Showing truncated surfaces ; $\,$ Reading off projected 3D points by mouse pointing;

Two questions:

Wish to remove parts of the surface outside the pie cutting planes and show the remaining truncated object/intersection edges without cutting planes.

al = Pi/4; x := Sin[al] Cosh[v]; y := Cos[al] Sinh[v];
obj = ParametricPlot3D[{x Cos[u] + y Sin[u] + 6, x Sin[u] - y Cos[u],
u Cos[al] + v Sin[al]}, {u, 0, 2 Pi}, {v, -2.25, 2.25},
PlotPoints -> {36, 10}];
bt = Pi/6;
pl1 = ParametricPlot3D[{u Cos[bt], u Sin[bt], w}, {u, 0, 10}, {w, -3,
7}];
bt = -Pi/8;
pl2 = ParametricPlot3D[{u Cos[bt], u Sin[bt], w}, {u, 0, 10}, {w, -3,
7}];
Show[{obj, pl1, pl2}, PlotRange -> All]


Secondly, is it possible at all by pinpointing with a mouse on an unambiguous projected point on surface (first seen/encountered incident from a given view-point ), to read off the XYZ coordinates in a window ? Or by any other command? A fixed image /projection is obtained by prescribing a view-point. To avoid conflict when using ParametricPlot3D movable image is not used or dynamic mouse-locked.

Thanks.

• If I understand correctly, the first question can probably be handled with the option RegionFunction which you can find in the docs for ParametricPlot3D. – N.J.Evans Oct 17 '16 at 14:11
• Thanks, That solved my first question. – Narasimham Oct 19 '16 at 13:17