Mouse / Canvas X, Y to Three.js World X, Y, Z

Question

I've searched around for an example that matches my use case but cannot find one. I'm trying to convert screen mouse co-ordinates into 3D world co-ordinates taking into account the camera.

Solutions I've found all do ray intersection to achieve object picking.

What I am trying to do is position the center of a Three.js object at the co-ordinates that the mouse is currently "over".

My camera is at x:0, y:0, z:500 (although it will move during the simulation) and all my objects are at z = 0 with varying x and y values so I need to know the world X, Y based on assuming a z = 0 for the object that will follow the mouse position.

This question looks like a similar issue but doesn't have a solution: Getting coordinates of the mouse in relation to 3D space in THREE.js

Given the mouse position on screen with a range of "top-left = 0, 0 | bottom-right = window.innerWidth, window.innerHeight", can anyone provide a solution to move a Three.js object to the mouse co-ordinates along z = 0?

Answer 1

In r.58 this code works for me:

var planeZ = new THREE.Plane(new THREE.Vector3(0, 0, 1), 0);
var mv = new THREE.Vector3(
    (event.clientX / window.innerWidth) * 2 - 1,
    -(event.clientY / window.innerHeight) * 2 + 1,
    0.5 );
var raycaster = projector.pickingRay(mv, camera);
var pos = raycaster.ray.intersectPlane(planeZ);
console.log("x: " + pos.x + ", y: " + pos.y);

Answer 2

to get the mouse coordinates of a 3d object use projectVector:

var width = 640, height = 480;
var widthHalf = width / 2, heightHalf = height / 2;

var projector = new THREE.Projector();
var vector = projector.projectVector( object.matrixWorld.getPosition().clone(), camera );

vector.x = ( vector.x * widthHalf ) + widthHalf;
vector.y = - ( vector.y * heightHalf ) + heightHalf;

to get the three.js 3D coordinates that relate to specific mouse coordinates, use the opposite, unprojectVector:

var elem = renderer.domElement, 
    boundingRect = elem.getBoundingClientRect(),
    x = (event.clientX - boundingRect.left) * (elem.width / boundingRect.width),
    y = (event.clientY - boundingRect.top) * (elem.height / boundingRect.height);

var vector = new THREE.Vector3( 
    ( x / WIDTH ) * 2 - 1, 
    - ( y / HEIGHT ) * 2 + 1, 
    0.5 
);

projector.unprojectVector( vector, camera );
var ray = new THREE.Ray( camera.position, vector.subSelf( camera.position ).normalize() );
var intersects = ray.intersectObjects( scene.children );

There is a great example here. However, to use project vector, there must be an object where the user clicked. intersects will be an array of all objects at the location of the mouse, regardless of their depth.

Answer 3

Below is an ES6 class I wrote based on WestLangley's reply, which works perfectly for me in THREE.js r77.

Note that it assumes your render viewport takes up your entire browser viewport.

class CProjectMousePosToXYPlaneHelper
{
    constructor()
    {
        this.m_vPos = new THREE.Vector3();
        this.m_vDir = new THREE.Vector3();
    }

    Compute( nMouseX, nMouseY, Camera, vOutPos )
    {
        let vPos = this.m_vPos;
        let vDir = this.m_vDir;

        vPos.set(
            -1.0 + 2.0 * nMouseX / window.innerWidth,
            -1.0 + 2.0 * nMouseY / window.innerHeight,
            0.5
        ).unproject( Camera );

        // Calculate a unit vector from the camera to the projected position
        vDir.copy( vPos ).sub( Camera.position ).normalize();

        // Project onto z=0
        let flDistance = -Camera.position.z / vDir.z;
        vOutPos.copy( Camera.position ).add( vDir.multiplyScalar( flDistance ) );
    }
}

You can use the class like this:

// Instantiate the helper and output pos once.
let Helper = new CProjectMousePosToXYPlaneHelper();
let vProjectedMousePos = new THREE.Vector3();

...

// In your event handler/tick function, do the projection.
Helper.Compute( e.clientX, e.clientY, Camera, vProjectedMousePos );

vProjectedMousePos now contains the projected mouse position on the z=0 plane.

Answer 4

Here is my take at creating an es6 class out of it. Working with Three.js r83. The method of using rayCaster comes from mrdoob here: Three.js Projector and Ray objects

    export default class RaycasterHelper
    {
      constructor (camera, scene) {
        this.camera = camera
        this.scene = scene
        this.rayCaster = new THREE.Raycaster()
        this.tapPos3D = new THREE.Vector3()
        this.getIntersectsFromTap = this.getIntersectsFromTap.bind(this)
      }
      // objects arg below needs to be an array of Three objects in the scene 
      getIntersectsFromTap (tapX, tapY, objects) {
        this.tapPos3D.set((tapX / window.innerWidth) * 2 - 1, -(tapY / 
        window.innerHeight) * 2 + 1, 0.5) // z = 0.5 important!
        this.tapPos3D.unproject(this.camera)
        this.rayCaster.set(this.camera.position, 
        this.tapPos3D.sub(this.camera.position).normalize())
        return this.rayCaster.intersectObjects(objects, false)
      }
    }

You would use it like this if you wanted to check against all your objects in the scene for hits. I made the recursive flag false above because for my uses I did not need it to be.

var helper = new RaycasterHelper(camera, scene)
var intersects = helper.getIntersectsFromTap(tapX, tapY, 
this.scene.children)
...

Answer 5

Although the provided answers can be useful in some scenarios, I hardly can imagine those scenarios (maybe games or animations) because they are not precise at all (guessing around target's NDC z?). You can't use those methods to unproject screen coordinates to the world ones if you know target z-plane. But for the most scenarios, you should know this plane.

For example, if you draw sphere by center (known point in model space) and radius - you need to get radius as delta of unprojected mouse coordinates - but you can't! With all due respect @WestLangley's method with targetZ doesn't work, it gives incorrect results (I can provide jsfiddle if needed). Another example - you need to set orbit controls target by mouse double click, but without "real" raycasting with scene objects (when you have nothing to pick).

The solution for me is to just create the virtual plane in target point along z-axis and use raycasting with this plane afterward. Target point can be current orbit controls target or vertex of object you need to draw step by step in existing model space etc. This works perfectly and it is simple (example in typescript):

screenToWorld(v2D: THREE.Vector2, camera: THREE.PerspectiveCamera = null, target: THREE.Vector3 = null): THREE.Vector3 {
    const self = this;

    const vNdc = self.toNdc(v2D);
    return self.ndcToWorld(vNdc, camera, target);
}

//get normalized device cartesian coordinates (NDC) with center (0, 0) and ranging from (-1, -1) to (1, 1)
toNdc(v: THREE.Vector2): THREE.Vector2 {
    const self = this;

    const canvasEl = self.renderers.WebGL.domElement;

    const bounds = canvasEl.getBoundingClientRect();        

    let x = v.x - bounds.left;      

    let y = v.y - bounds.top;       

    x = (x / bounds.width) * 2 - 1;     

    y = - (y / bounds.height) * 2 + 1;      

    return new THREE.Vector2(x, y);     
}

ndcToWorld(vNdc: THREE.Vector2, camera: THREE.PerspectiveCamera = null, target: THREE.Vector3 = null): THREE.Vector3 {
    const self = this;      

    if (!camera) {
        camera = self.camera;
    }

    if (!target) {
        target = self.getTarget();
    }

    const position = camera.position.clone();

    const origin = self.scene.position.clone();

    const v3D = target.clone();

    self.raycaster.setFromCamera(vNdc, camera);

    const normal = new THREE.Vector3(0, 0, 1);

    const distance = normal.dot(origin.sub(v3D));       

    const plane = new THREE.Plane(normal, distance);

    self.raycaster.ray.intersectPlane(plane, v3D);

    return v3D; 
}

Answer 6

You do not need to have any objects in your scene to do this.

You already know the camera position.

Using vector.unproject( camera ) you can get a ray pointing in the direction you want.

You just need to extend that ray, from the camera position, until the z-coordinate of the tip of the ray is zero.

You can do that like so:

var vec = new THREE.Vector3(); // create once and reuse
var pos = new THREE.Vector3(); // create once and reuse

vec.set(
    ( event.clientX / window.innerWidth ) * 2 - 1,
    - ( event.clientY / window.innerHeight ) * 2 + 1,
    0.5 );

vec.unproject( camera );

vec.sub( camera.position ).normalize();

var distance = - camera.position.z / vec.z;

pos.copy( camera.position ).add( vec.multiplyScalar( distance ) );

The variable pos is the position of the point in 3D space, "under the mouse", and in the plane z=0.

---

EDIT: If you need the point "under the mouse" and in the plane z = targetZ, replace the distance computation with:

var distance = ( targetZ - camera.position.z ) / vec.z;

three.js r.98