Package icyllis.arc3d.core

Class ColorSpace.Rgb

java.lang.Object
icyllis.arc3d.core.ColorSpace
icyllis.arc3d.core.ColorSpace.Rgb
Enclosing class:
ColorSpace
public static class ColorSpace.Rgb extends ColorSpace

An RGB color space is an additive color space using the RGB color model (a color is therefore represented by a tuple of 3 numbers).

A specific RGB color space is defined by the following properties:

  • Three chromaticities of the red, green and blue primaries, which define the gamut of the color space.
  • A white point chromaticity that defines the stimulus to which color space values are normalized (also just called "white").
  • An opto-electronic transfer function, also called opto-electronic conversion function or often, and approximately, gamma function.
  • An electro-optical transfer function, also called electo-optical conversion function or often, and approximately, gamma function.
  • A range of valid RGB values (most commonly \([0..1]\)).

The most commonly used RGB color space is sRGB.

Primaries and white point chromaticities

In this implementation, the chromaticity of the primaries and the white point of an RGB color space is defined in the CIE xyY color space. This color space separates the chromaticity of a color, the x and y components, and its luminance, the Y component. Since the primaries and the white point have full brightness, the Y component is assumed to be 1 and only the x and y components are needed to encode them.

For convenience, this implementation also allows to define the primaries and white point in the CIE XYZ space. The tristimulus XYZ values are internally converted to xyY.

sRGB primaries and white point

Transfer functions

A transfer function is a color component conversion function, defined as a single variable, monotonic mathematical function. It is applied to each individual component of a color. They are used to perform the mapping between linear tristimulus values and non-linear electronic signal value.

The opto-electronic transfer function (OETF or OECF) encodes tristimulus values in a scene to a non-linear electronic signal value. An OETF is often expressed as a power function with an exponent between 0.38 and 0.55 (the reciprocal of 1.8 to 2.6).

The electro-optical transfer function (EOTF or EOCF) decodes a non-linear electronic signal value to a tristimulus value at the display. An EOTF is often expressed as a power function with an exponent between 1.8 and 2.6.

Transfer functions are used as a compression scheme. For instance, linear sRGB values would normally require 11 to 12 bits of precision to store all values that can be perceived by the human eye. When encoding sRGB values using the appropriate OETF (see sRGB for an exact mathematical description of that OETF), the values can be compressed to only 8 bits precision.

When manipulating RGB values, particularly sRGB values, it is safe to assume that these values have been encoded with the appropriate OETF (unless noted otherwise). Encoded values are often said to be in "gamma space". They are therefore defined in a non-linear space. This in turns means that any linear operation applied to these values is going to yield mathematically incorrect results (any linear interpolation such as gradient generation for instance, most image processing functions such as blurs, etc.).

To properly process encoded RGB values you must first apply the EOTF to decode the value into linear space. After processing, the RGB value must be encoded back to non-linear ("gamma") space. Here is a formal description of the process, where \(f\) is the processing function to apply:

$$RGB_{out} = OETF(f(EOTF(RGB_{in})))$$

If the transfer functions of the color space can be expressed as an ICC parametric curve as defined in ICC.1:2004-10, the numeric parameters can be retrieved by calling getTransferParameters(). This can be useful to match color spaces for instance.

Some RGB color spaces, such as ColorSpace.Named.ACES and scRGB, are said to be linear because their transfer functions are the identity function: \(f(x) = x\). If the source and/or destination are known to be linear, it is not necessary to invoke the transfer functions.

Range

Most RGB color spaces allow RGB values in the range \([0..1]\). There are however a few RGB color spaces that allow much larger ranges. For instance, scRGB is used to manipulate the range \([-0.5..7.5]\) while ACES can be used throughout the range \([-65504, 65504]\).

Extended sRGB and its large range

Converting between RGB color spaces

Conversion between two color spaces is achieved by using an intermediate color space called the profile connection space (PCS). The PCS used by this implementation is CIE XYZ. The conversion operation is defined as such:

$$RGB_{out} = OETF(T_{dst}^{-1} \cdot T_{src} \cdot EOTF(RGB_{in}))$$

Where \(T_{src}\) is the RGB to XYZ transform of the source color space and \(T_{dst}^{-1}\) the XYZ to RGB transform of the destination color space.

Many RGB color spaces commonly used with electronic devices use the standard illuminant D65. Care must be take however when converting between two RGB color spaces if their white points do not match. This can be achieved by either calling ColorSpace.adapt(ColorSpace, float[]) to adapt one or both color spaces to a single common white point. This can be achieved automatically by calling ColorSpace.connect(ColorSpace, ColorSpace), which also handles non-RGB color spaces.

To learn more about the white point adaptation process, refer to the documentation of ColorSpace.Adaptation.

  • Constructor Details

    • Rgb

      public Rgb(@Nonnull @Size(min=1L) String name, @Nonnull @Size(9L) float[] toXYZ, @Nonnull DoubleUnaryOperator oetf, @Nonnull DoubleUnaryOperator eotf)

      Creates a new RGB color space using a 3x3 column-major transform matrix. The transform matrix must convert from the RGB space to the profile connection space CIE XYZ.

      The range of the color space is imposed to be \([0..1]\).

      Parameters:
      name - Name of the color space, cannot be null, its length must be >= 1
      toXYZ - 3x3 column-major transform matrix from RGB to the profile connection space CIE XYZ as an array of 9 floats, cannot be null
      oetf - Opto-electronic transfer function, cannot be null
      eotf - Electro-optical transfer function, cannot be null
      Throws:
      IllegalArgumentException - If any of the following conditions is met:
      • The name is null or has a length of 0.
      • The OETF is null or the EOTF is null.
      • The minimum valid value is >= the maximum valid value.
      See Also:

    • Rgb

      public Rgb(@Nonnull @Size(min=1L) String name, @Nonnull @Size(min=6L,max=9L) float[] primaries, @Nonnull @Size(min=2L,max=3L) float[] whitePoint, @Nonnull DoubleUnaryOperator oetf, @Nonnull DoubleUnaryOperator eotf, float min, float max)

      Creates a new RGB color space using a specified set of primaries and a specified white point.

      The primaries and white point can be specified in the CIE xyY space or in CIE XYZ. The length of the arrays depends on the chosen space:

      SpacePrimaries lengthWhite point length
      xyY62
      XYZ93

      When the primaries and/or white point are specified in xyY, the Y component does not need to be specified and is assumed to be 1.0. Only the xy components are required.

      The ID, areturned by ColorSpace.getId(), of an object created by this constructor is always ColorSpace.MIN_ID.

      Parameters:
      name - Name of the color space, cannot be null, its length must be >= 1
      primaries - RGB primaries as an array of 6 (xy) or 9 (XYZ) floats
      whitePoint - Reference white as an array of 2 (xy) or 3 (XYZ) floats
      oetf - Opto-electronic transfer function, cannot be null
      eotf - Electro-optical transfer function, cannot be null
      min - The minimum valid value in this color space's RGB range
      max - The maximum valid value in this color space's RGB range
      Throws:
      IllegalArgumentException -

      If any of the following conditions is met:

      • The name is null or has a length of 0.
      • The primaries array is null or has a length that is neither 6 or 9.
      • The white point array is null or has a length that is neither 2 or 3.
      • The OETF is null or the EOTF is null.
      • The minimum valid value is >= the maximum valid value.
      See Also:

    • Rgb

      public Rgb(@Nonnull @Size(min=1L) String name, @Nonnull @Size(9L) float[] toXYZ, @Nonnull ColorSpace.Rgb.TransferParameters function)

      Creates a new RGB color space using a 3x3 column-major transform matrix. The transform matrix must convert from the RGB space to the profile connection space CIE XYZ.

      The range of the color space is imposed to be \([0..1]\).

      Parameters:
      name - Name of the color space, cannot be null, its length must be >= 1
      toXYZ - 3x3 column-major transform matrix from RGB to the profile connection space CIE XYZ as an array of 9 floats, cannot be null
      function - Parameters for the transfer functions
      Throws:
      IllegalArgumentException - If any of the following conditions is met:
      • The name is null or has a length of 0.
      • Gamma is negative.
      See Also:

    • Rgb

      public Rgb(@Nonnull @Size(min=1L) String name, @Nonnull @Size(min=6L,max=9L) float[] primaries, @Nonnull @Size(min=2L,max=3L) float[] whitePoint, @Nonnull ColorSpace.Rgb.TransferParameters function)

      Creates a new RGB color space using a specified set of primaries and a specified white point.

      The primaries and white point can be specified in the CIE xyY space or in CIE XYZ. The length of the arrays depends on the chosen space:

      SpacePrimaries lengthWhite point length
      xyY62
      XYZ93

      When the primaries and/or white point are specified in xyY, the Y component does not need to be specified and is assumed to be 1.0. Only the xy components are required.

      Parameters:
      name - Name of the color space, cannot be null, its length must be >= 1
      primaries - RGB primaries as an array of 6 (xy) or 9 (XYZ) floats
      whitePoint - Reference white as an array of 2 (xy) or 3 (XYZ) floats
      function - Parameters for the transfer functions
      Throws:
      IllegalArgumentException - If any of the following conditions is met:
      • The name is null or has a length of 0.
      • The primaries array is null or has a length that is neither 6 or 9.
      • The white point array is null or has a length that is neither 2 or 3.
      • The transfer parameters are invalid.
      See Also:

    • Rgb

      public Rgb(@Nonnull @Size(min=1L) String name, @Nonnull @Size(9L) float[] toXYZ, double gamma)

      Creates a new RGB color space using a 3x3 column-major transform matrix. The transform matrix must convert from the RGB space to the profile connection space CIE XYZ.

      The range of the color space is imposed to be \([0..1]\).

      Parameters:
      name - Name of the color space, cannot be null, its length must be >= 1
      toXYZ - 3x3 column-major transform matrix from RGB to the profile connection space CIE XYZ as an array of 9 floats, cannot be null
      gamma - Gamma to use as the transfer function
      Throws:
      IllegalArgumentException - If any of the following conditions is met:
      • The name is null or has a length of 0.
      • Gamma is negative.
      See Also:

    • Rgb

      public Rgb(@Nonnull @Size(min=1L) String name, @Nonnull @Size(min=6L,max=9L) float[] primaries, @Nonnull @Size(min=2L,max=3L) float[] whitePoint, double gamma)

      Creates a new RGB color space using a specified set of primaries and a specified white point.

      The primaries and white point can be specified in the CIE xyY space or in CIE XYZ. The length of the arrays depends on the chosen space:

      SpacePrimaries lengthWhite point length
      xyY62
      XYZ93

      When the primaries and/or white point are specified in xyY, the Y component does not need to be specified and is assumed to be 1.0. Only the xy components are required.

      Parameters:
      name - Name of the color space, cannot be null, its length must be >= 1
      primaries - RGB primaries as an array of 6 (xy) or 9 (XYZ) floats
      whitePoint - Reference white as an array of 2 (xy) or 3 (XYZ) floats
      gamma - Gamma to use as the transfer function
      Throws:
      IllegalArgumentException - If any of the following conditions is met:
      • The name is null or has a length of 0.
      • The primaries array is null or has a length that is neither 6 or 9.
      • The white point array is null or has a length that is neither 2 or 3.
      • Gamma is negative.
      See Also:

  • Method Details

    • getWhitePoint

      @Nonnull @Size(min=2L) public float[] getWhitePoint(@Nonnull @Size(min=2L) float[] whitePoint)
      Copies the non-adapted CIE xyY white point of this color space in specified array. The Y component is assumed to be 1 and is therefore not copied into the destination. The x and y components are written in the array at positions 0 and 1 respectively.
      Parameters:
      whitePoint - The destination array, cannot be null, its length must be >= 2
      Returns:
      The destination array passed as a parameter
      See Also:

    • getWhitePoint

      @Nonnull @Size(2L) public float[] getWhitePoint()
      Returns the non-adapted CIE xyY white point of this color space as a new array of 2 floats. The Y component is assumed to be 1 and is therefore not copied into the destination. The x and y components are written in the array at positions 0 and 1 respectively.
      Returns:
      A new non-null array of 2 floats
      See Also:

    • getPrimaries

      @Nonnull @Size(min=6L) public float[] getPrimaries(@Nonnull @Size(min=6L) float[] primaries)
      Copies the primaries of this color space in specified array. The Y component is assumed to be 1 and is therefore not copied into the destination. The x and y components of the first primary are written in the array at positions 0 and 1 respectively.

      Note: Some ColorSpaces represent gray profiles. The concept of primaries for such a ColorSpace does not make sense, so we use a special set of primaries that are all 1s.

      Parameters:
      primaries - The destination array, cannot be null, its length must be >= 6
      Returns:
      The destination array passed as a parameter
      See Also:

    • getPrimaries

      @Nonnull @Size(6L) public float[] getPrimaries()
      Returns the primaries of this color space as a new array of 6 floats. The Y component is assumed to be 1 and is therefore not copied into the destination. The x and y components of the first primary are written in the array at positions 0 and 1 respectively.

      Note: Some ColorSpaces represent gray profiles. The concept of primaries for such a ColorSpace does not make sense, so we use a special set of primaries that are all 1s.

      Returns:
      A new non-null array of 2 floats
      See Also:

    • getTransform

      @Nonnull @Size(min=9L) public float[] getTransform(@Nonnull @Size(min=9L) float[] transform)

      Copies the transform of this color space in specified array. The transform is used to convert from RGB to XYZ (with the same white point as this color space). To connect color spaces, you must first adapt them to the same white point.

      It is recommended to use ColorSpace.connect(ColorSpace, ColorSpace) to convert between color spaces.

      Parameters:
      transform - The destination array, cannot be null, its length must be >= 9
      Returns:
      The destination array passed as a parameter
      See Also:

    • getTransform

      @Nonnull @Size(9L) public float[] getTransform()

      Returns the transform of this color space as a new array. The transform is used to convert from RGB to XYZ (with the same white point as this color space). To connect color spaces, you must first adapt them to the same white point.

      It is recommended to use ColorSpace.connect(ColorSpace, ColorSpace) to convert between color spaces.

      Returns:
      A new array of 9 floats
      See Also:

    • getInverseTransform

      @Nonnull @Size(min=9L) public float[] getInverseTransform(@Nonnull @Size(min=9L) float[] inverseTransform)

      Copies the inverse transform of this color space in specified array. The inverse transform is used to convert from XYZ to RGB (with the same white point as this color space). To connect color spaces, you must first adapt them to the same white point.

      It is recommended to use ColorSpace.connect(ColorSpace, ColorSpace) to convert between color spaces.

      Parameters:
      inverseTransform - The destination array, cannot be null, its length must be >= 9
      Returns:
      The destination array passed as a parameter
      See Also:

    • getInverseTransform

      @Nonnull @Size(9L) public float[] getInverseTransform()

      Returns the inverse transform of this color space as a new array. The inverse transform is used to convert from XYZ to RGB (with the same white point as this color space). To connect color spaces, you must first adapt them to the same white point.

      It is recommended to use ColorSpace.connect(ColorSpace, ColorSpace) to convert between color spaces.

      Returns:
      A new array of 9 floats
      See Also:

    • getOetf

      @Nonnull public DoubleUnaryOperator getOetf()

      Returns the opto-electronic transfer function (OETF) of this color space. The inverse function is the electro-optical transfer function (EOTF) returned by getEotf(). These functions are defined to satisfy the following equality for \(x \in [0..1]\):

      $$OETF(EOTF(x)) = EOTF(OETF(x)) = x$$

      For RGB colors, this function can be used to convert from linear space to "gamma space" (gamma encoded). The terms gamma space and gamma encoded are frequently used because many OETFs can be closely approximated using a simple power function of the form \(x^{\frac{1}{\gamma}}\) (the approximation of the sRGB OETF uses \(\gamma=2.2\) for instance).

      Returns:
      A transfer function that converts from linear space to "gamma space"
      See Also:

    • getEotf

      @Nonnull public DoubleUnaryOperator getEotf()

      Returns the electro-optical transfer function (EOTF) of this color space. The inverse function is the opto-electronic transfer function (OETF) returned by getOetf(). These functions are defined to satisfy the following equality for \(x \in [0..1]\):

      $$OETF(EOTF(x)) = EOTF(OETF(x)) = x$$

      For RGB colors, this function can be used to convert from "gamma space" (gamma encoded) to linear space. The terms gamma space and gamma encoded are frequently used because many EOTFs can be closely approximated using a simple power function of the form \(x^\gamma\) (the approximation of the sRGB EOTF uses \(\gamma=2.2\) for instance).

      Returns:
      A transfer function that converts from "gamma space" to linear space
      See Also:

    • getTransferParameters

      @Nullable public ColorSpace.Rgb.TransferParameters getTransferParameters()

      Returns the parameters used by the electro-optical and opto-electronic transfer functions. If the transfer functions do not match the ICC parametric curves defined in ICC.1:2004-10 (section 10.15), this method returns null.

      See ColorSpace.Rgb.TransferParameters for a full description of the transfer functions.

      Returns:
      An instance of ColorSpace.Rgb.TransferParameters or null if this color space's transfer functions do not match the equation defined in ColorSpace.Rgb.TransferParameters

    • isSrgb

      public boolean isSrgb()
      Description copied from class: ColorSpace

      Indicates whether this color space is the sRGB color space or equivalent to the sRGB color space.

      A color space is considered sRGB if it meets all the following conditions:

      • Its color model is ColorSpace.Model.RGB.
      • Its primaries are within 1e-3 of the true sRGB primaries.
      • Its white point is within 1e-3 of the CIE standard illuminant D65.
      • Its opto-electronic transfer function is not linear.
      • Its electro-optical transfer function is not linear.
      • Its transfer functions yield values within 1e-3 of ColorSpace.Named.SRGB.
      • Its range is \([0..1]\).

      This method always returns true for ColorSpace.Named.SRGB.

      Overrides:
      isSrgb in class ColorSpace
      Returns:
      True if this color space is the sRGB color space (or a close approximation), false otherwise

    • isWideGamut

      public boolean isWideGamut()
      Description copied from class: ColorSpace
      Returns whether this color space is a wide-gamut color space. An RGB color space is wide-gamut if its gamut entirely contains the sRGB gamut and if the area of its gamut is 90% of greater than the area of the NTSC gamut.
      Specified by:
      isWideGamut in class ColorSpace
      Returns:
      True if this color space is a wide-gamut color space, false otherwise

    • getMinValue

      public float getMinValue(int component)
      Description copied from class: ColorSpace
      Returns the minimum valid value for the specified component of this color space's color model.
      Specified by:
      getMinValue in class ColorSpace
      Parameters:
      component - The index of the component
      Returns:
      A floating point value less than ColorSpace.getMaxValue(int)
      See Also:

    • getMaxValue

      public float getMaxValue(int component)
      Description copied from class: ColorSpace
      Returns the maximum valid value for the specified component of this color space's color model.
      Specified by:
      getMaxValue in class ColorSpace
      Parameters:
      component - The index of the component
      Returns:
      A floating point value greater than ColorSpace.getMinValue(int)
      See Also:

    • toLinear

      @Nonnull @Size(3L) public float[] toLinear(float r, float g, float b)

      Decodes an RGB value to linear space. This is achieved by applying this color space's electro-optical transfer function to the supplied values.

      Refer to the documentation of ColorSpace.Rgb for more information about transfer functions and their use for encoding and decoding RGB values.

      Parameters:
      r - The red component to decode to linear space
      g - The green component to decode to linear space
      b - The blue component to decode to linear space
      Returns:
      A new array of 3 floats containing linear RGB values
      See Also:

    • toLinear

      @Nonnull @Size(min=3L) public float[] toLinear(@Nonnull @Size(min=3L) float[] v)

      Decodes an RGB value to linear space. This is achieved by applying this color space's electro-optical transfer function to the first 3 values of the supplied array. The result is stored back in the input array.

      Refer to the documentation of ColorSpace.Rgb for more information about transfer functions and their use for encoding and decoding RGB values.

      Parameters:
      v - A non-null array of non-linear RGB values, its length must be at least 3
      Returns:
      The specified array
      See Also:

    • fromLinear

      @Nonnull @Size(3L) public float[] fromLinear(float r, float g, float b)

      Encodes an RGB value from linear space to this color space's "gamma space". This is achieved by applying this color space's opto-electronic transfer function to the supplied values.

      Refer to the documentation of ColorSpace.Rgb for more information about transfer functions and their use for encoding and decoding RGB values.

      Parameters:
      r - The red component to encode from linear space
      g - The green component to encode from linear space
      b - The blue component to encode from linear space
      Returns:
      A new array of 3 floats containing non-linear RGB values
      See Also:

    • fromLinear

      @Nonnull @Size(min=3L) public float[] fromLinear(@Nonnull @Size(min=3L) float[] v)

      Encodes an RGB value from linear space to this color space's "gamma space". This is achieved by applying this color space's opto-electronic transfer function to the first 3 values of the supplied array. The result is stored back in the input array.

      Refer to the documentation of ColorSpace.Rgb for more information about transfer functions and their use for encoding and decoding RGB values.

      Parameters:
      v - A non-null array of linear RGB values, its length must be at least 3
      Returns:
      A new array of 3 floats containing non-linear RGB values
      See Also:

    • toXyz

      @Nonnull @Size(min=3L) public float[] toXyz(@Nonnull @Size(min=3L) float[] v)
      Description copied from class: ColorSpace

      Converts a color value from this color space's model to tristimulus CIE XYZ values. If the color model of this color space is not RGB, it is assumed that the target CIE XYZ space uses a D50 standard illuminant.

      The specified array's length must be at least equal to to the number of color components as returned by ColorSpace.Model.getComponentCount().

      Specified by:
      toXyz in class ColorSpace
      Parameters:
      v - An array of color components containing the color space's color value to convert to XYZ, and large enough to hold the resulting tristimulus XYZ values
      Returns:
      The array passed in parameter
      See Also:

    • fromXyz

      @Nonnull @Size(min=3L) public float[] fromXyz(@Nonnull @Size(min=3L) float[] v)
      Description copied from class: ColorSpace

      Converts tristimulus values from the CIE XYZ space to this color space's color model. The resulting value is passed back in the specified array.

      The specified array's length must be at least equal to to the number of color components as returned by ColorSpace.Model.getComponentCount(), and its first 3 values must be the XYZ components to convert from.

      Specified by:
      fromXyz in class ColorSpace
      Parameters:
      v - An array of color components containing the XYZ values to convert from, and large enough to hold the number of components of this color space's model
      Returns:
      The array passed in parameter
      See Also:

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class ColorSpace

    • equals

      public boolean equals(Object o)
      Overrides:
      equals in class ColorSpace