I have the following equations which I use to describe a color in three dimensions (x and y are chromaticity coordinates and z is lightness):
$x = \frac{t^{2.4}}{t^{2.4} + (0.4t + 0.6)^{2.4} + 1}$
$y = \frac{1}{t^{2.4} + (0.4t + 0.6)^{2.4} + 1}$
$z = 0.0722 + (0.2126(t^{2.4})) + (0.7152((0.4t + 0.6)^{2.4}))$
where $0 \le t \le 1$
How would I go about eliminating the parameter $t$? The fractional exponent (which represents gamma transformation) seems to make this feat impossible.
Thank you!
Hint: divide the first two equations:
$$ t^{2.4} = \frac{x}{y} \tag{1} $$
Invert the second equation, and use $(1)\,$:
$$ (0.4t+0.6)^{2.4} = \frac{1}{y} - t^{2.4}-1 = \frac{1-x}{y} - 1 \tag{2} $$
Substitute $(1)$ and $(2)$ in the third equation to eliminate $t$ and get a relation between $x,y,z\,$.