Determine that a Luv Color is non-imaginary

Suppose I have a triple of coordinates in the Luv color space. What is the best way to determine that these correspond to a real color?

Assuming your L* is in domain [0, 100], you can construct the boundaries of the Visible Spectrum and then determine if your CIE L*u*v* coordinates are within it.

import colour
import numpy as np


def generate_square_waves(samples):
    square_waves = []
    square_waves_basis = np.tril(np.ones((samples, samples)))[0:-1, :]
    for i in range(samples):
        square_waves.append(np.roll(square_waves_basis, i))
    return np.vstack((np.zeros(samples), np.vstack(square_waves),
                    np.ones(samples)))


def XYZ_outer_surface(samples):
    XYZ = []
    wavelengths = np.linspace(colour.DEFAULT_SPECTRAL_SHAPE.start,
                            colour.DEFAULT_SPECTRAL_SHAPE.end, samples)

    for wave in generate_square_waves(samples):
        spd = colour.SpectralPowerDistribution(
            wave, wavelengths, interpolator=colour.LinearInterpolator).align(
                colour.DEFAULT_SPECTRAL_SHAPE)
        XYZ.append(colour.spectral_to_XYZ(spd))

    return np.array(XYZ).reshape(len(XYZ), -1, 3)

mesh = XYZ_outer_surface(43).reshape((-1, 3))

E = colour.ILLUMINANTS['CIE 1931 2 Degree Standard Observer']['E']

XYZ1 = colour.Luv_to_XYZ([50, 50, 50], E)
print(colour.is_within_mesh_volume(XYZ1, mesh))
# True

XYZ2 = colour.Luv_to_XYZ([50, 250, -250], E)
print(colour.is_within_mesh_volume(XYZ2, mesh))
# False

I would highly recommend caching the mesh as it is quite heavy to compute.