src/2geom/sbasis-geometric.h

   1 #ifndef _SBASIS_GEOMETRIC
   2 #define _SBASIS_GEOMETRIC
   3 #include "d2.h"
   4 #include "piecewise.h"
   5 #include <vector>
   6
   7 /** two-dimensional geometric operators.
   8  * Copyright 2007, JFBarraud
   9  * Copyright 2007, njh
  10  *
  11  * These operators are built on a more 'polynomially robust'
  12  * transformation to map a function that takes a [0,1] parameter to a
  13  * 2d vector into a function that takes the same [0,1] parameter to a
  14  * unit vector with the same direction.
  15  *
  16  * Rather that using (X/sqrt(X))(t) which involves two unstable
  17  * operations, sqrt and divide, this approach forms a curve directly
  18  * from the various tangent directions at each end (angular jet).  As
  19  * a result, the final path has a convergence behaviour derived from
  20  * that of the sin and cos series. -- njh
  21  */
  22
  23 namespace Geom{
  24
  25 Piecewise<D2<SBasis> >
  26 cutAtRoots(Piecewise<D2<SBasis> > const &M, double tol=1e-4);
  27
  28 Piecewise<SBasis>
  29 atan2(D2<SBasis> const &vect,
  30            double tol=.01, unsigned order=3);
  31
  32 Piecewise<SBasis>
  33 atan2(Piecewise<D2<SBasis> >const &vect,
  34            double tol=.01, unsigned order=3);
  35
  36 Piecewise<D2<SBasis> >
  37 unitVector(D2<SBasis> const &vect,
  38            double tol=.01, unsigned order=3);
  39 Piecewise<D2<SBasis> >
  40 unitVector(Piecewise<D2<SBasis> > const &vect,
  41            double tol=.01, unsigned order=3);
  42
  43 // Piecewise<D2<SBasis> >
  44 // uniform_speed(D2<SBasis> const M,
  45 //               double tol=.1);
  46
  47 Piecewise<SBasis> curvature(          D2<SBasis>   const &M, double tol=.01);
  48 Piecewise<SBasis> curvature(Piecewise<D2<SBasis> > const &M, double tol=.01);
  49
  50 Piecewise<SBasis> arcLengthSb(          D2<SBasis>   const &M, double tol=.01);
  51 Piecewise<SBasis> arcLengthSb(Piecewise<D2<SBasis> > const &M, double tol=.01);
  52
  53 double length(          D2<SBasis>   const &M, double tol=.01);
  54 double length(Piecewise<D2<SBasis> > const &M, double tol=.01);
  55
  56 Piecewise<D2<SBasis> >
  57 arc_length_parametrization(D2<SBasis> const &M,
  58                            unsigned order=3,
  59                            double tol=.01);
  60 Piecewise<D2<SBasis> >
  61 arc_length_parametrization(Piecewise<D2<SBasis> > const &M,
  62                            unsigned order=3,
  63                            double tol=.01);
  64
  65
  66 unsigned centroid(Piecewise<D2<SBasis> > const &p, Point& centroid, double &area);
  67
  68 };
  69
  70 #endif
  71
  72 /*
  73   Local Variables:
  74   mode:c++
  75   c-file-style:"stroustrup"
  76   c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
  77   indent-tabs-mode:nil
  78   fill-column:99
  79   End:
  80 */
  81 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
  82
  83