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...

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...

unsigned long 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...

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.