netgen/libsrc/gprim/spline.hpp
2020-08-13 19:52:55 +02:00

764 lines
18 KiB
C++

#ifndef FILE_SPLINE_HPP
#define FILE_SPLINE_HPP
/**************************************************************************/
/* File: spline.hpp */
/* Author: Joachim Schoeberl */
/* Date: 24. Jul. 96 */
/**************************************************************************/
namespace netgen
{
/*
Spline curves for 2D mesh generation
*/
/// Geometry point
template < int D >
class GeomPoint : public Point<D>
{
public:
/// refinement factor at point
double refatpoint;
/// max mesh-size at point
double hmax;
/// hp-refinement
double hpref;
///
string name;
///
GeomPoint () { ; }
///
GeomPoint (const Point<D> & ap, double aref = 1, double ahpref=0)
: Point<D>(ap), refatpoint(aref), hmax(1e99), hpref(ahpref) { ; }
void DoArchive(Archive& ar)
{
Point<D>::DoArchive(ar);
ar & refatpoint & hmax & hpref;
}
};
/// base class for 2d - segment
template < int D >
class SplineSeg
{
public:
SplineSeg () { ; }
///
virtual ~SplineSeg() { ; }
/// calculates length of curve
virtual double Length () const;
/// returns point at curve, 0 <= t <= 1
virtual Point<D> GetPoint (double t) const = 0;
/// returns a (not necessarily unit-length) tangent vector for 0 <= t <= 1
virtual Vec<D> GetTangent (const double t) const
{
cerr << "GetTangent not implemented for spline base-class" << endl;
Vec<D> dummy; return dummy;
}
virtual void GetDerivatives (const double t,
Point<D> & point,
Vec<D> & first,
Vec<D> & second) const
{
double eps = 1e-6;
point = GetPoint (t);
Point<D> pl = GetPoint (t-eps);
Point<D> pr = GetPoint (t+eps);
first = 1.0/(2*eps) * (pr-pl);
second = 1.0/sqr(eps) * ( (pr-point)+(pl-point));
}
virtual void DoArchive(Archive& ar) = 0;
/// returns initial point on curve
virtual const GeomPoint<D> & StartPI () const = 0;
/// returns terminal point on curve
virtual const GeomPoint<D> & EndPI () const = 0;
/** writes curve description for fepp:
for implicitly given quadratic curves, the 6 coefficients of
the polynomial
$$ a x^2 + b y^2 + c x y + d x + e y + f = 0 $$
are written to ost */
void PrintCoeff (ostream & ost) const;
virtual void GetCoeff (Vector & coeffs) const = 0;
virtual void GetCoeff (Vector & coeffs, Point<D> p0) const { ; }
virtual void GetPoints (int n, NgArray<Point<D> > & points) const;
/** calculates (2D) lineintersections:
for lines $$ a x + b y + c = 0 $$ the interecting points are calculated
and stored in points */
virtual void LineIntersections (const double a, const double b, const double c,
NgArray < Point<D> > & points, const double eps) const
{points.SetSize(0);}
// is the point in the convex hull (increased by eps) of the spline ?
virtual bool InConvexHull (Point<D> p, double eps) const = 0;
virtual double MaxCurvature(void) const = 0;
virtual string GetType(void) const {return "splinebase";}
virtual void Project (const Point<D> point, Point<D> & point_on_curve, double & t) const
{ cerr << "Project not implemented for spline base-class" << endl;}
virtual void GetRawData (NgArray<double> & data) const
{ cerr << "GetRawData not implemented for spline base-class" << endl;}
};
/// Straight line form p1 to p2
template< int D >
class LineSeg : public SplineSeg<D>
{
///
GeomPoint<D> p1, p2;
public:
///
LineSeg (const GeomPoint<D> & ap1, const GeomPoint<D> & ap2);
///
// default constructor for archive
LineSeg() {}
virtual void DoArchive(Archive& ar)
{
ar & p1 & p2;
}
virtual double Length () const;
///
inline virtual Point<D> GetPoint (double t) const;
///
virtual Vec<D> GetTangent (const double t) const;
virtual void GetDerivatives (const double t,
Point<D> & point,
Vec<D> & first,
Vec<D> & second) const;
///
virtual const GeomPoint<D> & StartPI () const { return p1; };
///
virtual const GeomPoint<D> & EndPI () const { return p2; }
///
virtual void GetCoeff (Vector & coeffs) const;
virtual void GetCoeff (Vector & coeffs, Point<D> p0) const;
virtual string GetType(void) const {return "line";}
virtual void LineIntersections (const double a, const double b, const double c,
NgArray < Point<D> > & points, const double eps) const;
virtual bool InConvexHull (Point<D> p, double eps) const
{
return MinDistLP2 (p1, p2, p) < sqr(eps);
}
virtual double MaxCurvature(void) const {return 0;}
virtual void Project (const Point<D> point, Point<D> & point_on_curve, double & t) const;
virtual void GetRawData (NgArray<double> & data) const;
};
/// curve given by a rational, quadratic spline (including ellipses)
template< int D >
class SplineSeg3 : public SplineSeg<D>
{
///
GeomPoint<D> p1, p2, p3;
double weight;
mutable double proj_latest_t;
public:
///
SplineSeg3 (const GeomPoint<D> & ap1,
const GeomPoint<D> & ap2,
const GeomPoint<D> & ap3);
SplineSeg3 (const GeomPoint<D> & ap1,
const GeomPoint<D> & ap2,
const GeomPoint<D> & ap3,
double aweight);
// default constructor for archive
SplineSeg3() {}
///
virtual void DoArchive(Archive& ar)
{
ar & p1 & p2 & p3 & weight & proj_latest_t;
}
virtual Point<D> GetPoint (double t) const;
///
virtual Vec<D> GetTangent (const double t) const;
DLL_HEADER virtual void GetDerivatives (const double t,
Point<D> & point,
Vec<D> & first,
Vec<D> & second) const;
///
virtual const GeomPoint<D> & StartPI () const { return p1; };
///
virtual const GeomPoint<D> & EndPI () const { return p3; }
///
virtual void GetCoeff (Vector & coeffs) const;
virtual void GetCoeff (Vector & coeffs, Point<D> p0) const;
virtual string GetType(void) const {return "spline3";}
const GeomPoint<D> & TangentPoint (void) const { return p2; }
DLL_HEADER virtual void LineIntersections (const double a, const double b, const double c,
NgArray < Point<D> > & points, const double eps) const;
virtual bool InConvexHull (Point<D> p, double eps) const
{
return MinDistTP2 (p1, p2, p3, p) < sqr(eps);
}
DLL_HEADER virtual double MaxCurvature(void) const;
DLL_HEADER virtual void Project (const Point<D> point, Point<D> & point_on_curve, double & t) const;
DLL_HEADER virtual void GetRawData (NgArray<double> & data) const;
};
// Gundolf Haase 8/26/97
/// A circle
template < int D >
class CircleSeg : public SplineSeg<D>
{
///
private:
GeomPoint<D> p1, p2, p3;
//const GeomPoint<D> &p1, &p2, &p3;
Point<D> pm;
double radius, w1,w3;
public:
///
CircleSeg (const GeomPoint<D> & ap1,
const GeomPoint<D> & ap2,
const GeomPoint<D> & ap3);
// default constructor for archive
CircleSeg() {}
virtual void DoArchive(Archive& ar)
{
ar & p1 & p2 & p3 & pm & radius & w1 & w3;
}
///
virtual Point<D> GetPoint (double t) const;
///
virtual const GeomPoint<D> & StartPI () const { return p1; }
///
virtual const GeomPoint<D> & EndPI () const { return p3; }
///
virtual void GetCoeff (Vector & coeffs) const;
///
double Radius() const { return radius; }
///
double StartAngle() const { return w1; }
///
double EndAngle() const { return w3; }
///
const Point<D> & MidPoint(void) const {return pm; }
virtual string GetType(void) const {return "circle";}
virtual void LineIntersections (const double a, const double b, const double c,
NgArray < Point<D> > & points, const double eps) const;
virtual bool InConvexHull (Point<D> p, double eps) const
{
return (Dist2 (p, pm) < sqr(radius+eps));
}
virtual double MaxCurvature(void) const {return 1./radius;}
};
///
template<int D>
class DiscretePointsSeg : public SplineSeg<D>
{
NgArray<Point<D> > pts;
GeomPoint<D> p1n, p2n;
public:
///
DiscretePointsSeg (const NgArray<Point<D> > & apts);
// default constructor for archive
DiscretePointsSeg() {}
virtual void DoArchive(Archive& ar)
{
ar & pts & p1n & p2n;
}
///
virtual ~DiscretePointsSeg ();
///
virtual Point<D> GetPoint (double t) const;
///
virtual const GeomPoint<D> & StartPI () const { return p1n; };
///
virtual const GeomPoint<D> & EndPI () const { return p2n; }
///
virtual void GetCoeff (Vector & coeffs) const {;}
virtual double MaxCurvature(void) const {return 1;}
// needs implementation ...
virtual bool InConvexHull (Point<D> p, double eps) const
{ return true; }
};
// calculates length of spline-curve
template<int D>
double SplineSeg<D> :: Length () const
{
int n = 100;
double dt = 1.0 / n;
Point<D> pold = GetPoint (0);
double l = 0;
for (int i = 1; i <= n; i++)
{
Point<D> p = GetPoint (i * dt);
l += Dist (p, pold);
pold = p;
}
return l;
}
template<int D>
void SplineSeg<D> :: GetPoints (int n, NgArray<Point<D> > & points) const
{
points.SetSize (n);
if (n >= 2)
for (int i = 0; i < n; i++)
points[i] = GetPoint(double(i) / (n-1));
}
template<int D>
void SplineSeg<D> :: PrintCoeff (ostream & ost) const
{
Vector u(6);
GetCoeff(u);
for ( int i=0; i<6; i++)
ost << u[i] << " ";
ost << endl;
}
/*
Implementation of line-segment from p1 to p2
*/
template<int D>
LineSeg<D> :: LineSeg (const GeomPoint<D> & ap1,
const GeomPoint<D> & ap2)
: p1(ap1), p2(ap2)
{
;
}
template<int D>
inline Point<D> LineSeg<D> :: GetPoint (double t) const
{
return p1 + t * (p2 - p1);
}
template<int D>
Vec<D> LineSeg<D> :: GetTangent (const double t) const
{
return p2-p1;
}
template<int D>
void LineSeg<D> :: GetDerivatives (const double t,
Point<D> & point,
Vec<D> & first,
Vec<D> & second) const
{
first = p2 - p1;
point = p1 + t * first;
second = 0;
}
template<int D>
double LineSeg<D> :: Length () const
{
return Dist (p1, p2);
}
template<int D>
void LineSeg<D> :: GetCoeff (Vector & coeffs) const
{
coeffs.SetSize(6);
double dx = p2(0) - p1(0);
double dy = p2(1) - p1(1);
coeffs[0] = coeffs[1] = coeffs[2] = 0;
coeffs[3] = -dy;
coeffs[4] = dx;
coeffs[5] = -dx * p1(1) + dy * p1(0);
}
template<int D>
void LineSeg<D> :: GetCoeff (Vector & coeffs, Point<D> p) const
{
coeffs.SetSize(6);
double dx = p2(0) - p1(0);
double dy = p2(1) - p1(1);
coeffs[0] = coeffs[1] = coeffs[2] = 0;
coeffs[3] = -dy;
coeffs[4] = dx;
coeffs[5] = -dx * (p1(1)-p(1)) + dy * (p1(0)-p(0));
}
template<int D>
void LineSeg<D> :: LineIntersections (const double a, const double b, const double c,
NgArray < Point<D> > & points, const double eps) const
{
points.SetSize(0);
double denom = -a*p2(0)+a*p1(0)-b*p2(1)+b*p1(1);
if(fabs(denom) < 1e-20)
return;
double t = (a*p1(0)+b*p1(1)+c)/denom;
if((t > -eps) && (t < 1.+eps))
points.Append(GetPoint(t));
}
template<int D>
void LineSeg<D> :: Project (const Point<D> point, Point<D> & point_on_curve, double & t) const
{
Vec<D> v = p2-p1;
double l = v.Length();
v *= 1./l;
t = (point-p1)*v;
if(t<0) t = 0;
if(t>l) t = l;
point_on_curve = p1+t*v;
t *= 1./l;
}
template<int D>
void LineSeg<D> :: GetRawData (NgArray<double> & data) const
{
data.Append(2);
for(int i=0; i<D; i++)
data.Append(p1[i]);
for(int i=0; i<D; i++)
data.Append(p2[i]);
}
/*
template<int D>
double SplineSeg3<D> :: MaxCurvature(void) const
{
Vec<D> v1 = p1-p2;
Vec<D> v2 = p3-p2;
double l1 = v1.Length();
double l2 = v2.Length();
(*testout) << "v1 " << v1 << " v2 " << v2 << endl;
double cosalpha = v1*v2/(l1*l2);
(*testout) << "cosalpha " << cosalpha << endl;
return sqrt(cosalpha + 1.)/(min2(l1,l2)*(1.-cosalpha));
}
*/
//########################################################################
// circlesegment
template<int D>
CircleSeg<D> :: CircleSeg (const GeomPoint<D> & ap1,
const GeomPoint<D> & ap2,
const GeomPoint<D> & ap3)
: p1(ap1), p2(ap2), p3(ap3)
{
Vec<D> v1,v2;
v1 = p1 - p2;
v2 = p3 - p2;
Point<D> p1t(p1+v1);
Point<D> p2t(p3+v2);
// works only in 2D!!!!!!!!!
Line2d g1t,g2t;
g1t.P1() = Point<2>(p1(0),p1(1));
g1t.P2() = Point<2>(p1t(0),p1t(1));
g2t.P1() = Point<2>(p3(0),p3(1));
g2t.P2() = Point<2>(p2t(0),p2t(1));
Point<2> mp = CrossPoint (g1t,g2t);
pm(0) = mp(0); pm(1) = mp(1);
radius = Dist(pm,StartPI());
Vec2d auxv;
auxv.X() = p1(0)-pm(0); auxv.Y() = p1(1)-pm(1);
w1 = Angle(auxv);
auxv.X() = p3(0)-pm(0); auxv.Y() = p3(1)-pm(1);
w3 = Angle(auxv);
if ( fabs(w3-w1) > M_PI )
{
if ( w3>M_PI ) w3 -= 2*M_PI;
if ( w1>M_PI ) w1 -= 2*M_PI;
}
}
/*
template<int D>
Point<D> CircleSeg<D> :: GetPoint (double t) const
{
if (t >= 1.0) { return p3; }
double phi = StartAngle() + t*(EndAngle()-StartAngle());
Vec<D> tmp(cos(phi),sin(phi));
return pm + Radius()*tmp;
}
*/
template<>
inline Point<3> CircleSeg<3> :: GetPoint (double t) const
{
// not really useful, but keep it as it was ...
if (t >= 1.0) { return p3; }
double phi = StartAngle() + t*(EndAngle()-StartAngle());
Vec<3> tmp(cos(phi),sin(phi),0);
return pm + Radius()*tmp;
}
template<>
inline Point<2> CircleSeg<2> :: GetPoint (double t) const
{
if (t >= 1.0) { return p3; }
double phi = StartAngle() + t*(EndAngle()-StartAngle());
Vec<2> tmp(cos(phi),sin(phi));
return pm + Radius()*tmp;
}
template<int D>
void CircleSeg<D> :: GetCoeff (Vector & coeff) const
{
coeff[0] = coeff[1] = 1.0;
coeff[2] = 0.0;
coeff[3] = -2.0 * pm[0];
coeff[4] = -2.0 * pm[1];
coeff[5] = sqr(pm[0]) + sqr(pm[1]) - sqr(Radius());
}
template<int D>
DiscretePointsSeg<D> :: DiscretePointsSeg (const NgArray<Point<D> > & apts)
: pts (apts)
{
for(int i=0; i<D; i++)
{
p1n(i) = apts[0](i);
p2n(i) = apts.Last()(i);
}
p1n.refatpoint = 1;
p2n.refatpoint = 1;
p1n.hmax = 1e99;
p2n.hmax = 1e99;
}
template<int D>
DiscretePointsSeg<D> :: ~DiscretePointsSeg ()
{ ; }
template<int D>
Point<D> DiscretePointsSeg<D> :: GetPoint (double t) const
{
double t1 = t * (pts.Size()-1);
int segnr = int(t1);
if (segnr < 0) segnr = 0;
if (segnr >= pts.Size()) segnr = pts.Size()-1;
double rest = t1 - segnr;
return pts[segnr] + rest*Vec<D>(pts[segnr+1]-pts[segnr]);
}
// *************************************
// Template for B-Splines of order ORDER
// thx to Gerhard Kitzler
// *************************************
template<int D, int ORDER>
class BSplineSeg : public SplineSeg<D>
{
NgArray<Point<D> > pts;
GeomPoint<D> p1n, p2n;
NgArray<int> ti;
public:
///
BSplineSeg (const NgArray<Point<D> > & apts);
///
//default constructor for archive
BSplineSeg() {}
virtual ~BSplineSeg();
///
virtual void DoArchive(Archive& ar)
{
ar & pts & p1n & p2n & ti;
}
virtual Point<D> GetPoint (double t) const;
///
virtual const GeomPoint<D> & StartPI () const { return p1n; };
///
virtual const GeomPoint<D> & EndPI () const { return p2n; }
///
virtual void GetCoeff (Vector & coeffs) const {;}
virtual double MaxCurvature(void) const {return 1;}
// needs implementation ...
virtual bool InConvexHull (Point<D> p, double eps) const
{ return true; }
};
// Constructor
template<int D,int ORDER>
BSplineSeg<D,ORDER> :: BSplineSeg (const NgArray<Point<D> > & apts)
: pts (apts)
{
/*
for(int i=0; i<D; i++)
{
p1n(i) = apts[0](i);
p2n(i) = apts.Last()(i);
}
*/
p1n = apts[0];
p2n = apts.Last();
/*
p1n.refatpoint = 1;
p2n.refatpoint = 1;
p1n.hmax = 1e99;
p2n.hmax = 1e99;
*/
int m=pts.Size()+ORDER;
ti.SetSize(m);
// b.SetSize(m-1);
ti=0;
// b=0.0;
for(int i=ORDER;i<m-ORDER+1;i++)
ti[i]=i-ORDER+1;
for(int i=m-ORDER+1;i<m;i++)
ti[i]=m-2*ORDER+1;
}
// Destructor
template<int D,int ORDER>
BSplineSeg<D, ORDER> :: ~BSplineSeg ()
{ ; }
// GetPoint Method...(evaluation of BSpline Curve)
template<int D,int ORDER>
Point<D> BSplineSeg<D,ORDER> :: GetPoint (double t_in) const
{
int m=pts.Size()+ORDER;
double t = t_in * (m-2*ORDER+1);
double b[ORDER];
int interval_nr = int(t)+ORDER-1;
if (interval_nr < ORDER-1) interval_nr = ORDER-1;
if (interval_nr > m-ORDER-1) interval_nr = m-ORDER-1;
b[ORDER-1] = 1.0;
for(int degree=1;degree<ORDER;degree++)
for (int k = 0; k <= degree; k++)
{
int j = interval_nr-degree+k;
double bnew = 0;
if (k != 0)
bnew += (t-ti[j]) / ( ti[j+degree]-ti[j] ) * b[k-degree+ORDER-1];
if (k != degree)
bnew += (ti[j+degree+1]-t) / ( ti[j+degree+1]-ti[j+1] ) * b[k-degree+ORDER];
b[k-degree+ORDER-1] = bnew;
}
Point<D> p = 0.0;
for(int i=0; i < ORDER; i++)
p += b[i] * Vec<D> (pts[i+interval_nr-ORDER+1]);
return p;
}
}
#endif