: MaxCurvature(void) const
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{
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Vec<2> v1 = p1-p2;
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Vec<2> v2 = p3-p2;
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double l1 = v1.Length();
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double l2 = v2.Length();
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double cosalpha = (v1*v2)/(l1*l2);
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return sqrt(cosalpha + 1.)/(min2(l1,l2)*(1.-cosalpha));
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}
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template<>
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double SplineSeg3<3> :: MaxCurvature(void) const
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{
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Vec<3> v1 = p1-p2;
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Vec<3> v2 = p3-p2;
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double l1 = v1.Length();
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double l2 = v2.Length();
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double cosalpha = v1*v2/(l1*l2);
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return sqrt(cosalpha + 1.)/(min2(l1,l2)*(1.-cosalpha));
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}
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}
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