Approx_BSplineApproxInterp Class Reference

Constrained least-squares B-spline curve approximation with exact interpolation constraints. More...

#include <Approx_BSplineApproxInterp.hxx>

Public Member Functions
	Approx_BSplineApproxInterp (const NCollection_Array1< gp_Pnt > &thePoints, int theNbControlPts, int theDegree=3, bool theContinuousIfClosed=false)
	Creates a constrained approximation solver.
void	InterpolatePoint (int thePointIndex, bool theWithKink=false)
	Marks a point to be exactly interpolated rather than approximated.
void	Perform ()
	Performs the fit using automatically computed parameters. Parameters are computed from input points using current parametrization alpha.
void	Perform (const NCollection_Array1< double > &theParams)
	Performs the fit with given parameters.
void	PerformOptimal (int theMaxIter)
	Performs the fit with iterative parameter optimization using automatically computed initial parameters.
void	PerformOptimal (const NCollection_Array1< double > &theParams, int theMaxIter)
	Performs the fit with iterative parameter optimization. Parameters of approximated points are re-projected onto the curve after each iteration to improve the fit.
bool	IsDone () const
	Returns true if the fit was successfully computed.
const occ::handle< Geom_BSplineCurve > &	Curve () const
	Returns the resulting B-spline curve.
double	MaxError () const
	Returns the maximum approximation error (distance at approximated points).
void	SetParametrizationAlpha (double theAlpha)
	Sets the parametrization power for automatic parameter computation. 0.0 = uniform, 0.5 = centripetal (default), 1.0 = chord-length.
void	SetMinPivot (double theMinPivot)
	Sets the minimum pivot value for the Gauss solver. Matrices with pivots below this threshold are treated as singular.
void	SetClosedTolerance (double theRelTol)
	Sets the relative tolerance for detecting closed curves. Closedness is detected when first/last points are within theRelTol * (bounding box diagonal).
void	SetKnotInsertionTolerance (double theTol)
	Sets the tolerance for detecting duplicate knot positions during insertion.
void	SetConvergenceTolerance (double theTol)
	Sets the convergence tolerance for parameter optimization. Optimization stops when relative error reduction falls below this value.
void	SetProjectionTolerance (double theTol)
	Sets the tolerance for point projection onto curve during optimization.

Detailed Description

Constrained least-squares B-spline curve approximation with exact interpolation constraints.

This class fits a B-spline curve through a set of 3D points, where each point can be either approximated (in the least-squares sense) or exactly interpolated. Selected interpolation points can additionally be marked as "kinks" - the solver then inserts high-multiplicity knots at the corresponding parameters to preserve C0 discontinuities.

The algorithm solves a KKT (Karush-Kuhn-Tucker) saddle-point system:

| A^T*A  C^T  L^T |   | x |   | A^T*b |
| C       0    0  | * | l | = |   d   |
| L       0    0  |   | m |   |   0   |

where:

• A is the basis matrix for approximated points
• C is the basis matrix for interpolated points
• L encodes continuity constraints (C1/C2 for closed curves)
• x are the control point coordinates
• l, m are Lagrange multipliers

Usage:

NCollection_Array1<gp_Pnt> aPts(1, 100);
// ... fill points ...
Approx_BSplineApproxInterp anApprox(aPts, 20);
anApprox.InterpolatePoint(0);        // first point exact
anApprox.InterpolatePoint(99);       // last point exact
anApprox.InterpolatePoint(50, true); // kink at midpoint
anApprox.Perform(aParams);
if (anApprox.IsDone())
{
  const occ::handle<Geom_BSplineCurve>& aCurve = anApprox.Curve();
  double aMaxErr = anApprox.MaxError();
}

Constructor & Destructor Documentation

Approx_BSplineApproxInterp()

Approx_BSplineApproxInterp::Approx_BSplineApproxInterp	(	const NCollection_Array1< gp_Pnt > &	thePoints,
		int	theNbControlPts,
		int	theDegree = 3,
		bool	theContinuousIfClosed = false )

Creates a constrained approximation solver.

Parameters

[in]	thePoints	array of 3D points to fit (1-based indexing)
[in]	theNbControlPts	desired number of control points for the B-spline
[in]	theDegree	degree of the B-spline (default 3)
[in]	theContinuousIfClosed	if true, enforces C2 continuity for closed curves

Member Function Documentation

Curve()

const occ::handle< Geom_BSplineCurve > & Approx_BSplineApproxInterp::Curve

(

)

const

Returns the resulting B-spline curve.

InterpolatePoint()

void Approx_BSplineApproxInterp::InterpolatePoint	(	int	thePointIndex,
		bool	theWithKink = false )

Marks a point to be exactly interpolated rather than approximated.

Parameters

[in]	thePointIndex	0-based index of the point
[in]	theWithKink	if true, a kink (C0 break) is inserted at this parameter

IsDone()

bool Approx_BSplineApproxInterp::IsDone ( ) const

inline

Returns true if the fit was successfully computed.

MaxError()

double Approx_BSplineApproxInterp::MaxError ( ) const

inline

Returns the maximum approximation error (distance at approximated points).

Perform() [1/2]

void Approx_BSplineApproxInterp::Perform

(

)

Performs the fit using automatically computed parameters. Parameters are computed from input points using current parametrization alpha.

Perform() [2/2]

void Approx_BSplineApproxInterp::Perform

(

const NCollection_Array1< double > &

theParams

)

Performs the fit with given parameters.

Parameters

[in]

theParams

parameter values for each point (size must match point count)

PerformOptimal() [1/2]

void Approx_BSplineApproxInterp::PerformOptimal	(	const NCollection_Array1< double > &	theParams,
		int	theMaxIter )

Performs the fit with iterative parameter optimization. Parameters of approximated points are re-projected onto the curve after each iteration to improve the fit.

Parameters

[in]	theParams	initial parameter values
[in]	theMaxIter	maximum number of optimization iterations

PerformOptimal() [2/2]

void Approx_BSplineApproxInterp::PerformOptimal

(

int

theMaxIter

)

Performs the fit with iterative parameter optimization using automatically computed initial parameters.

Parameters

[in]

theMaxIter

maximum number of optimization iterations

SetClosedTolerance()

void Approx_BSplineApproxInterp::SetClosedTolerance ( double theRelTol )

inline

Sets the relative tolerance for detecting closed curves. Closedness is detected when first/last points are within theRelTol * (bounding box diagonal).

Parameters

[in]

theRelTol

relative tolerance (default 1e-12)

SetConvergenceTolerance()

void Approx_BSplineApproxInterp::SetConvergenceTolerance ( double theTol )

inline

Sets the convergence tolerance for parameter optimization. Optimization stops when relative error reduction falls below this value.

Parameters

[in]

theTol

convergence tolerance (default 1e-3)

SetKnotInsertionTolerance()

void Approx_BSplineApproxInterp::SetKnotInsertionTolerance ( double theTol )

inline

Sets the tolerance for detecting duplicate knot positions during insertion.

Parameters

[in]

theTol

knot matching tolerance (default 1e-4)

SetMinPivot()

void Approx_BSplineApproxInterp::SetMinPivot ( double theMinPivot )

inline

Sets the minimum pivot value for the Gauss solver. Matrices with pivots below this threshold are treated as singular.

Parameters

[in]

theMinPivot

minimum pivot threshold (default 1e-20)

SetParametrizationAlpha()

void Approx_BSplineApproxInterp::SetParametrizationAlpha ( double theAlpha )

inline

Sets the parametrization power for automatic parameter computation. 0.0 = uniform, 0.5 = centripetal (default), 1.0 = chord-length.

Parameters

[in]

theAlpha

parametrization exponent in [0, 1]

SetProjectionTolerance()

void Approx_BSplineApproxInterp::SetProjectionTolerance ( double theTol )

inline

Sets the tolerance for point projection onto curve during optimization.

Parameters

[in]

theTol

projection accuracy (default 1e-6)

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The documentation for this class was generated from the following file:

• Approx_BSplineApproxInterp.hxx