javax.media.jai Class Interpolation

```java.lang.Object
|
+--javax.media.jai.Interpolation
```
All Implemented Interfaces:
Serializable
Direct Known Subclasses:
InterpolationBilinear, InterpolationNearest, InterpolationTable

public abstract class Interpolation
extends Object
implements Serializable

An object encapsulating a particular algorithm for image interpolation (resampling). An Interpolation captures the notion of performing sampling on a regular grid of pixels using a local neighborhood. It is intended to be used by operations that resample their sources, including affine mapping and warping.

Resampling is the action of computing a pixel value at a possibly non-integral position of an image. The image defines pixel values at integer lattice points, and it is up to the resampler to produce a reasonable value for positions not falling on the lattice. A number of techniques are used in practice, the most common being nearest-neighbor, which simply takes the value of the closest lattice point; bilinear, which interpolates linearly between the four closest lattice points; and bicubic, which applies a piecewise polynomial function to a 4x4 neighborhood of nearby points. The area over which a resampling function needs to be computed is referred to as its support; thus the standard resampling functions have supports of 1, 4, and 16 pixels respectively. Mathematically, the ideal resampling function for a band-limited image (one containing no energy above a given frequency) is the sinc function, equal to sin(x)/x. This has practical limitations, in particular its infinite support, which lead to the use of the standard approximations described above.

Other interpolation functions may be required to solve problems other than the resampling of band-limited image data. When shrinking an image, it is common to use a function that combines area averaging with resampling in order to remove undesirable high frequencies as part of the interpolation process. Other application areas may use interpolating functions that operate under other assumptions about image data, such as taking the maximum value of a 2x2 neighborhood. The interpolation class provides a framework in which a variety of interpolation schemes may be expressed.

Many interpolations are separable, that is, they may be equivalently rewritten as a horizontal interpolation followed by a vertical one (or vice versa). In practice, some precision may be lost by the rounding and truncation that takes place between the passes. The Interpolation class assumes separability and implements all vertical interpolation methods in terms of corresponding horizontal methods, and defines isSeparable() to return true. A subclass may override these methods to provide distinct implementations of horizontal and vertical interpolation. Some subclasses may implement the two-dimensional interpolation methods directly, yielding more precise results, while others may implement these using a two-pass approach.

A minimal Interpolation subclass must call the Interpolation constructor (super()) and then set at least the following fields.

```   leftPadding
width
height
subsampleBitsH
subsampleBitsV
```

It must also implement at least the following methods.

```   int interpolateH(int[] samples, int xfrac)
float interpolateH(float[] samples, float xfrac)
double interpolateH(double[] samples, float xfrac)
```
All other methods are defined in terms of these methods for ease of implementation of new Interpolation subclasses.

Since interpolation is generally performed for every pixel of a destination image, efficiency is important. In particular, passing source samples by means of arrays is likely to be unacceptably slow. Accordingly, methods are provided for the common cases of 2x1, 1x2, 4x1, 1x4, 2x2, and 4x4 input grids. These methods are defined in the superclass to package their arguments into arrays and forward the call to the array versions, in order to simplify implementation. They should be called only on Interpolation objects with the correct width and height. In other words, an implementor of an Interpolation subclass may implement "interpolateH(int s0, int s1, int xfrac)" assuming that the interpolation width is in fact equal to 2, and does not need to enforce this constraint.

The fractional position of interpolation (xfrac, yfrac) is always between 0.0 and 1.0 (not including 1.0). For integral image data, the fraction is represented as a scaled integer between 0 and 2n - 1, where n is a small integer. The value of n in the horizontal and vertical directions may be obtained by calling getSubsampleBitsH() and getSubsampleBitsV(). In general, code that makes use of an externally-provided Interpolation object must query that object to determine its desired positional precision.

For float and double images, a float between 0.0F and 1.0F (not including 1.0F) is used as a positional specifier in the interest of greater accuracy.

It is important to understand that the subsampleBits precision is used only to indicate the scaling implicit in the fractional locations (xfrac, yfrac) for integral image data types. For example, for subsampleBitsH=8, xfrac must lie between 0 and 255 inclusive. An implementation is not required to actually quantize its interpolation coefficients to match the specified subsampling precision.

The diagrams below illustrate the pixels involved in one-dimensional interpolation. Point s0 is the interpolation kernel key position. xfrac and yfrac, indicated by the dots, represent the point of interpolation between two pixels. This value lies between 0.0 and 1.0 exclusive for floating point and 0 and 2subsampleBits exclusive for integer interpolations.

```
Horizontal              Vertical

s_    s0 .  s1    s2            s_
^
xfrac                   s0
.< yfrac
s1

s2

```

The diagram below illustrates the pixels involved in two-dimensional interpolation. Point s00 is the interpolation kernel key position.

```

s__    s_0    s_1    s_2

s0_    s00    s01    s02

.             < yfrac

s1_    s10    s11    s12

s2_    s20    s21    s22
^
xfrac

```

The subclasses of Interpolation include InterpolationNearest, InterpolationBilinear, InterpolationBicubic, and InterpolationBicubic2 (a variant defined by a different polynomial function). These subclasses are marked 'final,' so users may identify them by name (using 'instanceof') and write specialized code for them. This may also allow inlining to occur on some virtual machines. These classes do provide correct, if less than optimal code for performing their interpolations, so it is possible to use any Interpolation object in a generic manner. The Sun-provided InterpolationBilinear and InterpolationBicubic classes provide a more optimal implementation while using the same semantics.

The InterpolationTable class is a subclass of Interpolation that divides the set of subsample positions into a fixed number of "bins" and stores a kernel for each bin. InterpolationBicubic and InterpolationBicubic2 are implemented in terms of InterpolationTable since a direct implementation is very expensive.

`InterpolationNearest`, `InterpolationBilinear`, `InterpolationBicubic`, `InterpolationBicubic2`, `InterpolationTable`, Serialized Form

 Field Summary `protected  int` `bottomPadding`           The number of pixels lying below the interpolation kernel key position. `protected  int` `height`           The height of the interpolation kernel in pixels. `static int` `INTERP_BICUBIC`           A constant specifying interpolation by the InterpolationBicubic class. `static int` `INTERP_BICUBIC_2`           A constant specifying interpolation by the InterpolationBicubic2 class. `static int` `INTERP_BILINEAR`           A constant specifying interpolation by the InterpolationBilinear class. `static int` `INTERP_NEAREST`           A constant specifying interpolation by the InterpolationNearest class. `protected  int` `leftPadding`           The number of pixels lying to the left of the interpolation kernel key position. `protected  int` `rightPadding`           The number of pixels lying to the right of the interpolation kernel key position. `protected  int` `subsampleBitsH`           The numbers of bits used for the horizontal subsample position. `protected  int` `subsampleBitsV`           The number of bits used for the vertical subsample position. `protected  int` `topPadding`           The number of pixels lying above the interpolation kernel key position. `protected  int` `width`           The width of the interpolation kernel in pixels.

 Constructor Summary `protected ` `Interpolation()`           Constructs an Interpolation object with no fields set. ` ` ```Interpolation(int width, int height, int leftPadding, int rightPadding, int topPadding, int bottomPadding, int subsampleBitsH, int subsampleBitsV)```           Construct interpolation object with all parameters set.

 Method Summary ` int` `getBottomPadding()`           Returns the number of samples required below the key element. ` int` `getHeight()`           Returns the number of samples required for vertical resampling. `static Interpolation` `getInstance(int type)`           Creates an interpolation of one of the standard types. ` int` `getLeftPadding()`           Returns the number of samples required to the left of the key element. ` int` `getRightPadding()`           Returns the number of samples required to the right of the key element. ` int` `getSubsampleBitsH()`           Returns the number of bits used to index subsample positions in the horizontal direction. ` int` `getSubsampleBitsV()`           Returns the number of bits used to index subsample positions in the vertical direction. ` int` `getTopPadding()`           Returns the number of samples required above the key element. ` int` `getWidth()`           Returns the number of samples required for horizontal resampling. ` double` ```interpolate(double[][] samples, float xfrac, float yfrac)```           Performs interpolation on a 2-dimensional array of double samples. ` double` ```interpolate(double s__, double s_0, double s_1, double s_2, double s0_, double s00, double s01, double s02, double s1_, double s10, double s11, double s12, double s2_, double s20, double s21, double s22, float xfrac, float yfrac)```           Performs interpolation on a 4x4 grid of double samples. ` double` ```interpolate(double s00, double s01, double s10, double s11, float xfrac, float yfrac)```           Performs interpolation on a 2x2 grid of double samples. ` float` ```interpolate(float[][] samples, float xfrac, float yfrac)```           Performs interpolation on a 2-dimensional array of floating-point samples. ` float` ```interpolate(float s00, float s01, float s10, float s11, float xfrac, float yfrac)```           Performs interpolation on a 2x2 grid of floating-point samples. ` float` ```interpolate(float s__, float s_0, float s_1, float s_2, float s0_, float s00, float s01, float s02, float s1_, float s10, float s11, float s12, float s2_, float s20, float s21, float s22, float xfrac, float yfrac)```           Performs interpolation on a 4x4 grid of floating-point samples. ` int` ```interpolate(int[][] samples, int xfrac, int yfrac)```           Performs interpolation on a 2-dimensional array of integral samples. ` int` ```interpolate(int s00, int s01, int s10, int s11, int xfrac, int yfrac)```           Performs interpolation on a 2x2 grid of integral samples. ` int` ```interpolate(int s__, int s_0, int s_1, int s_2, int s0_, int s00, int s01, int s02, int s1_, int s10, int s11, int s12, int s2_, int s20, int s21, int s22, int xfrac, int yfrac)```           Performs interpolation on a 4x4 grid of integral samples. `abstract  double` ```interpolateH(double[] samples, float xfrac)```           Performs horizontal interpolation on a 1-dimensional array of double samples representing a row of samples. ` double` ```interpolateH(double s_, double s0, double s1, double s2, float xfrac)```           Performs horizontal interpolation on a quadruple of double samples. ` double` ```interpolateH(double s0, double s1, float xfrac)```           Performs horizontal interpolation on a pair of double samples. `abstract  float` ```interpolateH(float[] samples, float xfrac)```           Performs horizontal interpolation on a 1-dimensional array of floating-point samples representing a row of samples. ` float` ```interpolateH(float s0, float s1, float xfrac)```           Performs horizontal interpolation on a pair of floating-point samples. ` float` ```interpolateH(float s_, float s0, float s1, float s2, float xfrac)```           Performs horizontal interpolation on a quadruple of floating-point samples. `abstract  int` ```interpolateH(int[] samples, int xfrac)```           Performs horizontal interpolation on a 1-dimensional array of integral samples. ` int` ```interpolateH(int s0, int s1, int xfrac)```           Performs horizontal interpolation on a pair of integral samples. ` int` ```interpolateH(int s_, int s0, int s1, int s2, int xfrac)```           Performs horizontal interpolation on a quadruple of integral samples. ` double` ```interpolateV(double[] samples, float yfrac)```           Performs vertical interpolation on a 1-dimensional array of double samples representing a column of samples. ` double` ```interpolateV(double s_, double s0, double s1, double s2, float yfrac)```           Performs vertical interpolation on a quadruple of double samples. ` double` ```interpolateV(double s0, double s1, float yfrac)```           Performs vertical interpolation on a pair of double samples. ` float` ```interpolateV(float[] samples, float yfrac)```           Performs vertical interpolation on a 1-dimensional array of floating-point samples representing a column of samples. ` float` ```interpolateV(float s0, float s1, float yfrac)```           Performs vertical interpolation on a pair of floating-point samples. ` float` ```interpolateV(float s_, float s0, float s1, float s2, float yfrac)```           Performs vertical interpolation on a quadruple of floating-point samples. ` int` ```interpolateV(int[] samples, int yfrac)```           Performs vertical interpolation on a 1-dimensional array of integral samples. ` int` ```interpolateV(int s0, int s1, int yfrac)```           Performs vertical interpolation on a pair of integral samples. ` int` ```interpolateV(int s_, int s0, int s1, int s2, int yfrac)```           Performs vertical interpolation on a quadruple of integral samples. ` boolean` `isSeparable()`           Returns true if the interpolation can be performed in a separable manner, that is, by performing a separate pass in each dimension.

 Methods inherited from class java.lang.Object `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

 Field Detail

INTERP_NEAREST

`public static final int INTERP_NEAREST`
A constant specifying interpolation by the InterpolationNearest class.

INTERP_BILINEAR

`public static final int INTERP_BILINEAR`
A constant specifying interpolation by the InterpolationBilinear class.

INTERP_BICUBIC

`public static final int INTERP_BICUBIC`
A constant specifying interpolation by the InterpolationBicubic class.

INTERP_BICUBIC_2

`public static final int INTERP_BICUBIC_2`
A constant specifying interpolation by the InterpolationBicubic2 class.

`protected int leftPadding`
The number of pixels lying to the left of the interpolation kernel key position.

`protected int rightPadding`
The number of pixels lying to the right of the interpolation kernel key position.

`protected int topPadding`
The number of pixels lying above the interpolation kernel key position.

`protected int bottomPadding`
The number of pixels lying below the interpolation kernel key position.

subsampleBitsH

`protected int subsampleBitsH`
The numbers of bits used for the horizontal subsample position. This value determines how integer fractional positons are to be interpreted.

subsampleBitsV

`protected int subsampleBitsV`
The number of bits used for the vertical subsample position. This value determines how integer fractional positons are to be interpreted.

width

`protected int width`
The width of the interpolation kernel in pixels.

height

`protected int height`
The height of the interpolation kernel in pixels.
 Constructor Detail

Interpolation

`protected Interpolation()`
Constructs an Interpolation object with no fields set. This constructor is only invoked by subclasses which will subsequently set all fields themselves.

Interpolation

```public Interpolation(int width,
int height,
int subsampleBitsH,
int subsampleBitsV)```
Construct interpolation object with all parameters set. Subclasses must supply all parameters.
 Method Detail

getInstance

`public static Interpolation getInstance(int type)`
Creates an interpolation of one of the standard types. This is intended strictly as a convenience method. The resulting static object is cached for later reuse.
Parameters:
`type` - one of: INTERP_NEAREST, INTERP_BILINEAR, INTERP_BICUBIC, or INTERP_BICUBIC_2
Returns:
an appropriate Interpolation object.
Throws:
`IllegalArgumentException` - if an unrecognized type is supplied.

`public int getLeftPadding()`
Returns the number of samples required to the left of the key element.

`public int getRightPadding()`
Returns the number of samples required to the right of the key element.

`public int getTopPadding()`
Returns the number of samples required above the key element.

`public int getBottomPadding()`
Returns the number of samples required below the key element.

getWidth

`public int getWidth()`
Returns the number of samples required for horizontal resampling.

getHeight

`public int getHeight()`
Returns the number of samples required for vertical resampling.

isSeparable

`public boolean isSeparable()`
Returns true if the interpolation can be performed in a separable manner, that is, by performing a separate pass in each dimension. It is the caller's responsibility to deal with issues of precision. By default, true is returned.

getSubsampleBitsH

`public int getSubsampleBitsH()`
Returns the number of bits used to index subsample positions in the horizontal direction. All integral 'xfrac' parameters should range between 0 and 2(getSubsampleBitsH()) - 1.

In general, the caller is responsible for determining the number of subsample bits of any Interpolation object it receives and setting up its position variables accordingly. Some Interpolation objects allow the number of bits to be set at construction time.

getSubsampleBitsV

`public int getSubsampleBitsV()`
Returns the number of bits used to index subsample positions in the vertical direction. All integral 'yfrac' parameters should range between 0 and 2(getSubsampleBitsV()) - 1.

interpolateH

```public abstract int interpolateH(int[] samples,
int xfrac)```
Performs horizontal interpolation on a 1-dimensional array of integral samples.

An implementation is not required to actually quantize its interpolation coefficients to match the specified subsampling precision. However, the supplied value of xfrac (or yfrac) must match the precision of its corresponding subsampleBits. For example, with a subsampleBitsH value of 8, xfrac must lie between 0 and 255.

Parameters:
`samples` - an array of ints.
`xfrac` - the subsample position, multiplied by 2(subsampleBitsH).
Returns:
the interpolated value as an int.

interpolateV

```public int interpolateV(int[] samples,
int yfrac)```
Performs vertical interpolation on a 1-dimensional array of integral samples.

By default, vertical interpolation is defined to be the same as horizontal interpolation. Subclasses may choose to implement them differently.

Parameters:
`samples` - an array of ints.
`yfrac` - the Y subsample position, multiplied by 2(subsampleBitsV).
Returns:
the interpolated value as an int.
`interpolateH(int[], int)`

interpolate

```public int interpolate(int[][] samples,
int xfrac,
int yfrac)```
Performs interpolation on a 2-dimensional array of integral samples. By default, this is implemented using a two-pass approach.
Parameters:
`samples` - a two-dimensional array of ints.
`xfrac` - the X subsample position, multiplied by 2(subsampleBitsH).
`yfrac` - the Y subsample position, multiplied by 2(subsampleBitsV).
Returns:
the interpolated value as an int.
`interpolateH(int[], int)`

interpolateH

```public int interpolateH(int s0,
int s1,
int xfrac)```
Performs horizontal interpolation on a pair of integral samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == 2 and leftPadding == 0.
Parameters:
`s0` - the central sample.
`s1` - the sample to the right of the central sample.
`xfrac` - the subsample position, ranging from zero to 2(subsampleBitsH) - 1.
Returns:
the interpolated value as an int.
`interpolateH(int[], int)`

interpolateH

```public int interpolateH(int s_,
int s0,
int s1,
int s2,
int xfrac)```
Performs horizontal interpolation on a quadruple of integral samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == 4 and leftPadding == 1.
Parameters:
`s_` - the sample to the left of the central sample.
`s0` - the central sample.
`s1` - the sample to the right of the central sample.
`s2` - the sample to the right of s1.
`xfrac` - the subsample position, multiplied by 2(subsampleBitsH).
Returns:
the interpolated value as an int.
`interpolateH(int[], int)`

interpolateV

```public int interpolateV(int s0,
int s1,
int yfrac)```
Performs vertical interpolation on a pair of integral samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if height == 2 and topPadding == 0.

By default, vertical interpolation is identical to horizontal interpolation. Subclasses may choose to implement them differently.

Parameters:
`s0` - the central sample.
`s1` - the sample below the central sample.
`yfrac` - the Y subsample position, multiplied by 2(subsampleBitsV).
Returns:
the interpolated value as an int.
`interpolateH(int[], int)`

interpolateV

```public int interpolateV(int s_,
int s0,
int s1,
int s2,
int yfrac)```
Performs vertical interpolation on a quadruple of integral samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if height == 4 and topPadding == 1.

By default, vertical interpolation is identical to horizontal interpolation. Subclasses may choose to implement them differently.

Parameters:
`s_` - the sample above the central sample.
`s0` - the central sample.
`s1` - the sample below the central sample.
`s2` - the sample below s1.
`yfrac` - the Y subsample position, multiplied by 2(subsampleBitsV).
Returns:
the interpolated value as an int.
`interpolateH(int[], int)`

interpolate

```public int interpolate(int s00,
int s01,
int s10,
int s11,
int xfrac,
int yfrac)```
Performs interpolation on a 2x2 grid of integral samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == height == 2 and leftPadding == topPadding == 0.
Parameters:
`s00` - the central sample.
`s01` - the sample to the right of the central sample.
`s10` - the sample below the central sample.
`s11` - the sample below and to the right of the central sample.
`xfrac` - the X subsample position, multiplied by 2(subsampleBitsH).
`yfrac` - the Y subsample position, multiplied by 2(subsampleBitsV).
Returns:
the interpolated value as an int.
`interpolateH(int[], int)`

interpolate

```public int interpolate(int s__,
int s_0,
int s_1,
int s_2,
int s0_,
int s00,
int s01,
int s02,
int s1_,
int s10,
int s11,
int s12,
int s2_,
int s20,
int s21,
int s22,
int xfrac,
int yfrac)```
Performs interpolation on a 4x4 grid of integral samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == height == 4 and leftPadding == topPadding == 1.
Parameters:
`s__` - the sample above and to the left of the central sample.
`s_0` - the sample above the central sample.
`s_1` - the sample above and one to the right of the central sample.
`s_2` - the sample above and two to the right of the central sample.
`s0_` - the sample to the left of the central sample.
`s00` - the central sample.
`s01` - the sample to the right of the central sample.
`s02` - the sample two to the right of the central sample.
`s1_` - the sample below and one to the left of the central sample.
`s10` - the sample below the central sample.
`s11` - the sample below and one to the right of the central sample.
`s12` - the sample below and two to the right of the central sample.
`s2_` - the sample two below and one to the left of the central sample.
`s20` - the sample two below the central sample.
`s21` - the sample two below and one to the right of the central sample.
`s22` - the sample two below and two to the right of the central sample.
`xfrac` - the X subsample position, multiplied by 2(subsampleBitsH).
`yfrac` - the Y subsample position, multiplied by 2(subsampleBitsV).
Returns:
the interpolated value as an int.
`interpolateH(int[], int)`

interpolateH

```public abstract float interpolateH(float[] samples,
float xfrac)```
Performs horizontal interpolation on a 1-dimensional array of floating-point samples representing a row of samples. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`samples` - an array of floats.
`xfrac` - the X subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a float.

interpolateV

```public float interpolateV(float[] samples,
float yfrac)```
Performs vertical interpolation on a 1-dimensional array of floating-point samples representing a column of samples. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.

By default, vertical interpolation is identical to horizontal interpolation. Subclasses may choose to implement them differently.

Parameters:
`samples` - an array of floats.
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a float.

interpolate

```public float interpolate(float[][] samples,
float xfrac,
float yfrac)```
Performs interpolation on a 2-dimensional array of floating-point samples. By default, this is implemented using a two-pass approach. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`samples` - an array of floats.
`xfrac` - the X subsample position, in the range [0.0F, 1.0F).
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a float.

interpolateH

```public float interpolateH(float s0,
float s1,
float xfrac)```
Performs horizontal interpolation on a pair of floating-point samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == 2 and leftPadding == 0. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`s0` - the central sample.
`s1` - the sample to the right of the central sample.
`xfrac` - the subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a float.

interpolateH

```public float interpolateH(float s_,
float s0,
float s1,
float s2,
float xfrac)```
Performs horizontal interpolation on a quadruple of floating-point samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == 4 and leftPadding == 1. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`s_` - the sample to the left of the central sample.
`s0` - the central sample.
`s1` - the sample to the right of the central sample.
`s2` - the sample to the right of s1.
`xfrac` - the subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a float.

interpolateV

```public float interpolateV(float s0,
float s1,
float yfrac)```
Performs vertical interpolation on a pair of floating-point samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if height == 2 and topPadding == 0. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.

By default, vertical interpolation is identical to horizontal interpolation. Subclasses may choose to implement them differently.

Parameters:
`s0` - the central sample.
`s1` - the sample below the central sample.
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a float.

interpolateV

```public float interpolateV(float s_,
float s0,
float s1,
float s2,
float yfrac)```
Performs vertical interpolation on a quadruple of floating-point samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if height == 4 and topPadding == 1. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.

By default, vertical interpolation is identical to horizontal interpolation. Subclasses may choose to implement them differently.

Parameters:
`s_` - the sample above the central sample.
`s0` - the central sample.
`s1` - the sample below the central sample.
`s2` - the sample below s1.
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a float.

interpolate

```public float interpolate(float s00,
float s01,
float s10,
float s11,
float xfrac,
float yfrac)```
Performs interpolation on a 2x2 grid of floating-point samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == height == 2 and leftPadding == topPadding == 0. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`s00` - the central sample.
`s01` - the sample to the right of the central sample.
`s10` - the sample below the central sample.
`s11` - the sample below and to the right of the central sample.
`xfrac` - the X subsample position, in the range [0.0F, 1.0F).
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a float.

interpolate

```public float interpolate(float s__,
float s_0,
float s_1,
float s_2,
float s0_,
float s00,
float s01,
float s02,
float s1_,
float s10,
float s11,
float s12,
float s2_,
float s20,
float s21,
float s22,
float xfrac,
float yfrac)```
Performs interpolation on a 4x4 grid of floating-point samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == height == 4 and leftPadding == topPadding == 1. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`s__` - the sample above and to the left of the central sample.
`s_0` - the sample above the central sample.
`s_1` - the sample above and one to the right of the central sample.
`s_2` - the sample above and two to the right of the central sample.
`s0_` - the sample to the left of the central sample.
`s00` - the central sample.
`s01` - the sample to the right of the central sample.
`s02` - the sample two to the right of the central sample.
`s1_` - the sample below and one to the left of the central sample.
`s10` - the sample below the central sample.
`s11` - the sample below and one to the right of the central sample.
`s12` - the sample below and two to the right of the central sample.
`s2_` - the sample two below and one to the left of the central sample.
`s20` - the sample two below the central sample.
`s21` - the sample two below and one to the right of the central sample.
`s22` - the sample two below and two to the right of the central sample.
`xfrac` - the X subsample position, in the range [0.0F, 1.0F).
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a float.

interpolateH

```public abstract double interpolateH(double[] samples,
float xfrac)```
Performs horizontal interpolation on a 1-dimensional array of double samples representing a row of samples. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`samples` - an array of doubles.
`xfrac` - the X subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a double.

interpolateV

```public double interpolateV(double[] samples,
float yfrac)```
Performs vertical interpolation on a 1-dimensional array of double samples representing a column of samples. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.

By default, vertical interpolation is identical to horizontal interpolation. Subclasses may choose to implement them differently.

Parameters:
`samples` - an array of doubles.
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a double.

interpolate

```public double interpolate(double[][] samples,
float xfrac,
float yfrac)```
Performs interpolation on a 2-dimensional array of double samples. By default, this is implemented using a two-pass approach. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`samples` - an array of doubles.
`xfrac` - the X subsample position, in the range [0.0F, 1.0F).
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a double.

interpolateH

```public double interpolateH(double s0,
double s1,
float xfrac)```
Performs horizontal interpolation on a pair of double samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == 2 and leftPadding == 0. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`s0` - the central sample.
`s1` - the sample to the right of the central sample.
`xfrac` - the subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a double.

interpolateH

```public double interpolateH(double s_,
double s0,
double s1,
double s2,
float xfrac)```
Performs horizontal interpolation on a quadruple of double samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == 4 and leftPadding == 1. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`s_` - the sample to the left of the central sample.
`s0` - the central sample.
`s1` - the sample to the right of the central sample.
`s2` - the sample to the right of s1.
`xfrac` - the subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a double.

interpolateV

```public double interpolateV(double s0,
double s1,
float yfrac)```
Performs vertical interpolation on a pair of double samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if height == 2 and topPadding == 0. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.

By default, vertical interpolation is identical to horizontal interpolation. Subclasses may choose to implement them differently.

Parameters:
`s0` - the central sample.
`s1` - the sample below the central sample.
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a double.

interpolateV

```public double interpolateV(double s_,
double s0,
double s1,
double s2,
float yfrac)```
Performs vertical interpolation on a quadruple of double samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if height == 4 and topPadding == 1. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.

By default, vertical interpolation is identical to horizontal interpolation. Subclasses may choose to implement them differently.

Parameters:
`s_` - the sample above the central sample.
`s0` - the central sample.
`s1` - the sample below the central sample.
`s2` - the sample below s1.
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a double.

interpolate

```public double interpolate(double s00,
double s01,
double s10,
double s11,
float xfrac,
float yfrac)```
Performs interpolation on a 2x2 grid of double samples. Subclasses may implement this method to provide a speed improvement over the array method. This base class method merely calls the array method. It should only be called if width == height == 2 and leftPadding == topPadding == 0. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`s00` - the central sample.
`s01` - the sample to the right of the central sample.
`s10` - the sample below the central sample.
`s11` - the sample below and to the right of the central sample.
`xfrac` - the X subsample position, in the range [0.0F, 1.0F).
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a double.

interpolate

```public double interpolate(double s__,
double s_0,
double s_1,
double s_2,
double s0_,
double s00,
double s01,
double s02,
double s1_,
double s10,
double s11,
double s12,
double s2_,
double s20,
double s21,
double s22,
float xfrac,
float yfrac)```
Performs interpolation on a 4x4 grid of double samples. It should only be called if width == height == 4 and leftPadding == topPadding == 1. The setting of subsampleBits need not have any effect on the interpolation accuracy of an implementation of this method.
Parameters:
`s__` - the sample above and to the left of the central sample.
`s_0` - the sample above the central sample.
`s_1` - the sample above and one to the right of the central sample.
`s_2` - the sample above and two to the right of the central sample.
`s0_` - the sample to the left of the central sample.
`s00` - the central sample.
`s01` - the sample to the right of the central sample.
`s02` - the sample two to the right of the central sample.
`s1_` - the sample below and one to the left of the central sample.
`s10` - the sample below the central sample.
`s11` - the sample below and one to the right of the central sample.
`s12` - the sample below and two to the right of the central sample.
`s2_` - the sample two below and one to the left of the central sample.
`s20` - the sample two below the central sample.
`s21` - the sample two below and one to the right of the central sample.
`s22` - the sample two below and two to the right of the central sample.
`xfrac` - the X subsample position, in the range [0.0F, 1.0F).
`yfrac` - the Y subsample position, in the range [0.0F, 1.0F).
Returns:
the interpolated value as a double.