Add distance fade to his shader

Hey , i am new to shades and wanted to create a wall ,that renders a only the part close to the player . I found what i wanted from this Question : http://answers.unity3d.com/questions/529814/how-to-have-2-different-objects-at-the-same-place.html

But other that a outline color i want to fade the texture away at the edges so that i get a type of feather effect.

How do i modify the code to archive this ?

Shader :

  Shader "Custom/Proximity" {
      Properties {
          _MainTex ("Base (RGB)", 2D) = "white" {} // Regular object texture 
          _PlayerPosition ("Player Position", vector) = (0,0,0,0) // The location of the player - will be set by script
            _VisibleDistance ("Visibility Distance", float) = 10.0 // How close does the player have to be to make object visible
            _OutlineWidth ("Outline Width", float) = 3.0 // Used to add an outline around visible area a la Mario Galaxy - http://www.youtube.com/watch?v=91raP59am9U
            _OutlineColour ("Outline Colour", color) = (1.0,1.0,0.0,1.0) // Colour of the outline
      }
      SubShader {
          Tags { "RenderType"="Transparent" "Queue"="Transparent"}
          Pass {
          Blend SrcAlpha OneMinusSrcAlpha
          LOD 200
      
          CGPROGRAM
          #pragma vertex vert
          #pragma fragment frag
  
          // Access the shaderlab properties
          uniform sampler2D _MainTex;
          uniform float4 _PlayerPosition;
          uniform float _VisibleDistance;
          uniform float _OutlineWidth;
          uniform fixed4 _OutlineColour;
          
          // Input to vertex shader
          struct vertexInput {
              float4 vertex : POSITION;
              float4 texcoord : TEXCOORD0;
           };
          // Input to fragment shader
           struct vertexOutput {
              float4 pos : SV_POSITION;
              float4 position_in_world_space : TEXCOORD0;
              float4 tex : TEXCOORD1;
           };
           
           // VERTEX SHADER
           vertexOutput vert(vertexInput input) 
           {
              vertexOutput output; 
              output.pos =  mul(UNITY_MATRIX_MVP, input.vertex);
              output.position_in_world_space = mul(unity_ObjectToWorld, input.vertex);
              output.tex = input.texcoord;
              return output;
           }
   
           // FRAGMENT SHADER
          float4 frag(vertexOutput input) : COLOR 
          {
              // Calculate distance to player position
              float dist = distance(input.position_in_world_space, _PlayerPosition);
   
               // Return appropriate colour
              if (dist < _VisibleDistance) {
                 return tex2D(_MainTex, float4(input.tex)); // Visible
              }
              else if (dist < _VisibleDistance + _OutlineWidth) {
                  return _OutlineColour; // Edge of visible range
              }
              else {
                  float4 tex = tex2D(_MainTex, float4(input.tex)); // Outside visible range
                  tex.a = 0;
                  return tex;
 
              }
           }
  
          ENDCG
          }
      } 
      //FallBack "Diffuse"
  }

The _PlayerPosition is given to shade by this code :

 using UnityEngine;
 using System.Collections;
      
 public class ProximityXray : MonoBehaviour {
      
     public Transform player;
     Renderer render;
      
     void Start () {
      
         render = gameObject.GetComponent<Renderer>();
      
     }
          
     void Update () {
      
         render.sharedMaterial.SetVector("_PlayerPosition", player.position);
      
     } 
 }

Thanks