PPSolveFactory solves the system of linear equations to interpolate from a grid of points using higher order polynomials, creating a PolynomialPatch object. The order of the polynomial is user-defined. More...

#include <PPSolveFactory.h>

Collaboration diagram for interpolation::PPSolveFactory:

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Public Member Functions
	PPSolveFactory (Mesh *points, std::vector< std::vector< double > > values, int polyPatchOrder, int smoothingOrder)

	~PPSolveFactory ()

PolynomialPatch *	solve ()

Static Public Member Functions
static std::vector < std::vector< int > >	getNearbyPointsSquares (int pointDim, int polyOrderLower, int polyOrderUpper)

Private Member Functions
void	getPoints ()

void	getValues (Mesh::Iterator it)

void	getDerivPoints ()

void	getDerivs (Mesh::Iterator it)

std::vector< double >	outOfBoundsPosition (Mesh::Iterator outOfBoundsIt)

PolynomialCoefficient	getDeltaIterator (Mesh::Iterator it1, Mesh::Iterator it2, int valueIndex)

Static Private Member Functions
static void	nearbyPointsRecursive (std::vector< int > check, size_t checkIndex, size_t polyPower, std::vector< std::vector< int > > &nearbyPoints)

Private Attributes
int	polyPatchOrder_m

int	smoothingOrder_m

int	polyDim_m

int	valueDim_m

Mesh *	polyMesh_m

Mesh *	points_m

std::vector< std::vector < double > >	values_m

std::vector < SquarePolynomialVector * >	polynomials_m

std::vector< std::vector < double > >	thisPoints_m

std::vector< std::vector < double > >	thisValues_m

std::vector< std::vector < double > >	derivPoints_m

std::vector< std::vector < double > >	derivValues_m

std::vector< std::vector< int > >	derivOrigins_m

std::vector< std::vector< int > >	derivIndices_m

std::vector< MVector< double > >	derivPolyVec_m

std::vector< int >	derivIndexByPower_m

std::vector< std::vector < std::vector< int > > >	edgePoints_m

std::vector< std::vector< int > >	smoothingPoints_m

Detailed Description

PPSolveFactory solves the system of linear equations to interpolate from a grid of points using higher order polynomials, creating a PolynomialPatch object. The order of the polynomial is user-defined.

The PPSolveFactory can be used to match nearby points for smoothing or for straight fitting.

PPSolveFactory generates polynomials on a grid that is at the centre point of each of the mesh squares; PPSolveFactory picks nearby points in a square around the PPSolveFactory, picked by getNearbyPointsSquares. Two sets of points are chosen; the nearest points are used for fitting; smoothing is performed by choosing the points on the edge of the grid, and smoothing to derivatives on these points.

Because we work in a square grid, we have matching polynomials and derivatives; so e.g. 2D points are (0, 0), (1, 0), (0, 1), (1, 1) so corresponding polynomial coefficients that we solve for are x^0 y^0, x^1 y^0, x^0 y^1, x^1 y^1; note that hence we define "first order" to be all terms with no single x/y vector power > 1; i.e. "first order" in x OR first order in y, etc. We allow products so long as the maximum power in any one dimension <= 1

The PPSolveFactory sits on top of SolveFactory; PPSolveFactory has the job of picking values and derivatives for fitting, SolveFactory then does the actual solve for each individual polynomial.

Definition at line 65 of file PPSolveFactory.h.

Constructor & Destructor Documentation

interpolation::PPSolveFactory::PPSolveFactory	(	Mesh *	points,
		std::vector< std::vector< double > >	values,
		int	polyPatchOrder,
		int	smoothingOrder
	)

Constructor

Parameters

points	Set of points on which values are stored. Must be a rectangular grid. PPSolveFactory takes ownership of points (will delete on exit). The solve will return a wrong answer if the grid does not have regular spacing.
values	Set of values to which we fit. Must be one value per mesh point and each value must have the same size.
polyPatchOrder	The order of the fitted part of the polynomial.
smoothingOrder	The total order of the fitted and the smoothed part of the polynomial. Smoothing order should always be >= polyPatchOrder. So for example if polyPatchOrder is 2 and smoothing order is 2, we get a 2nd order function with no derivative matching. If polyPatchOrder is 2 and smoothing order is 3, we get a 3rd order function with derivative matching in first order at two mesh points from the centre.

Definition at line 63 of file PPSolveFactory.cpp.

References interpolation::Mesh::dual(), edgePoints_m, interpolation::Mesh::end(), getNearbyPointsSquares(), interpolation::Mesh::getPositionDimension(), polyDim_m, polyMesh_m, polyPatchOrder_m, smoothingPoints_m, and interpolation::Mesh::Iterator::toInteger().

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interpolation::PPSolveFactory::~PPSolveFactory ( )

inline

Destructor deletes points_

Definition at line 91 of file PPSolveFactory.h.

Member Function Documentation

PolynomialCoefficient interpolation::PPSolveFactory::getDeltaIterator	(	Mesh::Iterator	it1,
		Mesh::Iterator	it2,
		int	valueIndex
	)

private

void interpolation::PPSolveFactory::getDerivPoints ( )

private

Definition at line 185 of file PPSolveFactory.cpp.

References derivIndexByPower_m, derivIndices_m, derivOrigins_m, derivPoints_m, derivPolyVec_m, edgePoints_m, interpolation::Mesh::getPositionDimension(), interpolation::SquarePolynomialVector::IndexByPower(), interpolation::SquarePolynomialVector::NumberOfPolynomialCoefficients(), points_m, polyPatchOrder_m, pow(), smoothingOrder_m, and smoothingPoints_m.

Referenced by solve().

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void interpolation::PPSolveFactory::getDerivs ( Mesh::Iterator it )

private

Definition at line 258 of file PPSolveFactory.cpp.

References derivOrigins_m, derivPoints_m, derivPolyVec_m, derivValues_m, interpolation::Mesh::end(), interpolation::Mesh::Iterator::getMesh(), interpolation::Mesh::Iterator::getPosition(), interpolation::Mesh::Iterator::getState(), polyDim_m, polynomials_m, polyPatchOrder_m, smoothingOrder_m, and interpolation::Mesh::Iterator::toInteger().

Referenced by solve().

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std::vector< std::vector< int > > interpolation::PPSolveFactory::getNearbyPointsSquares	(	int	pointDim,
		int	polyOrderLower,
		int	polyOrderUpper
	)

static

Get nearby points in a square pattern

Get nearby points at least poly_order_lower distance away and less than poly_order_upper distance away; e.g. getNearbyPointsSquares(2, 4, 6) will get nearby points on a 2D grid at least 4 grid points and at most 6 grid points, like:

x x x o o x ... x x x o o x x x x o o x o o o o o x o o o o o x x x x x x x ...

Definition at line 347 of file PPSolveFactory.cpp.

References nearbyPointsRecursive().

Referenced by getPoints(), getValues(), PPSolveFactory(), and interpolation::SolveFactory::SolveFactory().

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void interpolation::PPSolveFactory::getPoints ( )

private

Definition at line 141 of file PPSolveFactory.cpp.

References getNearbyPointsSquares(), interpolation::Mesh::getPositionDimension(), points_m, polyPatchOrder_m, and thisPoints_m.

Referenced by solve().

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void interpolation::PPSolveFactory::getValues ( Mesh::Iterator it )

private

Definition at line 156 of file PPSolveFactory.cpp.

References interpolation::Mesh::end(), getNearbyPointsSquares(), interpolation::Mesh::Iterator::getState(), points_m, polyPatchOrder_m, thisValues_m, interpolation::Mesh::Iterator::toInteger(), and values_m.

Referenced by solve().

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void interpolation::PPSolveFactory::nearbyPointsRecursive	(	std::vector< int >	check,
		size_t	checkIndex,
		size_t	polyPower,
		std::vector< std::vector< int > > &	nearbyPoints
	)