Place a local vector-based child grid in Three.js

Question

I need help positioning the grid for specific points that are set according to local coordinates. I created pink cylinders with a height of 0.1 to demonstrate my local cubic points that I want to touch each other.

I also want cube2 to be a child of cube1, but at the moment this is not a deal interruption.

Expected result: cubes touch with their specific angles and correct rotation - pink cylinders should be perfectly overlapped by pixels.

I tried to solve this problem with

cube2.position.copy(cube_position.clone().add(cube2_position))
cube2.rotation.setFromVector3(cube_rotation.clone().add(cube2_rotation))

But this does not work as expected. Should I use some kind of Matrix transformation?

const scene = new THREE.Scene();
const camera = new THREE.PerspectiveCamera(45, window.innerWidth / window.innerHeight, 1, 1000);
camera.position.set(25, 25, 12);
// setup cubes

var geometry = new THREE.CubeGeometry(6, 6, 6);
var material = new THREE.MeshLambertMaterial({
  color: 0x00fff0
});
var cube = new THREE.Mesh(geometry, material);
scene.add(cube);

cube.position.set(0.3, 1, -2);
cube.rotation.set(Math.PI / 3, Math.PI / 2, 1)

var geometry2 = new THREE.CubeGeometry(4, 4, 4);
var material2 = new THREE.MeshLambertMaterial({
  color: 0x0fff00
});
var cube2 = new THREE.Mesh(geometry2, material2);
cube.add(cube2);

cube_position = new THREE.Vector3(3, 3, 3)
cube_rotation = new THREE.Vector3(Math.PI / 3, Math.PI / 4, 0)
cube2_position = new THREE.Vector3(2, -2, 2)
cube2_rotation = new THREE.Vector3(Math.PI / 2, Math.PI / 2, 0)

// visualize points
vmat = new THREE.MeshLambertMaterial({
  color: 0xFF00FF,
  opacity: 0.5,
  transparent: true
});
v1 = new THREE.Mesh(new THREE.CylinderGeometry(1, 1, 0.1, 10), vmat);
cube.add(v1)
v1.position.copy(cube_position)
v1.rotation.setFromVector3(cube_rotation)

v2 = new THREE.Mesh(new THREE.CylinderGeometry(1, 1, 0.1, 10), vmat);
cube2.add(v2)
v2.position.copy(cube2_position)
v2.rotation.setFromVector3(cube2_rotation)

// BUG: connect cube with cube2 on specified points

cube2.position.copy(cube_position.clone().add(cube2_position))
cube2.rotation.setFromVector3(cube_rotation.clone().add(cube2_rotation))

// setup rest
var pointLight = new THREE.PointLight(0xFFFFFF);
pointLight.position.x = 10;
pointLight.position.y = 50;
pointLight.position.z = 130;
scene.add(pointLight)

const renderer = new THREE.WebGLRenderer({
  antialias: true
});
renderer.setSize(window.innerWidth, window.innerHeight);
renderer.setClearColor(0x20252f);
renderer.setPixelRatio(window.devicePixelRatio);
document.body.appendChild(renderer.domElement);

const controls = new THREE.OrbitControls(camera, renderer.domElement);

animate();

function animate() {
  requestAnimationFrame(animate);
  render();
}

function render() {
  renderer.render(scene, camera);
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.2.3/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r82/three.js"></script>
<script src="https://yume.human-interactive.org/examples/buffer-geometry/OrbitControls.js"></script>

Run codeHide result

Answer 1

, Matrix . , cube2.

• cube1, cube2, v1, v2: v2 , v1 . , ( ). :

  V1opposite.w = V2.w
  V1opposite.l * C1.w = V2.l * C2.l * C1.l
  V1opposite.l = V2.l * C2.l
  C2.l = V1opposite.l * V2.l(-1)
  

  V1opposite.w v1 , V2.w - v2 , C cube, V2.l(-1) v2. cube2.

• v1 v2 . , : v2 cube2, cube2. cube2 v2 v1, cube2, cube2 cube1, cube1, cube2.

jsfiddle .

, .

, v1 v2.

//connect obj1 and obj2 on obj1 point1 and obj2 point2.
function connect(obj1,obj2,point1,point2)
{
    var point1World = new THREE.Vector3().copy(point1).applyMatrix4(obj1.matrixWorld);
    var point2World = new THREE.Vector3().copy(point2).applyMatrix4(obj2.matrixWorld);
    var translation = new THREE.Vector3().subVectors(point1World,point2World);
    var obj2World = new THREE.Vector3().copy(obj2.getWorldPosition());
    obj2World.add(translation);
    if(obj2.parent !== null)
    {
        var inverseMatrix = new THREE.Matrix4().getInverse(obj2.parent.matrixWorld);
        obj2World.applyMatrix4(inverseMatrix);
    }
    obj2.position.copy(obj2World);
}

, cube1 cube2. jsfiddle