Hide mesh intersection

I have 1 background mesh, which is pretty much just a plane (for now), and one generated mesh (not generated in Update())

I made 2 types of mesh generation, first one:
http://gfycat.com/CriminalGreenCollie

Second one (instead of a circle mesh, its just the outline with a Z scale)
http://gfycat.com/NervousSecondAurochs


Now, I need to just hide parts of the background mesh which are intersecting with one of these 2 meshes (i made the second one for a boolean intersection approach, which proved way too slow for real-time, maybe a shader would help here? I have zero experience in making shaders)

What would be the best approach for this?

Solution:
As the firsts reply by Gambit suggest, the solution was a stencil shader.
Background shader:

Code (CSharp):

1. Shader "Custom/FogBackground"  {
2.     Properties{
3.         _Color("Main Color", Color) = (1,1,1,1)
4.         _MainTex("Base (RGB)", 2D) = "white" {}
5.     }
6.         Category{
7.         Lighting Off
8.         ZWrite on
9.         Cull Back
10.         SubShader{
11.  
12.         Stencil{
13.         Ref 1
14.         Comp notequal
15.         Pass Zero
16.     }
17.  
18.         Tags{
19.         "Queue" = "Geometry"
20.         "LightMode" = "Always"
21.         "RenderType" = "Opaque"
22.         "IgnoreProjector" = "True"
23.     }
24.         Pass{
25.         SetTexture[_MainTex]{
26.         constantColor[_Color]
27.         Combine texture * constant, texture * constant
28.     }
29.     }
30.     }
31.     }
32. }

Custom mesh shader:

Code (CSharp):

1. Shader "Custom/Vision" {
2.  
3.     Category{
4.         Lighting Off
5.         Cull Back
6.         zwrite off
7.  
8.         SubShader{
9.  
10.         Colormask 0
11.  
12.         Stencil{
13.         Ref 1
14.         Comp always
15.         Pass replace
16.     }
17.  
18.         Tags{
19.         "Queue" = "Geometry-1"
20.         "LightMode" = "Always"
21.         "RenderType" = "Opaque"
22.         "IgnoreProjector" = "True"
23.     }
24.         Pass{
25.     }
26.     }
27.     }
28. }

Result:
http://gfycat.com/CoolPoliteAmericankestrel

 

That is going to make things difficult...
What you are trying to do can be done very well with Stenciling in your shaders. http://docs.unity3d.com/Manual/SL-Stencil.html

Shader code is very difficult when you're starting to learn it, but it becomes super easy. To avoid this rough learning curve in this project, you could download the built-in shader code under on the same web page you download Unity, then add stenciling to those shaders.

Graphics stuff is very touchy, let me know if you get stuck.

 

Thank you very much!

I'm nearly done, I reused this:
http://stackoverflow.com/questions/27740164/using-stencil-buffer-to-make-windows

And got it nearly working, but it isn't working from all distances/angles?
http://gfycat.com/OblongAcademicAtlanticblackgoby

Nevermind, fixed Check the OP for the shaders

 

Hi.
Any chance you could share this project?
I can't reprocude your results :S