Find the point of a line after which it dissapears - three.js

Question

I want to position x,y,z labels (sprites) on the axis I have in my scene. The problem is that zooming with the camera , should result to also moving the particles analogously so they stay in the side of the "screen".

So I just want to find a way to always know where the lines of x,y,z are out of the camera to update the labels' positions : fiddle (here they are just static).

the pseudocode of what I might need to acheve that :

    function update() { 
      var pointInLinePosition = calculateLastVisiblePointOfXline();
      xSprite.position.set(pointInLinePosition.x, pointInLinePosition.y, pointInLinePosition.z);
    }

    function calculateLastVisiblePointOfXline(){
    } 

Answer 1

I found a solution which is satisfying enough (for me at least) but not perfect.

Firstly I create a frustum using the scene's camera :

var frustum = new THREE.Frustum();
frustum.setFromMatrix( new THREE.Matrix4().multiplyMatrices(camera.projectionMatrix, camera.matrixWorldInverse ) );

Then, I check if any of the planes of the frustum intersects with any of the lines I have in the scene :

for (var i = frustum.planes.length - 1; i >= 0; i--) { 

      var py = frustum.planes[i].intersectLine( new THREE.Line3( new THREE.Vector3(0,0,0), new THREE.Vector3(1000,0,0) ) ) ; 
      if(py !== undefined) {
        ySprite.position.x = py.x-1 ;  
      }

      var px = frustum.planes[i].intersectLine( new THREE.Line3( new THREE.Vector3(0,0,0), new THREE.Vector3(0,0,1000) ) ) ; 
      if(px !== undefined) {
        xSprite.position.z = px.z-1 ; 
      }

    };

If there is an intersection, I update the labels' position using the return value of the intersectLine() which is the point of intersection.

This is the updated fiddle : fiddle

I hope that helps. In my case it fit.