Checking for a Tic-Tac-Toe winner using Rays with THREE.js. You can find more at my blog, blog.tempt3d.com.

createTTTrays.js

function createRays() {

  var setup = {
      xDirection: xDirection = new THREE.Vector3(-1,0,0),
      yDirection: yDirection = new THREE.Vector3(0,-1,0),
      zDirection: zDirection = new THREE.Vector3(0,0,-1),
      xy1Direction: xy1Direction = new THREE.Vector3(-1,-1,0).normalize(),
      xy2Direction: xy2Direction = new THREE.Vector3(-1,1,0).normalize(),
      xz1Direction: xz1Direction = new THREE.Vector3(-1,0,-1).normalize(),
      xz2Direction: xz2Direction = new THREE.Vector3(-1,0,1).normalize(),
      yz1Direction: yz1Direction = new THREE.Vector3(0,-1,-1).normalize(),
      yz2Direction: yz2Direction = new THREE.Vector3(0,1,-1).normalize(),
      xyz1Direction: xyz1Direction = new THREE.Vector3(-1,-1,-1).normalize(),
      xyz2Direction: xyz2Direction = new THREE.Vector3(1,-1,-1).normalize(),
      xyz3Direction: xyz3Direction = new THREE.Vector3(-1,-1,1).normalize(),
      xyz4Direction: xyz4Direction = new THREE.Vector3(1,-1,1).normalize(),
      length: 20
  };


  // should be 27 of these guys.
  create2DVectors(setup);

  // should be 18 of these guys  (for a 3x3x3)
  create2DDiagonals(setup);

  // should be 4 of these guys
  create3DDiagonals(setup);
}

function create2DVectors (setup) {

  var i,j,
      x,y,z,
      arrow,
      origin,
      ray;

  // create 9 rays looking down X
  for(i = 0; i < gameDimensions; i++){
    for(j = 0; j < gameDimensions; j++){

      x = 4 * cubeSeparation;
      y = (i - 1) * cubeSeparation;
      z = (j - 1) * cubeSeparation;

      origin = new THREE.Vector3(x,y,z);
      arrow = new THREE.ArrowHelper(setup.xDirection, origin, setup.length, 0xFF0000);

      _demo.scene.add(arrow);
      _demo.arrows.push(arrow);

      ray = new THREE.Raycaster(origin, setup.xDirection);
      ray.num = '6';
      rays.push(ray);
    }
  }

  // create 9 rays looking down Y
  for(i = 0; i < gameDimensions; i++){
    for(j = 0; j < gameDimensions; j++){

      y = 4 * cubeSeparation;
      x = (i - 1) * cubeSeparation;
      z = (j - 1) * cubeSeparation;

      origin = new THREE.Vector3(x,y,z);
      arrow = new THREE.ArrowHelper(setup.yDirection, origin, setup.length, 0x00FF00);

      _demo.scene.add(arrow);
      _demo.arrows.push(arrow);

      ray = new THREE.Raycaster(origin, setup.yDirection);
      ray.num = '6';
      rays.push(ray);

    }
  }

  // create 9 rays looking down Z
  for(i = 0; i < gameDimensions; i++){
    for(j = 0; j < gameDimensions; j++){

      z = 4 * cubeSeparation;
      y = (i - 1) * cubeSeparation;
      x = (j - 1) * cubeSeparation;

      origin = new THREE.Vector3(x,y,z);
      arrow = new THREE.ArrowHelper(setup.zDirection, origin, setup.length, 0x0000FF);

      _demo.scene.add(arrow);
      _demo.arrows.push(arrow);

      ray = new THREE.Raycaster(origin, setup.zDirection);
      ray.num = '6';
      rays.push(ray);
    }
  }
}

function create2DDiagonals(setup) {

  var i,j,
      x,y,z,
      arrow1,
      arrow2,
      origin1,
      origin2,
      ray1,
      ray2;

  // create 6 rays for XY diagonals
  for(i = 0; i < gameDimensions; i++){

      x = 4 * cubeSeparation;
      y = 4 * cubeSeparation;
      z = (i - 1) * cubeSeparation;

      origin1 = new THREE.Vector3(x,y,z).add(jigger);
      origin2 = new THREE.Vector3(x,-y,z).add(jigger);

      arrow1 = new THREE.ArrowHelper(setup.xy1Direction, origin1, setup.length, 0xCC0000);
      arrow2 = new THREE.ArrowHelper(setup.xy2Direction, origin2, setup.length, 0xCC0000);

      _demo.scene.add(arrow1);
      _demo.scene.add(arrow2);

      _demo.arrows.push(arrow1);
      _demo.arrows.push(arrow2);

      ray1 = new THREE.Raycaster(origin1, setup.xy1Direction);
      ray2 = new THREE.Raycaster(origin2, setup.xy2Direction);

      ray1.num = '3';
      ray2.num = '3';

      rays.push(ray1);
      rays.push(ray2);
  }

  // create 6 rays for XZ diagonals
  for(i = 0; i < gameDimensions; i++){

      x = 4 * cubeSeparation;
      y = (i - 1) * cubeSeparation;
      z = 4 * cubeSeparation;

      origin1 = new THREE.Vector3(x,y,z).add(jigger);
      origin2 = new THREE.Vector3(x,y,-z).add(jigger);

      arrow1 = new THREE.ArrowHelper(setup.xz1Direction, origin1, setup.length, 0x00CC00);
      arrow2 = new THREE.ArrowHelper(setup.xz2Direction, origin2, setup.length, 0x00CC00);

      _demo.scene.add(arrow1);
      _demo.scene.add(arrow2);

      _demo.arrows.push(arrow1);
      _demo.arrows.push(arrow2);

      ray1 = new THREE.Raycaster(origin1, setup.xz1Direction);
      ray2 = new THREE.Raycaster(origin2, setup.xz2Direction);

      ray1.num = '3';
      ray2.num = '3';

      rays.push(ray1);
      rays.push(ray2);
  }

  // create 6 rays for YZ diagonals
  for(i = 0; i < gameDimensions; i++){

      x = (i - 1) * cubeSeparation;
      y = 4 * cubeSeparation;
      z = 4 * cubeSeparation;

      origin1 = new THREE.Vector3(x,y,z).add(jigger);
      origin2 = new THREE.Vector3(x,-y,z).add(jigger);

      arrow1 = new THREE.ArrowHelper(setup.yz1Direction, origin1, setup.length, 0x0000CC);
      arrow2 = new THREE.ArrowHelper(setup.yz2Direction, origin2, setup.length, 0x0000CC);

      _demo.arrows.push(arrow1);
      _demo.arrows.push(arrow2);

      _demo.scene.add(arrow1);
      _demo.scene.add(arrow2);

      ray1 = new THREE.Raycaster(origin1, setup.yz1Direction);
      ray2 = new THREE.Raycaster(origin2, setup.yz2Direction);

      ray1.num = '3';
      ray2.num = '3';

      rays.push(ray1);
      rays.push(ray2);

  }
}

function create3DDiagonals (setup) {

  var i,j,
      x,y,z,
      arrow1, arrow2, arrow3, arrow4,
      origin1, origin2, origin3, origin4,
      ray1, ray2, ray3, ray4,
      distance = 4 * cubeSeparation;

  x = distance;
  y = distance;
  z = distance;

  origin1 = new THREE.Vector3(x,y,z);
  origin2 = new THREE.Vector3(-x,y,z);
  origin3 = new THREE.Vector3(x,y,-z);
  origin4 = new THREE.Vector3(-x,y,-z);

  arrow1 = new THREE.ArrowHelper(setup.xyz1Direction, origin1, setup.length, 0x333333);
  arrow2 = new THREE.ArrowHelper(setup.xyz2Direction, origin2, setup.length, 0x333333);
  arrow3 = new THREE.ArrowHelper(setup.xyz3Direction, origin3, setup.length, 0x333333);
  arrow4 = new THREE.ArrowHelper(setup.xyz4Direction, origin4, setup.length, 0x333333);

  _demo.arrows.push(arrow1);
  _demo.arrows.push(arrow2);
  _demo.arrows.push(arrow3);
  _demo.arrows.push(arrow4);

  _demo.scene.add(arrow1);
  _demo.scene.add(arrow2);
  _demo.scene.add(arrow3);
  _demo.scene.add(arrow4);

  ray1 = new THREE.Raycaster(origin1, setup.xyz1Direction);
  ray2 = new THREE.Raycaster(origin2, setup.xyz2Direction);
  ray3 = new THREE.Raycaster(origin3, setup.xyz3Direction);
  ray4 = new THREE.Raycaster(origin4, setup.xyz4Direction);

  rays.push(ray1);
  rays.push(ray2);
  rays.push(ray3);
  rays.push(ray4);

}