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577 lines
13 KiB
C++
577 lines
13 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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bool hpref;
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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, bool ahpref=false)
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: Point<D>(ap), refatpoint(aref), hpref(ahpref) { ; }
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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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public:
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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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{ cerr << "GetTangent not implemented for spline base-class" << endl; Vec<D> dummy; return dummy;}
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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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/// 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 GetPoints (int n, Array<Point<D> > & points) const;
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/** calculates (2D) lineintersections:
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for lines $$ a x + b y + c = 0 $$ the interecting 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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Array < Point<D> > & points, const double eps) const
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{points.SetSize(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 (Array<double> & data) const
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{ cerr << "GetRawData not implemented for spline base-class" << endl;}
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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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///
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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 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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Array < Point<D> > & points, const double eps) const;
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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 (Array<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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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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///
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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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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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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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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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Array < Point<D> > & points, const double eps) const;
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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 (Array<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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///
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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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Array < Point<D> > & points, const double eps) const;
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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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Array<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 Array<Point<D> > & apts);
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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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};
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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, Array<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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: 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> :: LineIntersections (const double a, const double b, const double c,
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Array < 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 (Array<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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template<int D>
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Point<D> CircleSeg<D> :: GetPoint (double t) const
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{
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if (t >= 1.0) { return p3; }
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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<int D>
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void CircleSeg<D> :: GetCoeff (Vector & coeff) const
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{
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coeff[0] = coeff[1] = 1.0;
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coeff[2] = 0.0;
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coeff[3] = -2.0 * pm[0];
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coeff[4] = -2.0 * pm[1];
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coeff[5] = sqr(pm[0]) + sqr(pm[1]) - sqr(Radius());
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}
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template<int D>
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void CircleSeg<D> :: LineIntersections (const double a, const double b, const double c,
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Array < Point<D> > & 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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Array<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<D> 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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DiscretePointsSeg<D> :: DiscretePointsSeg (const Array<Point<D> > & apts)
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: pts (apts)
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{
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for(int i=0; i<D; i++)
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{
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p1n(i) = apts[0](i);
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p2n(i) = apts.Last()(i);
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}
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p1n.refatpoint = 1;
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p2n.refatpoint = 1;
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p1n.hmax = 1e99;
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p2n.hmax = 1e99;
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}
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template<int D>
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DiscretePointsSeg<D> :: ~DiscretePointsSeg ()
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{ ; }
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template<int D>
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Point<D> DiscretePointsSeg<D> :: GetPoint (double t) const
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{
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double t1 = t * (pts.Size()-1);
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int segnr = int(t1);
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if (segnr < 0) segnr = 0;
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if (segnr >= pts.Size()) segnr = pts.Size()-1;
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double rest = t1 - segnr;
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return pts[segnr] + rest*Vec<D>(pts[segnr+1]-pts[segnr]);
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}
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}
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#endif
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