sbasis-geometric.h File Reference

two-dimensional geometric operators. More...

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Namespaces
namespace	Geom
	Various utility functions.

Functions
Piecewise< D2< SBasis > >	Geom::cutAtRoots (Piecewise< D2< SBasis > > const &M, double tol=1e-4)
Piecewise< SBasis >	Geom::atan2 (D2< SBasis > const &vect, double tol=.01, unsigned order=3)
Piecewise< SBasis >	Geom::atan2 (Piecewise< D2< SBasis > >const &vect, double tol=.01, unsigned order=3)
D2< Piecewise< SBasis > >	Geom::tan2 (SBasis const &angle, double tol=.01, unsigned order=3)
D2< Piecewise< SBasis > >	Geom::tan2 (Piecewise< SBasis > const &angle, double tol=.01, unsigned order=3)
Piecewise< D2< SBasis > >	Geom::unitVector (D2< SBasis > const &vect, double tol=.01, unsigned order=3)
Piecewise< D2< SBasis > >	Geom::unitVector (Piecewise< D2< SBasis > > const &vect, double tol=.01, unsigned order=3)
Piecewise< SBasis >	Geom::curvature (D2< SBasis > const &M, double tol=.01)
Piecewise< SBasis >	Geom::curvature (Piecewise< D2< SBasis > > const &M, double tol=.01)
Piecewise< SBasis >	Geom::arcLengthSb (D2< SBasis > const &M, double tol=.01)
Piecewise< SBasis >	Geom::arcLengthSb (Piecewise< D2< SBasis > > const &M, double tol=.01)
double	Geom::length (D2< SBasis > const &M, double tol=.01)
double	Geom::length (Piecewise< D2< SBasis > > const &M, double tol=.01)
void	Geom::length_integrating (D2< SBasis > const &B, double &result, double &abs_error, double tol)
Piecewise< D2< SBasis > >	Geom::arc_length_parametrization (D2< SBasis > const &M, unsigned order=3, double tol=.01)
Piecewise< D2< SBasis > >	Geom::arc_length_parametrization (Piecewise< D2< SBasis > > const &M, unsigned order=3, double tol=.01)
unsigned	Geom::centroid (Piecewise< D2< SBasis > > const &p, Point &centroid, double &area)
std::vector< D2< SBasis > >	Geom::cubics_fitting_curvature (Point const &M0, Point const &M1, Point const &dM0, Point const &dM1, double d2M0xdM0, double d2M1xdM1, int insist_on_speed_signs=1, double epsilon=1e-5)
std::vector< D2< SBasis > >	Geom::cubics_fitting_curvature (Point const &M0, Point const &M1, Point const &dM0, Point const &dM1, Point const &d2M0, Point const &d2M1, int insist_on_speed_signs=1, double epsilon=1e-5)
std::vector< D2< SBasis > >	Geom::cubics_with_prescribed_curvature (Point const &M0, Point const &M1, Point const &dM0, Point const &dM1, double k0, double k1, int insist_on_speed_signs=1, double error=1e-5)
std::vector< double >	Geom::find_tangents (Point P, D2< SBasis > const &A)
std::vector< double >	Geom::find_tangents_by_vector (Point V, D2< SBasis > const &A)
std::vector< double >	Geom::find_normals (Point P, D2< SBasis > const &A)
std::vector< double >	Geom::find_normals_by_vector (Point V, D2< SBasis > const &A)

Detailed Description

two-dimensional geometric operators.

These operators are built on a more 'polynomially robust' transformation to map a function that takes a [0,1] parameter to a 2d vector into a function that takes the same [0,1] parameter to a unit vector with the same direction.

Rather that using (X/sqrt(X))(t) which involves two unstable operations, sqrt and divide, this approach forms a curve directly from the various tangent directions at each end (angular jet). As a result, the final path has a convergence behaviour derived from that of the sin and cos series. – njh

Definition in file sbasis-geometric.h.