Casting a ray and randomly coloring a cube with THREE.js. See full code here: https://github.com/cubicleDowns/webgl-code-samples

rayprojection.js

    function listeners () {
      document.addEventListener('click', castRay, false);
    }

    function castRay (event) {

      event.preventDefault();

      var mouse = {};

      // since this isn't a full screen app, lets use the dimensions of the container div.
      mouse.x = (event.clientX / demo.jqContainer.width()) * 2 -1;
      mouse.y = -(event.clientY / demo.jqContainer.height()) * 2 + 1;

      var vector = new THREE.Vector3(mouse.x, mouse.y, 1);
      demo.projector.unprojectVector(vector, demo.cameras.liveCam);

      var ray = new THREE.Raycaster(demo.cameras.liveCam.position, vector.sub(demo.cameras.liveCam.position).normalize());

      // Casting a ray to find if there is an intersection.
      // Notice I reference an array of the cubes previously added to the scene.
      //   This is to prevent the ray from intersecting with any non-cube objects.
      var intersected = ray.intersectObjects( demo.collisions );

      // removing previous click marker
      $(".clickMarkers").remove();

      // appending a click marker.
      demo.jqContainer.append('<div class="clickMarkers" style="pointer-events:none; position: absolute; z-index: 100; left: ' + event.offsetX + 'px; top: ' + event.offsetY +'px">D</div>' );

      if(intersected.length > 0) {
        // slap a random color on that cube, yo.
        intersected[0].object.material.color = demo.setup.randomColor();
      }
    }