Subdivision vertex normal interpolation

Question

I'm using GLSL 4.0 to write a subdivision routine that divides the triangles on an object through a geometry shader. I'm not using barycentric co-ordinates but vector arithmetic to output the triangle vertices. I managed to get the subdivision working but I don't understand how to interpolate the vertex normals to produce the correct shading:

#version 400 

layout(triangles) in;
layout(triangle_strip, max_vertices = 93) out; //MAX 128

uniform mat4 mvMatrix;
uniform mat4 pMatrix;
uniform mat3 normalMatrix; //mv matrix without translation
uniform int subdivision_level;
uniform vec4 lightPosition_camSpace; //light Position in camera space

uniform int time;

in data
{
  vec4 position_camSpace;
  vec3 normal_camSpace;
  vec2 textureCoordinate;
  vec4 color;
}vertexIn[3];

out fragmentData
{
  vec4 position_camSpace;
  vec3 normal_camSpace;
  vec2 textureCoordinate;
  vec4 color;
} frag;


void emit_triangle(vec4 position, vec4 width, vec4 hyp, float s) {

    /* NORMALS NOT FIXED */

    //A
    gl_Position = position;
    frag.color = vertexIn[0].color;
    frag.position_camSpace = vertexIn[0].position_camSpace;
    frag.normal_camSpace = vertexIn[0].normal_camSpace;
    frag.textureCoordinate = vertexIn[0].textureCoordinate;
    EmitVertex();

    //B
    gl_Position = position + width;
    frag.color = vertexIn[1].color;
    frag.position_camSpace = vertexIn[1].position_camSpace;
    frag.normal_camSpace = vertexIn[1].normal_camSpace;
    frag.textureCoordinate = vertexIn[1].textureCoordinate;

    EmitVertex();

    //C
    gl_Position = position + hyp;
    frag.color = vertexIn[2].color;
    frag.position_camSpace = vertexIn[2].position_camSpace;
    frag.normal_camSpace = vertexIn[2].normal_camSpace;
    frag.textureCoordinate = vertexIn[2].textureCoordinate;

    EmitVertex();

    EndPrimitive();
}

void main() {

  // A gl_In[0].gl_Position;
  // B gl_In[1].gl_Position;
  // C gl_In[2].gl_Position;

  float s = 1/pow(2,subdivision_level);
  int triangles_render = int(1/s);


  vec4 hyp_off = vec4(0.0,0.0,0.0,0.0);
  vec4 width_off = vec4(0.0,0.0,0.0,0.0);

  vec4 position = gl_in[0].gl_Position;
  vec4 width = s*(gl_in[1].gl_Position - gl_in[0].gl_Position);
  vec4 hyp = s*(gl_in[2].gl_Position - gl_in[0].gl_Position);

  vec4 hyp_off_f = vec4(0.0,0.0,0.0,0.0);
  vec4 width_off_f = width;


  for (int i=0; i<=subdivision_level+1; i++) {
    for (int j=0; j<triangles_render-i; j++) {

      // Normal triangle
      emit_triangle(position + hyp_off + width_off, width, hyp,s);
      width_off += width;  

      // Flipped triangle
      if (j <triangles_render-i-1)
      {
        emit_triangle(position + width_off_f + hyp_off_f, hyp, hyp - width,s);
        width_off_f += width;
      }

    }
    hyp_off += hyp;
    width_off = vec4(0.0,0.0,0.0,0.0);

    hyp_off_f += hyp;
    width_off_f = width;

  }
}

Currently the result looks like flat shading because I just use the normals of the vertices from the vertex shader. How do I compute the correct normals so that the shading looks correct? Also do I need to modify the vertex position too? I'm unsure about this part. I've read Why does my OpenGL Phong shader behave like a flat shader? But they use barycentric co-ordinates for the solution.