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:

Shader "Custom/FogBackground"  {
    Properties{
        _Color("Main Color", Color) = (1,1,1,1)
        _MainTex("Base (RGB)", 2D) = "white" {}
    }
        Category{
        Lighting Off
        ZWrite on
        Cull Back
        SubShader{

        Stencil{
        Ref 1
        Comp notequal
        Pass Zero
    }

        Tags{
        "Queue" = "Geometry"
        "LightMode" = "Always"
        "RenderType" = "Opaque"
        "IgnoreProjector" = "True"
    }
        Pass{
        SetTexture[_MainTex]{
        constantColor[_Color]
        Combine texture * constant, texture * constant
    }
    }
    }
    }
}

Custom mesh shader:

Shader "Custom/Vision" {

    Category{
        Lighting Off
        Cull Back
        zwrite off

        SubShader{

        Colormask 0

        Stencil{
        Ref 1
        Comp always
        Pass replace
    }

        Tags{
        "Queue" = "Geometry-1"
        "LightMode" = "Always"
        "RenderType" = "Opaque"
        "IgnoreProjector" = "True"
    }
        Pass{
    }
    }
    }
}

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. Unity - Manual: ShaderLab command: Stencil

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:

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

Nevermind, fixed :slight_smile: Check the OP for the shaders

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