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https://github.com/NGSolve/netgen.git
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577 lines
13 KiB
C++
577 lines
13 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 <linalg.hpp>
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#include <gprim.hpp>
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#include "spline.hpp"
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#include <core/register_archive.hpp>
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namespace netgen
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{
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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 <>
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void CircleSeg<3> :: LineIntersections (const double a, const double b, const double c,
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NgArray < Point<3> > & points, const double eps) const
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{
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cerr << "CircleSeg<3>::LineIntersections not implemented" << endl;
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}
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template <>
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void CircleSeg<2> :: LineIntersections (const double a, const double b, const double c,
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NgArray < Point<2> > & points, const double eps) const
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{
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points.SetSize(0);
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double px=0,py=0;
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if(fabs(b) > 1e-20)
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py = -c/b;
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else
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px = -c/a;
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const double c1 = a*a + b*b;
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const double c2 = 2. * ( a*(py-pm(1)) - b*(px-pm(0)));
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const double c3 = pow(px-pm(0),2) + pow(py-pm(1),2) - pow(Radius(),2);
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const double discr = c2*c2 - 4*c1*c3;
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if(discr < 0)
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return;
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NgArray<double> t;
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if(fabs(discr) < 1e-20)
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t.Append(-0.5*c2/c1);
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else
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{
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t.Append((-c2+sqrt(discr))/(2.*c1));
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t.Append((-c2-sqrt(discr))/(2.*c1));
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}
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for(int i=0; i<t.Size(); i++)
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{
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Point<2> p (px-t[i]*b,py+t[i]*a);
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double angle = atan2(p(1),p(0))+M_PI;
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if(angle > StartAngle()-eps && angle < EndAngle()+eps)
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points.Append(p);
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}
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}
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template<int D>
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SplineSeg3<D> :: SplineSeg3 (const GeomPoint<D> & ap1,
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const GeomPoint<D> & ap2,
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const GeomPoint<D> & ap3,
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string bcname,
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double maxh)
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: SplineSeg<D>(maxh, bcname), p1(ap1), p2(ap2), p3(ap3)
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{
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weight = Dist (p1, p3) / sqrt (0.5 * (Dist2 (p1, p2) + Dist2 (p2, p3)));
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// weight = sqrt(2);
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// cout << "weight = " << weight << endl;
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proj_latest_t = 0.5;
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}
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template<int D>
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SplineSeg3<D> :: SplineSeg3 (const GeomPoint<D> & ap1,
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const GeomPoint<D> & ap2,
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const GeomPoint<D> & ap3,
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double aweight,
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string bcname,
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double maxh)
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: SplineSeg<D>(maxh, bcname), p1(ap1), p2(ap2), p3(ap3), weight(aweight)
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{
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proj_latest_t = 0.5;
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}
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template<int D>
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Point<D> SplineSeg3<D> :: GetPoint (double t) const
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{
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double b1, b2, b3;
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b1 = (1-t)*(1-t);
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b2 = weight * t * (1-t);
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b3 = t * t;
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Vec<D> hp = b1 * Vec<D>(p1) + b2 * Vec<D>(p2) + b3 * Vec<D>(p3);
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double w = b1+b2+b3;
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return Point<D> ((1.0/w)*hp);
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/*
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double x, y, w;
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x = p1(0) * b1 + p2(0) * b2 + p3(0) * b3;
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y = p1(1) * b1 + p2(1) * b2 + p3(1) * b3;
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w = b1 + b2 + b3;
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if(D==3)
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{
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double z = p1(2) * b1 + p2(2) * b2 + p3(2) * b3;
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return Point<D> (x/w, y/w, z/w);
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}
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else
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return Point<D> (x/w, y/w);
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*/
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}
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template<int D>
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Vec<D> SplineSeg3<D> :: GetTangent (const double t) const
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{
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const double b1 = (1.-t)*((weight-2.)*t-weight);
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const double b2 = weight*(1.-2.*t);
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const double b3 = t*((weight-2)*t+2.);
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Vec<D> retval;
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for(int i=0; i<D; i++)
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retval(i) = b1*p1(i) + b2*p2(i) + b3*p3(i);
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return retval;
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}
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template<int D>
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void SplineSeg3<D> :: GetCoeff (Vector & u) const
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{
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DenseMatrix a(6, 6);
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DenseMatrix ata(6, 6);
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Vector f(6);
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u.SetSize(6);
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// ata.SetSymmetric(1);
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double t = 0;
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for (int i = 0; i < 5; i++, t += 0.25)
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{
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Point<D> p = GetPoint (t);
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a(i, 0) = p(0) * p(0);
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a(i, 1) = p(1) * p(1);
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a(i, 2) = p(0) * p(1);
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a(i, 3) = p(0);
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a(i, 4) = p(1);
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a(i, 5) = 1;
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}
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a(5, 0) = 1;
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CalcAtA (a, ata);
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u = 0;
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u(5) = 1;
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a.MultTrans (u, f);
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ata.Solve (f, u);
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// the sign
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Point<D> p0 = GetPoint(0);
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Vec<D> ht = GetTangent(0);
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Vec<2> tang(ht(0), ht(1));
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double gradx = 2.*u(0)*p0(0) + u(2)*p0(1) + u(3);
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double grady = 2.*u(1)*p0(1) + u(2)*p0(0) + u(4);
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Vec<2> gradn (grady, -gradx);
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if (tang * gradn < 0) u *= -1;
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}
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template<int D>
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void SplineSeg3<D> :: GetCoeff (Vector & u, Point<D> pref) const
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{
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DenseMatrix a(6, 6);
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DenseMatrix ata(6, 6);
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Vector f(6);
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u.SetSize(6);
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// ata.SetSymmetric(1);
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double t = 0;
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for (int i = 0; i < 5; i++, t += 0.25)
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{
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Vec<D> p = GetPoint (t)-pref;
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a(i, 0) = p(0) * p(0);
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a(i, 1) = p(1) * p(1);
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a(i, 2) = p(0) * p(1);
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a(i, 3) = p(0);
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a(i, 4) = p(1);
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a(i, 5) = 1;
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}
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a(5, 0) = 1;
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CalcAtA (a, ata);
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u = 0;
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u(5) = 1;
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a.MultTrans (u, f);
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ata.Solve (f, u);
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// the sign
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// Point<D> p0 = GetPoint(0);
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Vec<D> ht = GetTangent(0);
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Vec<2> tang(ht(0), ht(1));
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double gradx = u(3);
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double grady = u(4);
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// double gradx = 2.*u(0)*p0(0) + u(2)*p0(1) + u(3);
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// double grady = 2.*u(1)*p0(1) + u(2)*p0(0) + u(4);
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Vec<2> gradn (grady, -gradx);
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if (tang * gradn < 0) u *= -1;
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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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/*
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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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*/
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double tmin = 1;
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double dist_min2 = Dist2 (GetPoint(tmin), point);
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for (double ti = 0; ti < 0.99; ti += 0.25)
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{
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double di = Dist2(GetPoint(ti), point);
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if (di < dist_min2)
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{
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tmin = ti;
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dist_min2 = di;
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}
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}
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t = tmin;
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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 = weight*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 = weight*(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.*weight;
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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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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<>
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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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template<int D>
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void SplineSeg3<D> :: LineIntersections (const double a, const double b, const double c,
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NgArray < Point<D> > & points, const double eps) const
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{
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points.SetSize(0);
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double t;
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const double c1 = a*p1(0) - weight*a*p2(0) + a*p3(0)
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+ b*p1(1) - weight*b*p2(1) + b*p3(1)
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+ (2.-weight)*c;
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const double c2 = -2.*a*p1(0) + weight*a*p2(0) -2.*b*p1(1) + weight*b*p2(1) + (weight-2.)*c;
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const double c3 = a*p1(0) + b*p1(1) + c;
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if(fabs(c1) < 1e-20)
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{
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if(fabs(c2) < 1e-20)
|
|
return;
|
|
|
|
t = -c3/c2;
|
|
if((t > -eps) && (t < 1.+eps))
|
|
points.Append(GetPoint(t));
|
|
return;
|
|
}
|
|
|
|
const double discr = c2*c2-4.*c1*c3;
|
|
|
|
if(discr < 0)
|
|
return;
|
|
|
|
if(fabs(discr/(c1*c1)) < 1e-14)
|
|
{
|
|
t = -0.5*c2/c1;
|
|
if((t > -eps) && (t < 1.+eps))
|
|
points.Append(GetPoint(t));
|
|
return;
|
|
}
|
|
|
|
t = (-c2 + sqrt(discr))/(2.*c1);
|
|
if((t > -eps) && (t < 1.+eps))
|
|
points.Append(GetPoint(t));
|
|
|
|
t = (-c2 - sqrt(discr))/(2.*c1);
|
|
if((t > -eps) && (t < 1.+eps))
|
|
points.Append(GetPoint(t));
|
|
}
|
|
|
|
|
|
template < int D >
|
|
void SplineSeg3<D> :: GetRawData (NgArray<double> & data) const
|
|
{
|
|
data.Append(3);
|
|
for(int i=0; i<D; i++)
|
|
data.Append(p1[i]);
|
|
for(int i=0; i<D; i++)
|
|
data.Append(p2[i]);
|
|
for(int i=0; i<D; i++)
|
|
data.Append(p3[i]);
|
|
}
|
|
|
|
|
|
|
|
template class SplineSeg3<2>;
|
|
template class SplineSeg3<3>;
|
|
|
|
RegisterClassForArchive<SplineSeg<2>> regss2;
|
|
RegisterClassForArchive<SplineSeg<3>> regss3;
|
|
RegisterClassForArchive<LineSeg<2>, SplineSeg<2>> regls2;
|
|
RegisterClassForArchive<LineSeg<3>, SplineSeg<3>> regls3;
|
|
RegisterClassForArchive<SplineSeg3<2>, SplineSeg<2>> regsss2;
|
|
RegisterClassForArchive<SplineSeg3<3>, SplineSeg<3>> regsss3;
|
|
}
|