Three js rotation of objects around a sphere

Question

I am using a particle system to evenly distribute points on a sphere. That works great. I then place instances of a given geometry on those points. This part also works. I would now like to rotate those geometries to match the surface angle of the sphere.

Here is the function so far :

function placeGeometryAtPlatonicPoints (points) {
  var len = points.length -1,
    x, y, z,
    geometry,
    // subgroup a group to apply the rotations to
    subgroup = new THREE.Object3D(),
    mesh,
    material = new THREE.MeshLambertMaterial({
      color: 0x0992299
    }),
    r,
    theta,
    varphi;

  // I wait to append this group because I am waiting for the 
  // particles to settle into there positions
  scene.add(group);

  for (len; len >= 0; len -= 1) {
    // Geometry could be any geometry I am just using a cube to test.
    geometry = new THREE.CubeGeometry( 25, 25, 25, 1, 1, 1 );
    x = points[len].x;
    y = points[len].y;
    z = points[len].z;

    // Move the geometry to the point on the sphere. 
    geometry.applyMatrix( new THREE.Matrix4().makeTranslation(x, y, z) );

    mesh = new THREE.Mesh( geometry, material );
    subgroup.add(mesh);

    // This next portion is just some guess work about 
    // polar and azimuth coordinates
    r = Math.sqrt(Math.pow(x,2) + Math.pow(y,2) + Math.pow(z,2));
    theta = Math.acos(z/r);
    varphi = Math.atan(y/x);

    theta = theta * (180/Math.PI);
    varphi = varphi * (180/Math.PI);

    console.log({
      theta : theta,
      varphi : varphi
    });

    // This would be the implementation of the rotation degrees.
    subgroup.rotation.x = 0;
    subgroup.rotation.y = 0;
    subgroup.rotation.z = 0;

    group.add(subgroup);
  }
}

I am new to Three js, so if there is a better way to do all of this please let me know. Here is my WIP. You will have to give it a second to place the particle correctly before rendering the geometry. I could speed this up but i like the animation : )

Answer 1

If you want you cubes to be rotated so they are tangent to the sphere, then think of each cube as being on the end of a stick.

The stick is an Object3D located at the origin. The cube is a child of the stick located at ( 0, 0, r ). Now rotate the stick to where you want. ( But avoid the north and south poles. )

var parent = new THREE.Object3D();
scene.add( parent );

var stick = new THREE.Object3D();
var point = new THREE.Vector3( x, y, z );
stick.lookAt( point );
parent.add( stick );

var geometry = new THREE.CubeGeometry( 25, 25, 25, 1, 1, 1 );
var mesh = new THREE.Mesh( geometry, material );
mesh.position.set( 0, 0, r );
stick.add( mesh );

three.js r.64