gsCurvatureSmoothing< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsCurvatureSmoothing< T >

Class for computing a closed B-spline curve with a smaller number of curvature extrema compared to a given closed B-spline curve.

i.e. some kind of smoothing the curvature of the curve with the help of two different methods

Collaboration diagram for gsCurvatureSmoothing< T >:

Public Member Functions
void	computeApproxError (T &error)
	computes approximation error of the smoother curve to the original point cloud
void	computeApproxErrorCoef (T &error)
	computes the max approximation error between the coeffeicientsof the original and the smoother curve
void	computeApproxErrorL2 (T &error)
	computes the L^{2}-norm approximation error of the smoother curve
void	computeApproxErrorLMax (T &error)
	computes the L-max-norm approximation error of the smoother curve
void	computeCurvatureError (T &error)
	computes the curvature error of the smoother curve
const gsBSpline< T > &	curveOriginal () const
	gives back the original B-spline curve
const gsBSpline< T > &	curveSmooth () const
	gives back the smoother B-spline curve
	gsCurvatureSmoothing ()
	default constructor
	gsCurvatureSmoothing (const gsBSpline< T > &init_curve, const gsMatrix< T > &param_values, const gsMatrix< T > &points)
	constructor
void	smoothAllHadenfeld (const unsigned smooth_degree=4, const unsigned iter=500)
void	smoothHadenfeld (const unsigned smooth_degree, const T delta, const index_t iter_step, const index_t iter_total, gsVector< index_t > &iterated, const bool original=true)
	smooth the curve by smoothing only one cofficient in each step using the Hadenfeld algorithm — the usual Hadenfeld algorithm –this method should be used
void	smoothTotalVariation (const T omega1, const T omega2, const T lamda, const T tau, const unsigned iter=50)
void	smoothTotalVariationSelectLamda (const T omega1, const T omega2, const gsMatrix< T > listlamdas, const unsigned iter=50)
void	smoothTotalVariationSelectLamda (const T omega1, const T omega2, const T lamda, const unsigned iter=50)
void	write (std::ostream &os)
	writes the smooth curve to a file, which can be visualized in Mathematica (Name of Mathematica File VisualizationCurvatureSmoothing)
	~gsCurvatureSmoothing ()
	Destructor.

Private Member Functions
void	compute_AllValues (gsBSplineBasis< T > *basis, gsMatrix< T > u, gsMatrix< T > *coefs, gsMatrix< T > &values0, gsMatrix< T > &values1, gsMatrix< T > &values2, gsMatrix< T > &values3)
	computes all values and derivatives (up to three) at the parameter values u for the given coefs
void	compute_ObjectiveFunction (gsBSplineBasis< T > *basis, gsMatrix< T > *coefs, const T omega1, const T omega2, T &value)
	computes the objective function for given coefs and omega1 and omega2 – objective function = omega1*ApproximationFunction + omega2*CurvatureFunction
void	reset (gsBSpline< T > *newCurve)
	set the smooth curve to the the original curve

Private Attributes
const gsBSpline< T > *	m_curve_original
	the original B-spline curve
gsBSpline< T > *	m_curve_smooth
	the smoother B-spline curve
gsMatrix< T >	m_param_values
	the parameter values of the original point cloud
gsMatrix< T >	m_points
	the points of the original point cloud

Member Function Documentation

void smoothAllHadenfeld	(	const unsigned	smooth_degree = 4,
		const unsigned	iter = 500
	)

smooth the curve in one step for all coefficients using the Hadenfeld algorithm. Be aware of the fact that it is not ensured that we get a nice result — can work but do not have to work (not sure that it will converge!!) if possible use method void smoothHadenfeld

void smoothTotalVariation	(	const T	omega1,
		const T	omega2,
		const T	lamda,
		const T	tau,
		const unsigned	iter = 50
	)

smooth the curve by total variation – computes the stepsize by itsself (with the help of a backtracking line search method) this method should be used instead of the two methods void smoothTotalVariationSelectLamda

void smoothTotalVariationSelectLamda	(	const T	omega1,
		const T	omega2,
		const gsMatrix< T >	listlamdas,
		const unsigned	iter = 50
	)

smooth the curve by total variation – uses different stepsizes (in listlamdas) in the gradient descent method (look for the best from the list!) if possible use the method void smoothTotalVariation

void smoothTotalVariationSelectLamda	(	const T	omega1,
		const T	omega2,
		const T	lamda,
		const unsigned	iter = 50
	)

smooth the curve by total variation – uses always the same stepsize lamda - but which has to be chosen!! if possible use the method void smoothTotalVariation