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