Shading device with variable thickness for vehicle and corresponding vehicle

The blind (10), which is moved between retracted and deployed positions, e.g. to shade a vehicle sun roof, is made from a supple material of variable thickness according to the pressure applied on it, and can have, for example, a thickness that is less when retracted than when deployed. It can be made from compressible and incompressible materials, and produced by moulding, weaving, three-dimensional knitting, extrusion-blowing, or by assembling parallel layers. The reduction in thickness when retracted can be achieved by a compression bar or rollers (23) located before a roller (12) on which the retracted blind is stored.