Reparameterize in Z direction?

How can a reparameterize a surface in the z direction? I am tying to use the image sampler, but it only reads in the u and v coordinates. Is there a way to use it for something going in the z direction?

u and v are surface domain directions, affected by parametrisation. z is a world direction. A surface may occupy a range of z-values, but it has nothing to do with the the parametrisation, only with the shape.

The surface direction perpendicular to u and v is sometimes called w or n (for normal), but it is an uncomfortable blend of surface and world metrics.

I think there’s some bug confusion here somewhere, but I’m not sure where.