How can I perform a Hit Test on one specifc 3d object in WPF?

Question

I have a SphereMesh (inherits from MeshGeneratorBase as part of the Petzold.Media3D.dll) in my WPF 3D Scene. I also have thousands of ScreenSpaceLines3D objects on that sphere. I want to ignore everything in my scene except the SphereMesh and find out the X-Y-Z coordinate of where my mouse ray intersects with the sphere only. Even if there is another object X between the sphere and the mouse, I still want to know where the mouse would hit the sphere, as if object X didn't exist.

I've tried the below code using HitTest, but as I add thousands/millions of other objects in my scene/world, it becomes extremely slow. And the object obstruction issue is another problem I can't resolve.

What do you recommend?

Current code:

Point mousePos = new Point(x, y);
PointHitTestParameters hitParams = new PointHitTestParameters(mousePos);
VisualTreeHelper.HitTest(
    viewPort,null,
    delegate(HitTestResult hr)
    {
        RayMeshGeometry3DHitTestResult rayHit = hr as RayMeshGeometry3DHitTestResult;
    if(rayHit != null)
    {
        // Mouse hits something
        Console.WriteLine("Point: " + rayHit.PointHit);
    }
    return HitTestResultBehavior.Continue;
}, hitParams);

Any help?

Thanks.