- Generate shadows over curved surfaces ?
Absolutely. Both shadow volumes and shadow mapping handles this perfectly. Any engine after Doom 3 should do it, provided the hardware is powerful enough.
- Generate reflection on curved surfaces ?
Yes and no. The effect would be convincing enough for most situations, but not physically correct. Especially self reflection is tricky.
Usually, an object would use a reflection cube map, rendered from a single sample point and use the object normal only to interpolate it.
Flat surfaces like water or building glass facades could use a reflection rendered to a normal texture, and just disort it based on the bump/normal map.
- Generate reflections from parts of a scene that haven't rendered before ?
Yes. Wether or not the reflected part has been rendered before is irrelevant.
You might be thinking about *refraction* where you could first render the lake bottom, disort it and render the water surface on top of it.
- Turn on / Off individual lights and have this lights affect the global illumination of the scene ?
- Move lights randomly at the scene and have these lights affect ambient occlusion and indirect illumination ?
Some engines can do this. If the engine supports dynamic global illumination, you should be able to move/turn on lights in realtime. Otherwise it would just be a precomputed lightmap.
Ambient Occlusion has nothing to do with light sources. It's kind of the point of it.
- Move / Destroy objects and have this affect shadows and illumination ?
Any effect that does not rely on precomputed light mapping woudl work just fine with this.
- Simulate prism like light decomposition ?
I have never heard of an engine that supports this. I guess it's a very minor effect in most games, not worth implementing.
There are however some shader demos showing off pretty convincing prismatic effects.
If it is the caustics you are after, they are very difficult to replicate accurately. I've seen some pretty nice faked ocean floor caustics in demos, though. Not sure if any engine does it out of the box.