How can I determine if two polygons overlap?

I have a sandcastle

What I am trying to do is determine whether two polygons overlap. However, I only care if they overlap if all of the points from the polygons could be visible.

To solve this problem, my plan is to:

  1. project the points from the polygons to the window
  2. using the projected polygons, perform an easy 2D polygon intersection
  3. win

Projecting points from the polygons is easy using Cesium.SceneTransforms.wgs84ToWindowCoordinates.

The problem I am having is I am not sure how to determine whether or not a point in a polygon is facing away from the window. How can I do that?

One idea I had was the following:

function testPolygon() {
  source.entities.values.forEach( (entity) => {
    const name =;
    const positions = entity.polygon.hierarchy.valueOf().positions;
    const camera =;
    const cameraDirection = camera.direction;
    const cameraFrustum = camera.frustum;
    const cameraNearDistance = cameraFrustum.near;
    const nearPlane = new Cesium.Plane( cameraDirection, cameraNearDistance )
    const origin = new Cesium.Cartesian3()
    positions.forEach( (position) => {
      const windowCoordinate = Cesium.SceneTransforms.wgs84ToWindowCoordinates(viewer.scene, position);
      console.log( "position", position );
      const positionRay = new Cesium.Ray( origin, position )
      const intersection = Cesium.IntersectionTests.rayPlane( positionRay, nearPlane )

The idea here is to construct the near plane from the camera, create a ray from the globe origin ( (0,0,0)? ), and then do an intersection test.

However, it is not working. But, I am not sure why. I am missing something fundamental, but I am not sure what that is yet.

Hi there,

There are some great geospatial helper libraries available which can help with these kinds of calculations, for example turf.js.

Thank you. I found turf as well. Turd did help resolve this issue.

I still needed to determine whether or not a polygon was visible or not. The reason was to limit the number of polygon intersection calculations I needed to do, which I believe is a more expensive operation. For that I used the core of the solution mentioned above. I thought it was not working, but it apparently does.

I had a fixed set of polygons that weren’t going to change. For that set, created a bounding sphere for each one. I could then use:

const cullingVolume = cameraFrustum.computeCullingVolume(camera.position, camera.direction, camera.up)

for an initial pass.

For that pass the cullingVolume check, I am doing one more check, but will probably get rid of it soon as it appears unnecessary.

const windowCoordinate = Cesium.SceneTransforms.wgs84ToWindowCoordinates(viewer.scene,
const positionRay = new Cesium.Ray(origin,
const intersection = Cesium.IntersectionTests.rayPlane(positionRay, nearPlane)

Then, I start using turf.intersect to check the polygons that get through both passes.

I am pretty sure I am not taking into account the curvature of the globe, but a few small errors in my calculation are acceptable.