I want to be able to define n shapes and find the intersection between them and a line. I’m treating the shapes as “one” shape, i.e. I do not want any internal intersections (hence the volume equations).

I can do this by typing out each shape and equation as follows:

line = InfiniteLine[{{0.5, 0.5, 0.5}, {0.5, 0.5, 1}}];   (*shapes - I can define these*)  shape1 = Ball[]; shape2 = Cone[{{0, 0, 0}, {1, 1, 1}}, 1/2];   (*------------ I want from here  automated ---------*)  (*surface equations *)  surfaceequations1 = RegionMember[RegionBoundary[shape1], {x, y, z}]; surfaceequations2 = RegionMember[RegionBoundary[shape2], {x, y, z}];  volumeequation1 = RegionMember[shape1, {x, y, z}]; volumeequation2 = RegionMember[shape2, {x, y, z}];  intersection =   NSolve[{x, y, z} \[Element]      line && (surfaceequations1 ||       surfaceequations2) && ! (volumeequation1 && volumeequation2), {x,     y, z}];  (* ---------- automation can stop here ---------- *)    points = Point[{x, y, z}] /. intersection  Graphics3D[{{Opacity[0.5], shape1}, {Opacity[0.7], shape2},    line, {Red, PointSize[0.015], points}}] 

But this method means I have to type out each equation for each shape. If I change the number of shapes, I have to go through code and delete some.

The Problem

I want to be able to define n shapes, then mathematica defines the n surface equations, and the n volume equations and puts them into NSolve.

Also; apologies for the bad question title – I’m not sure what to call this problem.