You can draw on a PGraphics pg and say pg.noLights();
The PGraphics must have the same size as your canvas.
Then you can perform checks on the canvas.
You can then draw objects (in the rotating 3d scene) with different unique colors and get() the colors from pg which would identify the single objects.
Use
color clickedObj = pg.get(mouseX,mouseY);
cf. Looking for more resources about ArrayLists - #45 by Chrisir