This is an 2.5D approach which first determines the bestfit plane of the point set (P_i = (x,y,z), i=1,...,n) to get a parametrisation of the points afterwards. More...

#include <Approximation.h>

Public Member Functions
float	Fit ()
	Fit a plane into the given points. More...

void	GetCoefficients (double &a, double &b, double &c, double &d, double &e, double &f) const

bool	GetCurvatureInfo (double x, double y, double z, double &rfCurv0, double &rfcurv1)

bool	GetCurvatureInfo (double x, double y, double z, double &rfCurv0, double &rfCurv1, Base::Vector3f &rkDir0, Base::Vector3f &rkDir1, double &dDistance)

	SurfaceFit ()
	Construction. More...

std::vector< Base::Vector3d >	toBezier (double umin=0.0, double umax=1.0, double vmin=0.0, double vmax=1.0) const
	toBezier More...

void	Transform (std::vector< Base::Vector3d > &) const

void	Transform (std::vector< Base::Vector3f > &) const
	Transform Transforms points from the local coordinate system to the world coordinate system. More...

double	Value (double x, double y) const

virtual	~SurfaceFit ()
	Destruction. More...

Public Member Functions inherited from MeshCore::PlaneFit
void	Dimension (float &length, float &width) const
	Get the dimension of the fitted plane. More...

float	Fit ()
	Fit a plane into the given points. More...

Base::Vector3f	GetBase () const

Base::BoundBox3f	GetBoundings () const
	Returns the local bounding box of the transformed points relative to the coordinate system of the plane. More...

Base::Vector3f	GetDirU () const

Base::Vector3f	GetDirV () const

float	GetDistanceToPlane (const Base::Vector3f &rcPoint) const
	Returns the distance from the point rcPoint to the fitted plane. More...

std::vector< Base::Vector3f >	GetLocalPoints () const
	Returns an array of the transformed points relative to the coordinate system of the plane. More...

Base::Vector3f	GetNormal () const
	Returns the normal of the fitted plane. More...

float	GetSignedStdDeviation () const
	Returns the standard deviation from the points to the fitted plane with respect to the orientation of the plane's normal. More...

float	GetStdDeviation () const
	Returns the standard deviation from the points to the fitted plane. More...

	PlaneFit ()
	Construction. More...

void	ProjectToPlane ()
	Projects the points onto the fitted plane. More...

virtual	~PlaneFit ()
	Destruction. More...

Public Member Functions inherited from MeshCore::Approximation
void	AddPoint (const Base::Vector3f &rcVector)
	Add point for the fit algorithm. More...

void	AddPoints (const MeshPointArray &points)
	Add points for the fit algorithm. More...

void	AddPoints (const std::list< Base::Vector3f > &rsPointList)
	Add points for the fit algorithm. More...

void	AddPoints (const std::set< Base::Vector3f > &rsPointSet)
	Add points for the fit algorithm. More...

void	AddPoints (const std::vector< Base::Vector3f > &rvPointVect)
	Add points for the fit algorithm. More...

	Approximation ()
	Construction. More...

void	Clear ()
	Deletes the inserted points and frees any allocated resources. More...

std::size_t	CountPoints () const
	Determines the number of the current added points. More...

bool	Done () const
	Returns true if Fit() has been called for the current set of points, false otherwise. More...

virtual float	Fit ()=0
	Pure virtual function to fit the geometry to the given points. More...

Base::Vector3f	GetGravity () const
	Returns the center of gravity of the current added points. More...

float	GetLastResult () const
	Returns the result of the last fit. More...

const std::list< Base::Vector3f > &	GetPoints () const
	Get all added points. More...

virtual	~Approximation ()
	Destroys the object and frees any allocated resources. More...

Protected Member Functions
double	PolynomFit ()

Protected Member Functions inherited from MeshCore::Approximation
void	GetMgcVectorArray (std::vector< Wm4::Vector3< double > > &rcPts) const
	Creates a vector of Wm4::Vector3 elements. More...

Detailed Description

This is an 2.5D approach which first determines the bestfit plane of the point set (P_i = (x,y,z), i=1,...,n) to get a parametrisation of the points afterwards.

The coordinates of the points with respect to the local coordinate system of the plane are determined and then a quadratic polynomial function of the form: w = f(u,v) = a*u^2 + b*v^2 + c*u*v + d*u + e*v + f is determined. This approach was developed as an alternative for the 3D approach with quadrics because the latter suffers from strange artifacts in planar areas.

Constructor & Destructor Documentation

◆ SurfaceFit()

SurfaceFit::SurfaceFit ( )

Construction.

◆ ~SurfaceFit()

virtual MeshCore::SurfaceFit::~SurfaceFit ( )

virtual

Destruction.

Member Function Documentation

◆ Fit()

float SurfaceFit::Fit ( )

virtual

Fit a plane into the given points.

We must have at least three non-collinear points to succeed. If the fit fails FLOAT_MAX is returned.

Reimplemented from MeshCore::PlaneFit.

References MeshCore::Approximation::CountPoints(), and PolynomFit().

Referenced by MeshCore::FacetCurvature::Compute().

◆ GetCoefficients()

void SurfaceFit::GetCoefficients	(	double &	a,
		double &	b,
		double &	c,
		double &	d,
		double &	e,
		double &	f
	)		const

◆ GetCurvatureInfo() [1/2]

bool SurfaceFit::GetCurvatureInfo	(	double	x,
		double	y,
		double	z,
		double &	rfCurv0,
		double &	rfcurv1
	)

References MeshCore::FunctionContainer::CurvatureInfo().

◆ GetCurvatureInfo() [2/2]

bool SurfaceFit::GetCurvatureInfo	(	double	x,
		double	y,
		double	z,
		double &	rfCurv0,
		double &	rfCurv1,
		Base::Vector3f &	rkDir0,
		Base::Vector3f &	rkDir1,
		double &	dDistance
	)

References MeshCore::FunctionContainer::CurvatureInfo(), MeshCore::FunctionContainer::GetGradient(), and Base::Vector3< _Precision >::Length().

Referenced by MeshCore::FacetCurvature::Compute().

◆ PolynomFit()

double SurfaceFit::PolynomFit ( )

protected

References MeshCore::FunctionContainer::F(), MeshCore::PlaneFit::Fit(), Base::Vector3< _Precision >::TransformToCoordinateSystem(), Base::Vector3< _Precision >::x, Base::Vector3< _Precision >::y, and Base::Vector3< _Precision >::z.

Referenced by Fit().

◆ toBezier()

std::vector< Base::Vector3d > SurfaceFit::toBezier	(	double	umin = `0.0`,
		double	umax = `1.0`,
		double	vmin = `0.0`,
		double	vmax = `1.0`
	)		const

toBezier

SurfaceFit::toBezier This function computes the Bezier representation of the polynomial surface of the form f(x,y) = a*x*x + b*y*y + c*x*y + d*y + e*f + f by getting the 3x3 control points.

Parameters

umin	Parameter range
umax	Parameter range
vmin	Parameter range
vmax	Parameter range

Returns: control points of the Bezier surface

References Value().

◆ Transform() [1/2]

void SurfaceFit::Transform ( std::vector< Base::Vector3d > & pts ) const

References Base::Vector3< _Precision >::x, Base::Vector3< _Precision >::y, and Base::Vector3< _Precision >::z.

◆ Transform() [2/2]

void SurfaceFit::Transform ( std::vector< Base::Vector3f > & pts ) const

Transform Transforms points from the local coordinate system to the world coordinate system.