src/2geom/sbasis-geometric.h

   1 #ifndef _SBASIS_GEOMETRIC
   2 #define _SBASIS_GEOMETRIC
   3 #include <2geom/d2.h>
   4 #include <2geom/piecewise.h>
   5 #include <vector>
   6
   7 /**
   8  * \file
   9  * \brief two-dimensional geometric operators.
  10  *
  11  * Copyright 2007, JFBarraud
  12  * Copyright 2007, njh
  13  *
  14  * These operators are built on a more 'polynomially robust'
  15  * transformation to map a function that takes a [0,1] parameter to a
  16  * 2d vector into a function that takes the same [0,1] parameter to a
  17  * unit vector with the same direction.
  18  *
  19  * Rather that using (X/sqrt(X))(t) which involves two unstable
  20  * operations, sqrt and divide, this approach forms a curve directly
  21  * from the various tangent directions at each end (angular jet).  As
  22  * a result, the final path has a convergence behaviour derived from
  23  * that of the sin and cos series. -- njh
  24  */
  25
  26 namespace Geom{
  27
  28 Piecewise<D2<SBasis> >
  29 cutAtRoots(Piecewise<D2<SBasis> > const &M, double tol=1e-4);
  30
  31 Piecewise<SBasis>
  32 atan2(D2<SBasis> const &vect,
  33            double tol=.01, unsigned order=3);
  34
  35 Piecewise<SBasis>
  36 atan2(Piecewise<D2<SBasis> >const &vect,
  37            double tol=.01, unsigned order=3);
  38
  39 D2<Piecewise<SBasis> >
  40 tan2(SBasis const &angle,
  41            double tol=.01, unsigned order=3);
  42
  43 D2<Piecewise<SBasis> >
  44 tan2(Piecewise<SBasis> const &angle,
  45            double tol=.01, unsigned order=3);
  46
  47 Piecewise<D2<SBasis> >
  48 unitVector(D2<SBasis> const &vect,
  49            double tol=.01, unsigned order=3);
  50 Piecewise<D2<SBasis> >
  51 unitVector(Piecewise<D2<SBasis> > const &vect,
  52            double tol=.01, unsigned order=3);
  53
  54 // Piecewise<D2<SBasis> >
  55 // uniform_speed(D2<SBasis> const M,
  56 //               double tol=.1);
  57
  58 Piecewise<SBasis> curvature(          D2<SBasis>   const &M, double tol=.01);
  59 Piecewise<SBasis> curvature(Piecewise<D2<SBasis> > const &M, double tol=.01);
  60
  61 Piecewise<SBasis> arcLengthSb(          D2<SBasis>   const &M, double tol=.01);
  62 Piecewise<SBasis> arcLengthSb(Piecewise<D2<SBasis> > const &M, double tol=.01);
  63
  64 double length(          D2<SBasis>   const &M, double tol=.01);
  65 double length(Piecewise<D2<SBasis> > const &M, double tol=.01);
  66
  67 void length_integrating(D2<SBasis> const &B, double &result, double &abs_error, double tol);
  68
  69 Piecewise<D2<SBasis> >
  70 arc_length_parametrization(D2<SBasis> const &M,
  71                            unsigned order=3,
  72                            double tol=.01);
  73 Piecewise<D2<SBasis> >
  74 arc_length_parametrization(Piecewise<D2<SBasis> > const &M,
  75                            unsigned order=3,
  76                            double tol=.01);
  77
  78
  79 unsigned centroid(Piecewise<D2<SBasis> > const &p, Point& centroid, double &area);
  80
  81 std::vector<D2<SBasis> >
  82 cubics_fitting_curvature(Point const &M0,   Point const &M1,
  83                          Point const &dM0,  Point const &dM1,
  84                          double d2M0xdM0,  double d2M1xdM1,
  85                          int insist_on_speed_signs = 1,
  86                          double epsilon = 1e-5);
  87
  88 std::vector<D2<SBasis> >
  89 cubics_fitting_curvature(Point const &M0,   Point const &M1,
  90                          Point const &dM0,  Point const &dM1,
  91                          Point const &d2M0, Point const &d2M1,
  92                          int insist_on_speed_signs = 1,
  93                          double epsilon = 1e-5);
  94
  95 std::vector<D2<SBasis> >
  96 cubics_with_prescribed_curvature(Point const &M0,   Point const &M1,
  97                                  Point const &dM0,  Point const &dM1,
  98                                  double k0,         double k1,
  99                                  int insist_on_speed_signs = 1,
 100                                  double error = 1e-5);
 101
 102
 103 std::vector<double> find_tangents(Point P, D2<SBasis> const &A);
 104
 105 };
 106
 107 #endif
 108
 109 /*
 110   Local Variables:
 111   mode:c++
 112   c-file-style:"stroustrup"
 113   c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
 114   indent-tabs-mode:nil
 115   fill-column:99
 116   End:
 117 */
 118 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
 119