Three-dimensional interpolation for irregularly-spaced data. More...

#include <Interpolation3D.hpp>

Public Types
enum	InterpolationMethod { INVERSE_DISTANCE_WEIGHTING, INVERSE_DISTANCE_WEIGHTING_KNN, NEAREST_NEIGHBOR }
typedef ValueType	value_type
typedef PointType	point_type
typedef DataType	data_type
typedef PointType	Point
	Alias for point_type.
Public Member Functions
	Interpolation3D (const DataType &default_value=DataType(), InterpolationMethod interpolation_method=INVERSE_DISTANCE_WEIGHTING_KNN)
	Constructs an instance of Interpolation3D.
	Interpolation3D (const std::vector< Point > &data_points, const std::vector< DataType > &data, const DataType &default_value=DataType(), InterpolationMethod interpolation_method=INVERSE_DISTANCE_WEIGHTING_KNN)
	Constructs an instance of Interpolation3D.
	~Interpolation3D ()
	Destructs the instance of Interpolation3D.
DataType	operator() (const Point &point) const
	Returns an interpolated value at the given position.
DataType	operator() (ValueType x, ValueType y, ValueType z) const
	Returns an interpolated value at the given position.
DataType	getData (const Point &point) const
	Returns an interpolated value at the given position.
DataType	getData (ValueType x, ValueType y, ValueType z) const
	Returns an interpolated value at the given position.
void	setData (const std::vector< Point > &data_points, const std::vector< DataType > &data)
	Sets the interpolation data.
void	setExponent (ValueType value=2.0)
	Sets the exponent for the inverse distance weighting.
void	setInterpolationMethod (InterpolationMethod interpolation_method)
	Sets the interpolation method.
void	setNumberOfNearestNeighbors (unsigned number=10)
	Sets the maximum number of nearest neighbors to take into account during computations.
void	setRadius (ValueType radius)
	Sets the radius for the nearest neighbor search.
Protected Member Functions
DataType	getDataInverseDistanceWeighting (ValueType x, ValueType y, ValueType z) const
	Performs an Inverse Distance Weighting.
DataType	getDataInverseDistanceWeightingKNN (ValueType x, ValueType y, ValueType z) const
	Performs an Inverse Distance Weighting.
DataType	getDataNearestNeighbor (ValueType x, ValueType y, ValueType z) const
	Performs a Nearest Neighbor Search.
Protected Attributes
DataType(Interpolation3D::*	interpolation_function )(ValueType, ValueType, ValueType) const
ValueType	exponent
ValueType	radius
unsigned	max_number_of_nearest_neighbors
flann::Index< flann::L2 < ValueType > > *	tree
const DataType	data_type_default_value
std::vector< DataType >	data
flann::Matrix< ValueType >	data_points
flann::Matrix< ValueType >	query_point
flann::Matrix< ValueType >	distances
flann::Matrix< int >	indices

Detailed Description

template<class ValueType = double, class PointType = Coordinate<double>, class DataType = Coordinate<double>>
class TRTK::Interpolation3D< ValueType, PointType, DataType >

Three-dimensional interpolation for irregularly-spaced data.

Template Parameters:

ValueType	Must be a floating point type.
PointType	Must provide `operator`[] for element access.
DataType	Type of the data associated with each point (e.g. intensity, RGB-value, etc.). `DataType` must support `operator+=` as well as the multiplication with a scalar of type `ValueType`.

This class provides a three-dimensional interpolation for irregularly-spaced data. The data types can be arbitrary and must be specified as templates parameters.

The following interpolation methods are available:

Inverse Distance Weighting: see getDataInverseDistanceWeighting() for more details.
Inverse Distance Weighting KNN: see getDataInverseDistanceWeightingKNN() for more details.
Nearest Neighbor: see getDataNearestNeighbor() for more details.

Here is an example of how to use the class:

 #include <iostream>
 #include <TRTK/Interpolation3D.hpp>

 using namespace TRTK;

 int main()
 {
     try
     {
         // Setup data.

         typedef Interpolation3D<double, Coordinate<double>, double> Interpolation3D;
         typedef Interpolation3D::Point Point;

         std::vector<Point> data_points;
         std::vector<Interpolation3D::data_type> data;

         data_points.push_back(Point(1 ,1, 2));
         data.push_back(1);

         data_points.push_back(Point(2, -1, 1));
         data.push_back(2);

         data_points.push_back(Point(0, 0, 0));
         data.push_back(3);

         data_points.push_back(Point(1, 0, -1));
         data.push_back(4);

         data_points.push_back(Point(-1, 1, 3));
         data.push_back(5);

         // Setup interpolation class.

         Interpolation3D interpolation(data_points, data, 0);

         interpolation.setInterpolationMethod(Interpolation3D::INVERSE_DISTANCE_WEIGHTING);
         interpolation.setNumberOfNearestNeighbors(10);
         interpolation.setRadius(10);

         // Get interpolated values.

         std::cout << interpolation(1.2, 1.0, 2.0) << std::endl;
     }
     catch (std::exception & error)
     {
         std::cout << error.what() << std::endl;
         return -1;
     }

     return 0;
 }

Output:

 1.00032

To process higher-dimensional data, you might want to use the Coordinate class...:

 // Setup data.

 typedef Interpolation3D<double> Interpolation3D;
 typedef Interpolation3D::Point Point;

 std::vector<Point> data_points;
 std::vector<Interpolation3D::data_type> data;

 data_points.push_back(Point(0, 0, 0));
 data.push_back(Point(100, 100, 0));

 data_points.push_back(Point(1 ,1, 1));
 data.push_back(Point(255, 255, 255));

 data_points.push_back(Point(2, -1, 3));
 data.push_back(Point(0, 0, 0));

 // Setup interpolation class.

 Interpolation3D interpolation(data_points, data, Point(0, 0, 0));

 // Get interpolated values.

 std::cout << interpolation(1.2, 0.1, 2) << std::endl;

Output:

 (173.451, 173.451, 165.952)

... or a self-defined class as below:

 #include <iostream>

 #include <TRTK/Interpolation3D.hpp>


 using namespace TRTK;


 class RGB
 {
 public:
     RGB(unsigned short red = 0, unsigned short green = 0, unsigned short blue = 0)
     {
         data[0] = red;
         data[1] = green;
         data[2] = blue;
     }

     RGB & operator+=(const RGB & other)
     {
         this->data[0] += other.data[0];
         this->data[1] += other.data[1];
         this->data[2] += other.data[2];

         return *this;
     }

     unsigned short operator[](size_t n) const
     {
         return data[n];
     };

 protected:
     unsigned short data[3];
 };


 RGB operator*(const RGB & rgb, float factor)
 {
     return RGB(rgb[0] * factor, rgb[1] * factor, rgb[2] * factor);
 }


 int main()
 {
     try
     {
         // Setup data.

         typedef Interpolation3D<double, Coordinate<double>, RGB> Interpolation3D;
         typedef Interpolation3D::Point Point;

         std::vector<Point> data_points;
         std::vector<Interpolation3D::data_type> data;

         data_points.push_back(Point(0, 0, 0));
         data.push_back(RGB(100, 100, 0));

         data_points.push_back(Point(1 ,1, 1));
         data.push_back(RGB(255, 255, 255));

         data_points.push_back(Point(2, -1, 3));
         data.push_back(RGB(0, 0, 0));

         // Setup interpolation class.

         Interpolation3D interpolation(data_points, data);

         interpolation.setInterpolationMethod(Interpolation3D::INVERSE_DISTANCE_WEIGHTING);
         interpolation.setRadius(10);

         // Get interpolated values.

         RGB value = interpolation(1.2, 0.1, 2);

         std::cout << "("  << value[0]
                   << ", " << value[1]
                   << ", " << value[2]
                   << ")"  << std::endl;
     }
     catch (std::exception & error)
     {
         std::cout << error.what() << std::endl;
         return -1;
     }

     return 0;
 }

Output:

 (171, 171, 164)

Author:: Christoph Haenisch

Version:: 0.1.2

Date:: last changed on 2013-08-20

Definition at line 285 of file Interpolation3D.hpp.

Member Enumeration Documentation

template<class ValueType = double, class PointType = Coordinate<double>, class DataType = Coordinate<double>>

enum TRTK::Interpolation3D::InterpolationMethod

Enumerator:

INVERSE_DISTANCE_WEIGHTING	Interpolation using Shepard's method. Only the k first nearest neighbors are taken into account. Searched is within a circle whose radius can be specified with `setRadius`.
INVERSE_DISTANCE_WEIGHTING_KNN	Interpolation using Shepard's method. Only the k first nearest neighbors are taken into account.
NEAREST_NEIGHBOR	Yields the datum of the nearest neighbor.

Definition at line 295 of file Interpolation3D.hpp.

Constructor & Destructor Documentation

template<class ValueType , class PointType , class DataType >

TRTK::Interpolation3D< ValueType, PointType, DataType >::Interpolation3D	(	const DataType &	default_value = `DataType()`,
		InterpolationMethod	interpolation_method = `INVERSE_DISTANCE_WEIGHTING_KNN`
	)

Constructs an instance of Interpolation3D.

Parameters:

[in]	default_value	Default value for DataType (e.g. null vector).
[in]	interpolation_method	Interpolation method to be used.

Definition at line 362 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

TRTK::Interpolation3D< ValueType, PointType, DataType >::Interpolation3D	(	const std::vector< Point > &	data_points,
		const std::vector< DataType > &	data,
		const DataType &	default_value = `DataType()`,
		InterpolationMethod	interpolation_method = `INVERSE_DISTANCE_WEIGHTING_KNN`
	)

Constructs an instance of Interpolation3D.

Parameters:

[in]	data_points	Positions (in 3D) of the below data.
[in]	data	Data associated with the above positions (e.g. RGB-values).
[in]	default_value	Default value for DataType (e.g. null vector).
[in]	interpolation_method	Interpolation method to be used.

Definition at line 384 of file Interpolation3D.hpp.

Member Function Documentation

template<class ValueType , class PointType , class DataType >

DataType TRTK::Interpolation3D< ValueType, PointType, DataType >::getData ( const Point & point ) const [inline]

Returns an interpolated value at the given position.

Note:: Depending on the currently set interpolation method, an exception might be thrown.

Definition at line 448 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

DataType TRTK::Interpolation3D< ValueType, PointType, DataType >::getData	(	ValueType	x,
		ValueType	y,
		ValueType	z
	)		const `[inline]`

Returns an interpolated value at the given position.

Note:: Depending on the currently set interpolation method, an exception might be thrown.

Definition at line 461 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

DataType TRTK::Interpolation3D< ValueType, PointType, DataType >::getDataInverseDistanceWeighting	(	ValueType	x,
		ValueType	y,
		ValueType	z
	)		const `[protected]`

Performs an Inverse Distance Weighting.

Parameters:

[in]	x	x position
[in]	y	y position
[in]	z	z position

An interpolated value \( data' \) at postion \( (x, y, z) \) is computed from its surrounding neighborhood \( \mathcal{N} \) by

\[ data' = \left( \sum_{i \in \mathcal{N}} {|d_i|}^{-p} \right)^{-1} \sum_{i \in \mathcal{N}} {|d_i|}^{-p} data_i \]

where \( d_i \) is the distance between the given point \( (x, y, z) \) and the location of the i-th data point. The Neighborhood is a circle whose radius can be specified by setRadius(). At most max_number_of_nearest_neighbors are used to compute the interpolant, which can be set by setNumberOfNearestNeighbors(). The exponent \( p \) can be set by setExponent().

Exceptions:

std::range_error	is thrown, if no data is given.
std::runtime_error	is thrown, if the search radius is too small and no nearest neighbor are found.

See also:: InterpolationMethod

Definition at line 492 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

DataType TRTK::Interpolation3D< ValueType, PointType, DataType >::getDataInverseDistanceWeightingKNN	(	ValueType	x,
		ValueType	y,
		ValueType	z
	)		const `[protected]`

Performs an Inverse Distance Weighting.

Parameters:

[in]	x	x position
[in]	y	y position
[in]	z	z position

An interpolated value \( data' \) at postion \( (x, y, z) \) is computed from its surrounding neighborhood \( \mathcal{N} \) by

\[ data' = \left( \sum_{i \in \mathcal{N}} {|d_i|}^{-p} \right)^{-1} \sum_{i \in \mathcal{N}} {|d_i|}^{-p} data_i \]

where \( d_i \) is the distance between the given point \( (x, y, z) \) and the location of the i-th data point. At most max_number_of_nearest_neighbors are used to compute the interpolant, which can be set by setNumberOfNearestNeighbors(). The exponent \( p \) can be set by setExponent().

Exceptions:

std::range_error is thrown, if no data is given.

See also:: InterpolationMethod

Definition at line 563 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

DataType TRTK::Interpolation3D< ValueType, PointType, DataType >::getDataNearestNeighbor	(	ValueType	x,
		ValueType	y,
		ValueType	z
	)		const `[protected]`

Performs a Nearest Neighbor Search.

Parameters:

[in]	x	x position
[in]	y	y position
[in]	z	z position

Returns:: The datum of the nearest neighbor is returned.

Exceptions:

std::range_error is thrown, if no data is given.

See also:: InterpolationMethod

Definition at line 620 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

DataType TRTK::Interpolation3D< ValueType, PointType, DataType >::operator()	(	ValueType	x,
		ValueType	y,
		ValueType	z
	)		const `[inline]`

Returns an interpolated value at the given position.

Note:: Depending on the currently set interpolation method, an exception might be thrown.

Definition at line 435 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

DataType TRTK::Interpolation3D< ValueType, PointType, DataType >::operator() ( const Point & point ) const [inline]

Returns an interpolated value at the given position.

Note:: Depending on the currently set interpolation method, an exception might be thrown.

Definition at line 422 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

void TRTK::Interpolation3D< ValueType, PointType, DataType >::setData	(	const std::vector< Point > &	data_points,
		const std::vector< DataType > &	data
	)

Sets the interpolation data.

Parameters:

[in]	data_points	Positions (in 3D) of the below data.
[in]	data	Data associated with the above positions (e.g. RGB-values).

The data may be irregularly spaced.

Exceptions:

std::logic_error	is thrown, if `data_points` and `data` do not have the same size.
std::runtime_error	is thrown, if the input data is emtpy.

Definition at line 649 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

void TRTK::Interpolation3D< ValueType, PointType, DataType >::setExponent ( ValueType value = 2.0 )

Sets the exponent for the inverse distance weighting.

Parameters:

[in] value Exponent.

See Detailed Description for more details.

Definition at line 695 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

void TRTK::Interpolation3D< ValueType, PointType, DataType >::setInterpolationMethod ( InterpolationMethod interpolation_method )

Sets the interpolation method.

Parameters:

[in] interpolation_method Interpolation method.

Exceptions:

std::logic_error is thrown, if interpolation_method is unknown.

See also:: InterpolationMethod

Definition at line 711 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

void TRTK::Interpolation3D< ValueType, PointType, DataType >::setNumberOfNearestNeighbors ( unsigned number = 10 )

Sets the maximum number of nearest neighbors to take into account during computations.

Parameters:

[in] number Must be greater than zero.

Exceptions:

std::logic_error is thrown, if number is equal to zero.

See also:: getDataInverseDistanceWeighting(), getDataInverseDistanceWeightingKNN(), getDataNearestNeighbor()

Definition at line 752 of file Interpolation3D.hpp.

template<class ValueType , class PointType , class DataType >

void TRTK::Interpolation3D< ValueType, PointType, DataType >::setRadius ( ValueType radius )

Sets the radius for the nearest neighbor search.

Parameters:

[in] radius Must be greater than zero.

Exceptions:

std::logic_error is thrown, if radius is less than or equal to zero.

See also:: getDataInverseDistanceWeighting(), getDataInverseDistanceWeightingKNN()

Definition at line 781 of file Interpolation3D.hpp.

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

D:/Programmierung/C/TRTK/include/TRTK/Interpolation3D.hpp

TRTK::Interpolation3D< ValueType, PointType, DataType > Class Template Reference

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<class ValueType = double, class PointType = Coordinate<double>, class DataType = Coordinate<double>> class TRTK::Interpolation3D< ValueType, PointType, DataType >

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<class ValueType = double, class PointType = Coordinate<double>, class DataType = Coordinate<double>>
class TRTK::Interpolation3D< ValueType, PointType, DataType >