How would I construct the CIE Yxy diagram? [closed]

Question

It seems most references showing a CIE Yxy diagram can be reduced to very few (one?) sources. If I wanted to construct the diagram myself from some published measurement values, how would I do it?

I'm assuming there is some parametric function f(wavelength) giving a vector (x, y) for each f. But how would that function f look like?

Actually I wanted to construct a CIE Luv* diagram, but when knowing the (x, y) vectors for CIE Yxy, I could easily convert those to (u*, v*), right?

Update (2019-09-03):

Drawing the outline (spectral line) is one part of the problem. Another part of the problem is filling in the correct colors (I'm aware that no existing computer display device can actually present them): Is it OK to put the C white at its position and use Gouraud-Shaded Triangle Meshes to interpolate the area between two points on the spectral line and that white point (Example Image connecting 470nm with 500nm and with Illuminant C)? That seems to be OK.

In case it's OK, how would I fill the "non-spectral triangle" outlines by both ends of the spectral line and the white-point? Trying that I found out that the ends of the spectral line practically represent black, so the triangle came out much more black than purple, and opposed to all diagrams I've seen before, there's a discontinuity where the non-spectral colors are (Example Image)

As an experiment, I cut off the end of the spectrum to 435-645nm, and the transition from spectral to non-spectral colors is rather smooth then. (Example Image)

However when you use normalized data the dark colors become bright, and the brighter colors become darker. Effectively I realized that the "white point" actually is a gray point (several diagrams seem to have that wrong), and it seems that Illuminant C is the correct one, too , so this is my final version so far.

Answer 1

The conversion path from CIE xyY to a given RGB colourspace, e.g. sRGB, is typically as follows:

CIE xyY --> CIE XYZ --> RGB

With that in mind, generating the diagram can be done by generating a regularly spaced 2D grid of samples in domain [0, 1] and apply the conversion path to them.

As you found out, no display device is capable of representing the visible spectrum, so you will be limited by its colorimetry boundaries.

Colour implements the three common Chromaticity Diagrams:

CIE 1931 Chromaticity Diagram CIE 1960 UCS Chromaticity Diagram CIE 1976 UCS Chromaticity Diagram

The Python code for drawing the colours and bounding them with the spectral locus is as follows:

@override_style()
def plot_chromaticity_diagram_colours(
        samples=256,
        diagram_opacity=1.0,
        diagram_clipping_path=None,
        cmfs='CIE 1931 2 Degree Standard Observer',
        method='CIE 1931',
        **kwargs):
    """
    Plots the *Chromaticity Diagram* colours according to given method.

    Parameters
    ----------
    samples : numeric, optional
        Samples count on one axis.
    diagram_opacity : numeric, optional
        Opacity of the *Chromaticity Diagram* colours.
    diagram_clipping_path : array_like, optional
        Path of points used to clip the *Chromaticity Diagram* colours.
    cmfs : unicode, optional
        Standard observer colour matching functions used for
        *Chromaticity Diagram* bounds.
    method : unicode, optional
        **{'CIE 1931', 'CIE 1960 UCS', 'CIE 1976 UCS'}**,
        *Chromaticity Diagram* method.

    Other Parameters
    ----------------
    \\**kwargs : dict, optional
        {:func:`colour.plotting.artist`, :func:`colour.plotting.render`},
        Please refer to the documentation of the previously listed definitions.

    Returns
    -------
    tuple
        Current figure and axes.

    Examples
    --------
    >>> plot_chromaticity_diagram_colours()  # doctest: +SKIP

    .. image:: ../_static/Plotting_Plot_Chromaticity_Diagram_Colours.png
        :align: center
        :alt: plot_chromaticity_diagram_colours
    """

    settings = {'uniform': True}
    settings.update(kwargs)

    _figure, axes = artist(**settings)

    method = method.upper()

    cmfs = first_item(filter_cmfs(cmfs).values())

    illuminant = COLOUR_STYLE_CONSTANTS.colour.colourspace.whitepoint

    ii, jj = np.meshgrid(
        np.linspace(0, 1, samples), np.linspace(1, 0, samples))
    ij = tstack([ii, jj])

    # NOTE: Various values in the grid have potential to generate
    # zero-divisions, they could be avoided by perturbing the grid, e.g. adding
    # a small epsilon. It was decided instead to disable warnings.
    with suppress_warnings(python_warnings=True):
        if method == 'CIE 1931':
            XYZ = xy_to_XYZ(ij)
            spectral_locus = XYZ_to_xy(cmfs.values, illuminant)
        elif method == 'CIE 1960 UCS':
            XYZ = xy_to_XYZ(UCS_uv_to_xy(ij))
            spectral_locus = UCS_to_uv(XYZ_to_UCS(cmfs.values))
        elif method == 'CIE 1976 UCS':
            XYZ = xy_to_XYZ(Luv_uv_to_xy(ij))
            spectral_locus = Luv_to_uv(
                XYZ_to_Luv(cmfs.values, illuminant), illuminant)
        else:
            raise ValueError(
                'Invalid method: "{0}", must be one of '
                '{{\'CIE 1931\', \'CIE 1960 UCS\', \'CIE 1976 UCS\'}}'.format(
                    method))

    RGB = normalise_maximum(
        XYZ_to_plotting_colourspace(XYZ, illuminant), axis=-1)

    polygon = Polygon(
        spectral_locus
        if diagram_clipping_path is None else diagram_clipping_path,
        facecolor='none',
        edgecolor='none')
    axes.add_patch(polygon)
    # Preventing bounding box related issues as per
    # https://github.com/matplotlib/matplotlib/issues/10529
    image = axes.imshow(
        RGB,
        interpolation='bilinear',
        extent=(0, 1, 0, 1),
        clip_path=None,
        alpha=diagram_opacity)
    image.set_clip_path(polygon)

    settings = {'axes': axes}
    settings.update(kwargs)

    return render(**kwargs)

It is obviously dependent on a lot of Colour functions but it should be enough to illustrate the algorithm.

Answer 2

You can find the coordinates to plot for all of the CIE Standards on the Web at the Color & Vision Research Laboratory
They are available as CSV (Comma separated variables) suitable for Excel or other applications.

Good luck