This image shows a couple of different isometric projections. In the black shows the figure's "true" dimensions in an orthographic projection while the red shows the dimensions in an isometric projection.
Is there a relation between the two numbers?
No there is not such a function you want. Functions are well defined but for different inputs we may have several outputs. For example in cylinder two segment with length 1 have different vision lengths 1 and $\frac{\sqrt{2}}{2}$.
We should know three parameters which describes 3D shape then we can calculate vision length with Pythagorean Theorem.