How can I project points through different coordinate spaces?

The OpenMayaUI API's M3dView class has several methods for doing this. An example of projecting a 3d worldspace point to 2d screen-space can be found here:

• How can I convert a 3d point to 2d screen space?

Here's an overview of the pertinent methods:

• viewToWorld : Takes a point in port coordinates and returns a corresponding ray in world coordinates. Takes a point in port coordinates and returns a point on the near and far clipping planes.
• viewToObjectSpace : Takes a point in port coordinates and returns a corresponding ray in object coordinates.
• worldToView : Converts a point in world space to port space.
• projectionMatrix : Returns the projection matrix currently being used by OpenGL in the current view.
• modelViewMatrix : Returns the modelview matrix currently being used by OpenGL in the current view.