# Mathematica only graphs the upper part of my cylinder

I have this code which first is supposed to make random points, draw lines through the points and then make these lines radical axes of cylinders. I have two problems with my code. First, it only draws the upper half of cylinders. Second, the perspectives are really messed up, somehow twisted and uneven. For example, Show[a, ViewPoint -> Front, ImageSize -> Large, Boxed -> False] should be looking from a perspective where xy-plane is completely straight (perpendicular to z axis) but thats not what is happening. Here is my code:

plane = InfinitePlane[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}];
pts = RandomPoint[plane, 20, {{-10, 10}, {-10, 10}, {0, 0}}];
a = Graphics3D[{plane,
Cylinder[{#, # + {#[], -#[],
4 Sqrt Sqrt[#[]^2 + #[]^2] + 7}}, 1/2] & /@ pts,
Red, InfiniteLine[#, {#[], -#[],
4 Sqrt Sqrt[#[]^2 + #[]^2] + 7}] & /@ pts, Black,
Sphere[{0, 0, 0}, 0.3], Blue, Sphere[pts, .1]},
PlotRange -> {{-10, 10}, {-10, 10}, {-10, 10}}]
Show[a, ImageSize -> Large, Boxed -> False]
Show[a, ViewPoint -> Above, ImageSize -> Large, Boxed -> False]
Show[a, ViewPoint -> Front, ImageSize -> Large, Boxed -> False]
Show[a, ViewPoint -> {0, 0, \[Infinity]}, ImageSize -> Large,
Boxed -> False]
Show[a, ViewPoint -> {0, -\[Infinity], 0}, ImageSize -> Large,
Boxed -> False]


Any help would be appreciated. Thank you!

• use Cylinder[{# - {#[], -#[], 4 Sqrt Sqrt[#[]^2 + #[]^2] + 7}, # + {#[], -#[], 4 Sqrt Sqrt[#[]^2 + #[]^2] + 7}}, 1/2] & /@ pts to have the cylinders extend below plane. – kglr Mar 6 '19 at 0:44
• @kglr that worked! What is the meaning behind $#-$ and $#+$ I did this by imitating someone else's code. Could you point me to a reference? That does not fix the perspective problem though, any ideas? – Sorfosh Mar 6 '19 at 0:48
• Sorfosh, look up Function and Slot in the docs. – kglr Mar 6 '19 at 1:24
• Solved! I just had to reset Mathematica and kglr helped with the main issue. This can be closed or @kglr add your comment as a response – Sorfosh Mar 6 '19 at 3:57

Cylinder[{# - {#[], -#[], 4 Sqrt Sqrt[#[]^2 + #[]^2] + 7},

in Graphics3D that poduces a to have the cylinders extend below plane.
Show[a, ViewPoint -> Front, ImageSize -> Large, Boxed -> False] 