mirror of
https://github.com/NGSolve/netgen.git
synced 2024-12-25 05:20:34 +05:00
764 lines
18 KiB
C++
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
|