(2D) Rendering only the parts of a sprite that are within specific bounds

Coincidentally this is the exact same problem I'm having and trying to fix right now. By googling I think the answer should be to use a custom shader which renders things based on a position, but I am not really fluent enough in shader writing to know if this is a good option. If you find a solution I'd love to hear it!

I got this half-working, (maybe somewhere to start from at least!) it works in the editor, but not in the game view, really it needs to do the world->screen calculation in the shader, not in update to cope with multiple cameras, but I haven't got the parent-bounds-world-to-screen conversion working yet.

I attach this script to the children-to-be-clipped objects(blue) under the parent (green)

 [ExecuteInEditMode]
 public class ClippedChild : MonoBehaviour {
 
     void Update () {
 
         Camera cam = Camera.current;
         if (!cam) {
             return;
         }
 
         GameObject Parent = transform.parent.gameObject;
         Vector4 ParentMin = cam.WorldToViewportPoint( Parent.renderer.bounds.min );
         Vector4 ParentMax = cam.WorldToViewportPoint (Parent.renderer.bounds.max);
 
         Material Mat = renderer.sharedMaterial;
         Mat.SetVector("_ParentMin", ParentMin );
         Mat.SetVector("_ParentMax", ParentMax );
 
     }
 }

Then this in a shader, also on the child object.

 Shader "Custom/ClippedChild" 
 {
     Properties {
         _ColourInside ("ColourInside", Color) = (0,1,0,1)
         _ColourOutside ("ColourOutside", Color) = (1,0,0,0.5)
         _ParentMin("ParentMin", Vector ) = (0,0,0,0)
         _ParentMax("ParentMax", Vector ) = (1,1,0,0)
     }
     
     SubShader {
         Tags { "RenderType"="Transparent" }
         LOD 200
         
         CGPROGRAM
         #pragma surface surf Lambert
 
         float4 _ColourInside;
         float4 _ColourOutside;
         float4 _ParentMin;
         float4 _ParentMax;
 
         struct Input {
             float3 worldPos;
             float2 screenPos;
         };
 
         void surf (Input IN, inout SurfaceOutput o) {
             float4 Colour = _ColourInside;
             
             float2 ScreenPos = IN.screenPos;
             float2 ScreenMin = _ParentMin.xy;
             float2 ScreenMax =  _ParentMax.xy;
             if ( ScreenPos.x < ScreenMin.x || ScreenPos.x > ScreenMax.x ||
                  ScreenPos.y < ScreenMin.y || ScreenPos.y > ScreenMax.y 
             )
             {
                 Colour =  _ColourOutside; 
                 //discard;
             }
                 
             o.Albedo = Colour;
             o.Alpha = Colour.a;
         }
         ENDCG
     } 
     FallBack "Diffuse"
 }

This code renders the pixel "in" or "out", but you could use discard; to just not draw the pixel entirely, (colours just helped debug/demo)

As you can see, not wholly working yet, but I'll see if I can get further. (I think just need to provide world-bounds positions to the shader and calculate the screen bounds there).

maybe this might help:

http://wiki.unity3d.com/index.php/DepthMask

and maybe this:

http://docs.unity3d.com/Documentation/Components/SL-Stencil.html