var DEFAULT_NORMALS_EPSILON = 1e-6;
var DEFAULT_FACE_EPSILON = 1e-6;

//Estimate the vertex normals of a mesh
exports.vertexNormals = function(faces, positions, specifiedEpsilon) {

  var N         = positions.length;
  var normals   = new Array(N);
  var epsilon   = specifiedEpsilon === void(0) ? DEFAULT_NORMALS_EPSILON : specifiedEpsilon;

  //Initialize normal array
  for(var i=0; i<N; ++i) {
    normals[i] = [0.0, 0.0, 0.0];
  }

  //Walk over all the faces and add per-vertex contribution to normal weights
  for(var i=0; i<faces.length; ++i) {
    var f = faces[i];
    var p = 0;
    var c = f[f.length-1];
    var n = f[0];
    for(var j=0; j<f.length; ++j) {

      //Shift indices back
      p = c;
      c = n;
      n = f[(j+1) % f.length];

      var v0 = positions[p];
      var v1 = positions[c];
      var v2 = positions[n];

      //Compute infineteismal arcs
      var d01 = new Array(3);
      var m01 = 0.0;
      var d21 = new Array(3);
      var m21 = 0.0;
      for(var k=0; k<3; ++k) {
        d01[k] = v0[k]  - v1[k];
        m01   += d01[k] * d01[k];
        d21[k] = v2[k]  - v1[k];
        m21   += d21[k] * d21[k];
      }

      //Accumulate values in normal
      if(m01 * m21 > epsilon) {
        var norm = normals[c];
        var w = 1.0 / Math.sqrt(m01 * m21);
        for(var k=0; k<3; ++k) {
          var u = (k+1)%3;
          var v = (k+2)%3;
          norm[k] += w * (d21[u] * d01[v] - d21[v] * d01[u]);
        }
      }
    }
  }

  //Scale all normals to unit length
  for(var i=0; i<N; ++i) {
    var norm = normals[i];
    var m = 0.0;
    for(var k=0; k<3; ++k) {
      m += norm[k] * norm[k];
    }
    if(m > epsilon) {
      var w = 1.0 / Math.sqrt(m);
      for(var k=0; k<3; ++k) {
        norm[k] *= w;
      }
    } else {
      for(var k=0; k<3; ++k) {
        norm[k] = 0.0;
      }
    }
  }

  //Return the resulting set of patches
  return normals;
}

//Compute face normals of a mesh
exports.faceNormals = function(faces, positions, specifiedEpsilon) {

  var N         = faces.length;
  var normals   = new Array(N);
  var epsilon   = specifiedEpsilon === void(0) ? DEFAULT_FACE_EPSILON : specifiedEpsilon;

  for(var i=0; i<N; ++i) {
    var f = faces[i];
    var pos = new Array(3);
    for(var j=0; j<3; ++j) {
      pos[j] = positions[f[j]];
    }

    var d01 = new Array(3);
    var d21 = new Array(3);
    for(var j=0; j<3; ++j) {
      d01[j] = pos[1][j] - pos[0][j];
      d21[j] = pos[2][j] - pos[0][j];
    }

    var n = new Array(3);
    var l = 0.0;
    for(var j=0; j<3; ++j) {
      var u = (j+1)%3;
      var v = (j+2)%3;
      n[j] = d01[u] * d21[v] - d01[v] * d21[u];
      l += n[j] * n[j];
    }
    if(l > epsilon) {
      l = 1.0 / Math.sqrt(l);
    } else {
      l = 0.0;
    }
    for(var j=0; j<3; ++j) {
      n[j] *= l;
    }
    normals[i] = n;
  }
  return normals;
}