I have two regions, each parametrized by different values of u and v. My goal is to subtract the first region from the second region, such that the resulting plot displays only the second region, with empty space wherever it intersects the first region. Essentially, I want to perform boolean algebra on ParametricPlot3D regions, so that I can get Region2 - Region1.

Show[

Region2 =

ParametricPlot3D[{Cos[u] v, Sin[u] v, Cos[u] Sin[u] v}, {u, 0, 2 \[Pi]}, {v, 0.5, 1}, MaxRecursion -> 1, PlotPoints -> 50,

Mesh -> False, PlotStyle -> {Opacity[0.5], Thickness[0.05]}],

Region1 =

ParametricPlot3D[{Cos[u ] - 1, Sin[u] + 1, u + v}, {u, - (\[Pi]/2), 0}, {v, 0.4, 0.7}, MaxRecursion -> 1, PlotPoints -> 50,

Mesh -> False, PlotStyle -> {Opacity[1], Thickness[0.5]}]]

I assume there must be a way to do this using

**Exclusions**, but I'm a little hazy on the syntax/ format.