Ocean::Interpolation Class Reference

This class implements data interpolation functions. More...

#include <Interpolation.h>

Data Structures
class	LinearInterpolation
	This class implements a helper linear interpolation helper class allowing to overload the interpolation function for specific data types. More...

Static Public Member Functions
template<typename T , typename TFactor >
static T	linear (const T &v0, const T &v1, const TFactor &t)
	Performs a linear interpolation between two values.
template<typename T , typename TFactor >
static T	bilinear (const T &v00, const T &v01, const T &v10, const T &v11, const TFactor &tx, const TFactor &ty)
	Performs a bi-linear interpolation between four values within a 2x2 neighborhood.
template<typename T , typename TFactor >
static T	bilinear (const T &v00, const T &v01, const T &v10, const T &v11, const bool valid00, const bool valid01, const bool valid10, const bool valid11, const TFactor &tx, const TFactor &ty)
	Performs a bi-linear interpolation between at most four values within a 2x2 neighborhood.
template<typename T , typename TFactor >
static T	cubic (const T &v0, const T &v1, const T &v2, const T &v3, const TFactor &t)
	Performs a cubic (Catmull-Rom) interpolation between mainly two values while two further supporting points are requested.
template<typename T , typename TFactor >
static VectorT3< T >	spherical (const VectorT3< T > &v0, const VectorT3< T > &v1, const TFactor &t)
	Performs a spherical linear interpolation (SLERP) between two unit vectors.
template<typename T , typename TKey >
static T	lagrange2 (const TKey &x0, const T &y0, const TKey &x1, const T &y1, const TKey &x)
	Performs a Lagrange interpolation for a polynomial with degree 2.
template<typename T , typename TKey >
static T	lagrange3 (const TKey &x0, const T &y0, const TKey &x1, const T &y1, const TKey &x2, const T &y2, const TKey &x)
	Performs a Lagrange interpolation for a polynomial with degree 3.

Detailed Description

This class implements data interpolation functions.

An interpolation value of 0 provides the first value, 1 provides the second value.

Member Function Documentation

bilinear() [1/2]

template<typename T , typename TFactor >

T Ocean::Interpolation::bilinear ( const T &  v00, const T &  v01, const T &  v10, const T &  v11, const bool  valid00, const bool  valid01, const bool  valid10, const bool  valid11, const TFactor &  tx, const TFactor &  ty  )

inlinestatic

Performs a bi-linear interpolation between at most four values within a 2x2 neighborhood.

This function allows the interpolation between a subset of the given four values.
Thus, boolean statements for each individual value define whether the corresponding value is applied for interpolation or not.
If only one value is provided, than the 'interpolation' result is the value itself without investigating the interpolation factors.
The layout of the four values are defined as follows:

v00 v01
v10 v11

Parameters

v00	Top left value
v01	Top right value
v10	Bottom left value
v11	Bottom right value
valid00	True, if the value v00 is valid and has to be applied for interpolation
valid01	True, if the value v01 is valid and has to be applied for interpolation
valid10	True, if the value v10 is valid and has to be applied for interpolation
valid11	True, if the value v11 is valid and has to be applied for interpolation
tx	Horizontal (left - right) interpolation factor, with range [0, 1]
ty	Vertical (top - bottom) interpolation factor, with range [0, 1]

Returns

Resulting interpolation value

Template Parameters

T	Data type of the values to be interpolated
TFactor	Data type of the interpolation value

bilinear() [2/2]

template<typename T , typename TFactor >

T Ocean::Interpolation::bilinear ( const T &  v00, const T &  v01, const T &  v10, const T &  v11, const TFactor &  tx, const TFactor &  ty  )

inlinestatic

Performs a bi-linear interpolation between four values within a 2x2 neighborhood.

The layout of the four values are defined as follows:

v00 v01
v10 v11

Parameters

v00	Top left value
v01	Top right value
v10	Bottom left value
v11	Bottom right value
tx	Horizontal (left - right) interpolation factor, with range [0, 1]
ty	Vertical (top - bottom) interpolation factor, with range [0, 1]

Returns

Resulting interpolation value

Template Parameters

T	Data type of the values to be interpolated
TFactor	Data type of the interpolation value

cubic()

template<typename T , typename TFactor >

T Ocean::Interpolation::cubic ( const T &  v0, const T &  v1, const T &  v2, const T &  v3, const TFactor &  t  )

inlinestatic

Performs a cubic (Catmull-Rom) interpolation between mainly two values while two further supporting points are requested.

Parameters

v0	Supporting value in front of the first value
v1	First value
v2	Second value
v3	Supporting value behind the second value
t	Interpolation factor, with range [0, 1]

Returns

Resulting interpolation value

Template Parameters

T	Data type of the values to be interpolated
TFactor	Data type of the interpolation value

lagrange2()

template<typename T , typename TKey >

T Ocean::Interpolation::lagrange2 ( const TKey &  x0, const T &  y0, const TKey &  x1, const T &  y1, const TKey &  x  )

static

Performs a Lagrange interpolation for a polynomial with degree 2.

Parameters

x0	Position of the first supporting value, must not be identical with x1
y0	First supporting value
x1	Position of the second supporting value, must not be identical with x0
y1	Second supporting value
x	Position for that the interpolation value is requested

Returns

Resulting Lagrange interpolation value

Template Parameters

T	Data type of the supporting values
TKey	Data type of the positions of the supporting values

lagrange3()

template<typename T , typename TKey >

T Ocean::Interpolation::lagrange3 ( const TKey &  x0, const T &  y0, const TKey &  x1, const T &  y1, const TKey &  x2, const T &  y2, const TKey &  x  )

static

Performs a Lagrange interpolation for a polynomial with degree 3.

Parameters

x0	Position of the first supporting value, must not be identical with x1 or x2
y0	First supporting value
x1	Position of the second supporting value, must not be identical with x0 or x2
y1	Second supporting value
x2	Position of the third supporting value, must not be identical with x0 or x1
y2	Third supporting value
x	Position for that the interpolation value is requested

Returns

Resulting Lagrange interpolation value

Template Parameters

T	Data type of the supporting values
TKey	Data type of the positions of the supporting values

linear()

template<typename T , typename TFactor >

T Ocean::Interpolation::linear ( const T &  v0, const T &  v1, const TFactor &  t  )

inlinestatic

Performs a linear interpolation between two values.

Parameters

v0	First value corresponding to the interpolation factor t = 0
v1	Second value corresponding to the interpolation factor t = 1
t	Interpolation factor, with range [0, 1]

Returns

Resulting interpolation value

Template Parameters

T	Data type of the values to be interpolated
TFactor	Data type of the interpolation value

spherical()

template<typename T , typename TFactor >

VectorT3< T > Ocean::Interpolation::spherical ( const VectorT3< T > &  v0, const VectorT3< T > &  v1, const TFactor &  t  )

inlinestatic

Performs a spherical linear interpolation (SLERP) between two unit vectors.

The interpolation follows the great circle path on the unit sphere, maintaining unit length throughout. This is the proper way to interpolate directional vectors (e.g., gravity, normals, orientations).

Parameters

v0	First unit vector corresponding to the interpolation factor t = 0
v1	Second unit vector corresponding to the interpolation factor t = 1
t	Interpolation factor, with range [0, 1]

Returns

Resulting interpolated unit vector

Template Parameters

T	Data type of the vector elements (float or double)
TFactor	Data type of the interpolation value

---

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

• Interpolation.h