Vector surface spline interpolation/approximation in two dimensions. More...

#include <SurfaceSpline.h>

Public Types
using	rbf_type = spline::rbf_type

using	spline = SurfaceSpline< double >

Public Member Functions
	PointSurfaceSpline ()=default

template<class point_list1 , class point_list2 , class weight_vector = FVector>
	PointSurfaceSpline (const point_list1 &P1, const point_list2 &P2, float smoothness=0, int order=2, const weight_vector &W=weight_vector(), rbf_type rbf=RadialBasisFunction::Default, double eps=0, bool polynomial=true)

	PointSurfaceSpline (const PointSurfaceSpline &)=default

	PointSurfaceSpline (const spline &Sx, const spline &Sy)

	PointSurfaceSpline (PointSurfaceSpline &&)=default

void	Clear ()

void	DisableIncrementalFunction (bool disable=true)

void	DisableSimplifiers (bool disable=true)

void	EnableIncrementalFunction (bool enable=true)

void	EnableSimplifiers (bool enable=true)

double	ErrorX () const

double	ErrorY () const

template<class PV >
Array< DPoint >	Evaluate (const PV &P) const

template<class V >
Array< DPoint >	Evaluate (const V &X, const V &Y) const

template<typename T >
void	Evaluate (T ZX, T ZY, const T X, const T Y, size_type n) const

bool	HasFastVectorEvaluation () const

bool	IncrementalFunctionEnabled () const

template<class point_list1 , class point_list2 , class weight_vector = FVector>
void	Initialize (const point_list1 &P1, const point_list2 &P2, float smoothness=0, const weight_vector &W=weight_vector(), int order=2, rbf_type rbf=RadialBasisFunction::Default, double eps=0, bool polynomial=true)

void	Initialize (const spline &Sx, const spline &Sy)

bool	IsValid () const

const Matrix &	LinearFunction () const

int	MaxSplinePoints () const

template<typename T >
DPoint	operator() (const GenericPoint< T > &p) const

DPoint	operator() (double x, double y) const

PointSurfaceSpline &	operator= (const PointSurfaceSpline &other)=default

PointSurfaceSpline &	operator= (PointSurfaceSpline &&)=default

void	SetLinearFunction (const Matrix &H)

void	SetMaxSplinePoints (int n)

void	SetSimplifierRejectFraction (float rejectFraction)

float	SimplifierRejectFraction () const

bool	SimplifiersEnabled () const

const spline &	SplineX () const

const spline &	SplineY () const

bool	Truncated () const

bool	TruncatedX () const

bool	TruncatedY () const

Detailed Description

The template parameter P represents an interpolation point in two dimensions. The type P must implement P::x and P::y data members accessible from the current PointSurfaceSpline template specialization. These members must provide the values of the horizontal and vertical coordinates, respectively, of an interpolation point. In addition, the scalar types of the P::x and P::y point members must support conversion to double semantics.

See also: SurfaceSpline, RecursivePointSurfaceSpline

Definition at line 1232 of file SurfaceSpline.h.

Member Typedef Documentation

◆ rbf_type

using pcl::PointSurfaceSpline::rbf_type = spline::rbf_type

Represents a radial basis function (RBF) supported by this point surface spline implementation.

Definition at line 1245 of file SurfaceSpline.h.

◆ spline

using pcl::PointSurfaceSpline::spline = SurfaceSpline<double>

Represents a coordinate interpolating/approximating surface spline.

Definition at line 1239 of file SurfaceSpline.h.

Constructor & Destructor Documentation

◆ PointSurfaceSpline() [1/5]

pcl::PointSurfaceSpline::PointSurfaceSpline ( )

default

Default constructor. Yields an empty instance that cannot be used without initialization.

◆ PointSurfaceSpline() [2/5]

pcl::PointSurfaceSpline::PointSurfaceSpline ( const PointSurfaceSpline & )

default

Copy constructor.

◆ PointSurfaceSpline() [3/5]

pcl::PointSurfaceSpline::PointSurfaceSpline ( PointSurfaceSpline && )

default

Move constructor.

◆ PointSurfaceSpline() [4/5]

template<class point_list1 , class point_list2 , class weight_vector = FVector>

pcl::PointSurfaceSpline::PointSurfaceSpline	(	const point_list1 &	P1,
		const point_list2 &	P2,
		float	smoothness = `0`,
		int	order = `2`,
		const weight_vector &	W = `weight_vector()`,
		rbf_type	rbf = `RadialBasisFunction::Default`,
		double	eps = `0`,
		bool	polynomial = `true`
	)

inline

Constructs a PointSurfaceSpline object initialized for the specified input data and interpolation parameters.

See the corresponding Initialize() member function for a detailed description of parameters.

Definition at line 1271 of file SurfaceSpline.h.

◆ PointSurfaceSpline() [5/5]

pcl::PointSurfaceSpline::PointSurfaceSpline	(	const spline &	Sx,
		const spline &	Sy
	)

inline

Constructs a PointSurfaceSpline object initialized with prescribed surface splines.

See the corresponding Initialize() member function for a more detailed description of parameters and their required conditions.

Definition at line 1288 of file SurfaceSpline.h.

Member Function Documentation

◆ Clear()

void pcl::PointSurfaceSpline::Clear ( )

inline

Deallocates internal structures, yielding an empty spline that cannot be used before a new call to Initialize().

Definition at line 1568 of file SurfaceSpline.h.

◆ DisableIncrementalFunction()

void pcl::PointSurfaceSpline::DisableIncrementalFunction ( bool disable = true )

inline

Disables the use of incremental functions for this point surface spline.

See also: IncrementalFunctionEnabled(), DisableIncrementalFunction()

Definition at line 1788 of file SurfaceSpline.h.

◆ DisableSimplifiers()

void pcl::PointSurfaceSpline::DisableSimplifiers ( bool disable = true )

inline

Disables the use of shape-preserving surface simplifiers to automatically reduce the complexity of 2-D surface splines. See the SurfaceSimplifier class for detailed information.

See also: SimplifiersEnabled(), EnableSimplifiers()

Definition at line 1656 of file SurfaceSpline.h.

◆ EnableIncrementalFunction()

void pcl::PointSurfaceSpline::EnableIncrementalFunction ( bool enable = true )

inline

Enables the use of incremental functions for this point surface spline.

See also: IncrementalFunctionEnabled(), DisableIncrementalFunction()

Definition at line 1778 of file SurfaceSpline.h.

◆ EnableSimplifiers()

void pcl::PointSurfaceSpline::EnableSimplifiers ( bool enable = true )

inline

Enables the use of shape-preserving surface simplifiers to automatically reduce the complexity of 2-D surface splines. See the SurfaceSimplifier class for detailed information.

See also: SimplifiersEnabled(), DisableSimplifiers()

Definition at line 1644 of file SurfaceSpline.h.

◆ ErrorX()

double pcl::PointSurfaceSpline::ErrorX ( ) const

inline

Returns the simplification tolerance achieved on the X axis after spline initialization with automatic surface simplification enabled.

Definition at line 1687 of file SurfaceSpline.h.

◆ ErrorY()

double pcl::PointSurfaceSpline::ErrorY ( ) const

inline

Returns the simplification tolerance achieved on the Y axis after spline initialization with automatic surface simplification enabled.

Definition at line 1696 of file SurfaceSpline.h.

◆ Evaluate() [1/3]

template<class PV >

Array<DPoint> pcl::PointSurfaceSpline::Evaluate ( const PV & P ) const

inline

Evaluates the surface spline for a list P of points in 2-D space, and returns the corresponding function values as an array of points in 64-bit floating point format.

The type PV must be a PCL array or vector of point structures, where each P[i] is expected to have public x and y members of numeric scalar type.

See Evaluate( T*, T*, const T*, const T*, int ) const for more information.

Definition at line 1884 of file SurfaceSpline.h.

◆ Evaluate() [2/3]

template<class V >

Array<DPoint> pcl::PointSurfaceSpline::Evaluate	(	const V &	X,
		const V &	Y
	)		const

inline

Evaluates the point surface spline for a set of points in 2-D space specified as the X and Y lists of n coordinates, and returns the corresponding function values as an array of points in 64-bit floating point format.

The type V must be a PCL array or vector with numeric scalar components.

See Evaluate( T*, T*, const T*, const T*, int ) const for more information.

Definition at line 1856 of file SurfaceSpline.h.

◆ Evaluate() [3/3]

template<typename T >

void pcl::PointSurfaceSpline::Evaluate	(	T *	ZX,
		T *	ZY,
		const T *	X,
		const T *	Y,
		size_type	n
	)		const

inline

Evaluates the point surface spline for a set of points in 2-D space specified as the X and Y contiguous sequences of n coordinates, and stores the corresponding function values in the specified ZX and ZY arrays.

For core DDM-RBF interpolation/approximation, this is a support function for fast multithreaded evaluation of the point surface spline at large-scale sets of interpolation points. For PCL RBF implementations this function can be convenient, but it does not provide any significant performance improvement.

Note: This function provides compatibility with the PointGridInterpolation class.

Definition at line 1830 of file SurfaceSpline.h.

◆ HasFastVectorEvaluation()

bool pcl::PointSurfaceSpline::HasFastVectorEvaluation ( ) const

inline

Returns true iff this object can be evaluated for vectors of points in 2-D space efficiently by calling the Evaluate() member functions. In current PCL versions, this member function only returns true for RBF interpolation/approximation algorithms with core implementations.

Note: This function provides compatibility with the PointGridInterpolation class.

Definition at line 1906 of file SurfaceSpline.h.

◆ IncrementalFunctionEnabled()

bool pcl::PointSurfaceSpline::IncrementalFunctionEnabled ( ) const

inline

Returns true iff the use of incremental functions is currently enabled for this point surface spline.

When the incremental function is enabled, surface splines compute the differences with respect to a fixed linear transformation function, which should be specified calling SetLinearFunction(). Incremental surface splines can yield more accurate representations of relatively complex two-dimensional functions when a linear transformation can work as a fixed reference to absorb the largest variations.

See also: EnableIncrementalFunction(), DisableIncrementalFunction()

Definition at line 1768 of file SurfaceSpline.h.

◆ Initialize() [1/2]

template<class point_list1 , class point_list2 , class weight_vector = FVector>

void pcl::PointSurfaceSpline::Initialize	(	const point_list1 &	P1,
		const point_list2 &	P2,
		float	smoothness = `0`,
		const weight_vector &	W = `weight_vector()`,
		int	order = `2`,
		rbf_type	rbf = `RadialBasisFunction::Default`,
		double	eps = `0`,
		bool	polynomial = `true`
	)

inline

Initializes this PointSurfaceSpline object for the specified input data and interpolation parameters.

Parameters

P1	A sequence of distinct interpolation node points.
P2	A sequence of interpolation values. For each point in P1, the coordinates of its counterpart point in P2 will be used as the interpolation node values in the X and Y directions.
smoothness	Smoothing factor. Must be ≥ 0. The default value is zero, that is, interpolating surface splines are generated by default.
W	Reference to a vector of positive node weights > 0, when the smoothing factor is > 0. This parameter is ignored for interpolating splines (that is, when smoothness = 0) and when surface simplification is enabled (see below). When relevant, this argument must be a reference to a vector or array of `float` values.
order	Derivative order of continuity. Must be ≥ 2. The default value is 2. This parameter is only taken into account when the rbf parameter is RadialBasisFunction::VariableOrder.
rbf	The type of radial basis function (RBF) used for surface spline generation. The default is RadialBasisFunction::ThinPlateSpline in the current implementation.
eps	The shape parameter used for decreasing radial basis functions. Increasing RBFs, such as thin plate splines and variable order functions, are parameter-free and hence ignore this parameter.
polynomial	If true, surface spline generation will include a first order polynomial part for stabilization. If false, only radial basis functions will be used without a polynomial component.

For smoothness <= 0, an interpolating spline will be generated: all node values will be reproduced exactly at their respective coordinates. In this case the W parameter will be ignored. The W vector will also be ignored when automatic surface simplification is enabled (see EnableSimplifiers()).

For smoothness > 0 without automatic simplification, a smoothing (or approximating) spline will be generated: increasing smoothness values will generate splines closer to the reference plane of the input node set. If nonempty, the specified vector W of node weights will be used to assign a different interpolation strength to each interpolation node. In this case the vector W must have at least the same length as the shortest of the P1 and P2 vectors, and must contain values greater than zero. A node weight larger than one will reduce the smoothness of the interpolating surface at the corresponding node coordinates, or in other words, it will give more prominence to the corresponding data point. A node weight of one will apply the specified smoothness at its node position. Contrarily, a node weight smaller than one will increase the interpolation smoothness locally.

When the variable order RBF is specified, the surface spline will be continuously differentiable up to the specified order. If this order is too high, an ill-conditioned linear system may result, especially for large data sets. The recommended values are 2, 3, 4 or 5, but order 2 is usually the most useful and safest option for most applications. Derivative orders greater than 5 may lead to numerically unstable interpolation devices, which should always be used with care. For the rest of RBFs the order parameter is ignored and second order functions are always used.

Note: The smoothness and W parameters are only used for the thin plate spline and variable order spline radial basis functions. For other RBFs only interpolation surface splines can be generated with this implementation, and hence these parameters are always ignored.

Definition at line 1381 of file SurfaceSpline.h.

◆ Initialize() [2/2]

void pcl::PointSurfaceSpline::Initialize	(	const spline &	Sx,
		const spline &	Sy
	)

inline

Initializes this PointSurfaceSpline object with prescribed surface splines.

Parameters

Sx	2-D surface spline for interpolation of function values in the X direction.
Sy	2-D surface spline for interpolation of function values in the Y direction.

Both surface splines must be valid. If one or both splines are invalid, calling this member function is equivalent to Clear().

After calling this member function successfuly, this object will store deep copies of the specified surface spline instances.

Definition at line 1552 of file SurfaceSpline.h.

◆ IsValid()

bool pcl::PointSurfaceSpline::IsValid ( ) const

inline

Returns true iff this is a valid, initialized object ready for interpolation.

Definition at line 1580 of file SurfaceSpline.h.

◆ LinearFunction()

const Matrix& pcl::PointSurfaceSpline::LinearFunction ( ) const

inline

Returns the 3x3 matrix of the projective transformation used as the reference function for an incremental surface spline. See the Homography class for detailed information on linear transformations.

See also: SetLinearFunction(), IncrementalFunctionEnabled()

Definition at line 1738 of file SurfaceSpline.h.

◆ MaxSplinePoints()

int pcl::PointSurfaceSpline::MaxSplinePoints ( ) const

inline

Returns the maximum number of interpolation points allowed for this point surface spline.

Definition at line 1607 of file SurfaceSpline.h.

◆ operator()() [1/2]

template<typename T >

DPoint pcl::PointSurfaceSpline::operator() ( const GenericPoint< T > & p ) const

inline

Returns an interpolated point at the given p.x and p.y coordinates.

Definition at line 1809 of file SurfaceSpline.h.

References pcl::GenericPoint< T >::x, and pcl::GenericPoint< T >::y.

◆ operator()() [2/2]

DPoint pcl::PointSurfaceSpline::operator()	(	double	x,
		double	y
	)		const

inline

Returns an interpolated point at the specified coordinates.

Definition at line 1796 of file SurfaceSpline.h.

◆ operator=() [1/2]

PointSurfaceSpline& pcl::PointSurfaceSpline::operator= ( const PointSurfaceSpline & other )

default

Copy assignment operator. Returns a reference to this object.

◆ operator=() [2/2]

PointSurfaceSpline& pcl::PointSurfaceSpline::operator= ( PointSurfaceSpline && )

default

Move assignment operator. Returns a reference to this object.

◆ SetLinearFunction()

void pcl::PointSurfaceSpline::SetLinearFunction ( const Matrix & H )

inline

Sets the 3x3 matrix of the projective transformation used as the reference function for an incremental surface spline. See the Homography class for detailed information on linear transformations.

See also: LinearFunction(), IncrementalFunctionEnabled()

Definition at line 1750 of file SurfaceSpline.h.

◆ SetMaxSplinePoints()

void pcl::PointSurfaceSpline::SetMaxSplinePoints ( int n )

inline

Sets the maximum number of interpolation points allowed for this point surface spline.

The default maximum number of interpolation points allowed for point surface splines is 2100 in current PCL versions. Take into account that surface spline generation has O(n^3) time complexity.

Definition at line 1620 of file SurfaceSpline.h.

References pcl::Max().

◆ SetSimplifierRejectFraction()

void pcl::PointSurfaceSpline::SetSimplifierRejectFraction ( float rejectFraction )

inline

Sets the fraction of outlier points rejected by surface simplifiers.

See SurfaceSimplifier::SetRejectFraction() for a detailed description of the role of this parameter.

Definition at line 1677 of file SurfaceSpline.h.

References pcl::Range().

◆ SimplifierRejectFraction()

float pcl::PointSurfaceSpline::SimplifierRejectFraction ( ) const

inline

Returns the fraction of outlier points rejected by surface simplifiers.

See SetSimplifierRejectFraction() for more information on this parameter.

Definition at line 1666 of file SurfaceSpline.h.

◆ SimplifiersEnabled()

bool pcl::PointSurfaceSpline::SimplifiersEnabled ( ) const

inline

Returns true iff automatic surface simplification is enabled for this point surface spline.

See also: EnableSimplifiers(),

Definition at line 1632 of file SurfaceSpline.h.

◆ SplineX()

const spline& pcl::PointSurfaceSpline::SplineX ( ) const

inline

Returns a reference to the internal surface spline object used for interpolation in the X plane direction.

Definition at line 1589 of file SurfaceSpline.h.

◆ SplineY()

const spline& pcl::PointSurfaceSpline::SplineY ( ) const

inline

Returns a reference to the internal surface spline object used for interpolation in the Y plane direction.

Definition at line 1598 of file SurfaceSpline.h.

◆ Truncated()

bool pcl::PointSurfaceSpline::Truncated ( ) const

inline

Returns true iff the set of interpolation nodes was truncated during automatic simplification, either on the X axis, on the Y axis, or both. This should never happen under normal working conditions.

Definition at line 1726 of file SurfaceSpline.h.

◆ TruncatedX()

bool pcl::PointSurfaceSpline::TruncatedX ( ) const

inline

Returns true iff the set of interpolation nodes on the X axis was truncated during automatic simplification. This should never happen under normal working conditions.

Definition at line 1706 of file SurfaceSpline.h.

◆ TruncatedY()

bool pcl::PointSurfaceSpline::TruncatedY ( ) const

inline

Returns true iff the set of interpolation nodes on the Y axis was truncated during automatic simplification. This should never happen under normal working conditions.

Definition at line 1716 of file SurfaceSpline.h.

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

SurfaceSpline.h

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ rbf_type

◆ spline

Constructor & Destructor Documentation

◆ PointSurfaceSpline() [1/5]

◆ PointSurfaceSpline() [2/5]

◆ PointSurfaceSpline() [3/5]

◆ PointSurfaceSpline() [4/5]

◆ PointSurfaceSpline() [5/5]

Member Function Documentation

◆ Clear()

◆ DisableIncrementalFunction()

◆ DisableSimplifiers()

◆ EnableIncrementalFunction()

◆ EnableSimplifiers()

◆ ErrorX()

◆ ErrorY()

◆ Evaluate() [1/3]

◆ Evaluate() [2/3]

◆ Evaluate() [3/3]

◆ HasFastVectorEvaluation()

◆ IncrementalFunctionEnabled()

◆ Initialize() [1/2]

◆ Initialize() [2/2]

◆ IsValid()

◆ LinearFunction()

◆ MaxSplinePoints()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ SetLinearFunction()

◆ SetMaxSplinePoints()

◆ SetSimplifierRejectFraction()

◆ SimplifierRejectFraction()

◆ SimplifiersEnabled()

◆ SplineX()

◆ SplineY()

◆ Truncated()

◆ TruncatedX()

◆ TruncatedY()