Noticing that in the HDRI only image, there's no shadow on the ground. Is there a particular trick to making one appear in HDRI-background type scenes?

Only thing I could think of is to make some kind of invisible shader that picks up the shadow, and apply that to a ground plane. Does that sound right? Is there such an invisible shader included anywhere, or is that something I'm going to have to make up on the fly?

What you want is the shadow catcher shader but it doesnt work with GI...you need DCG plugin to do work with GI:

http://www.digitalcarversguild.com/plugin.php?ProductId=13

In the top shader assing a Lightning Model > Shadow Catcher, but this dont work with GI like I said you will need the DCG plugin to work with Sky Light or Indirect Light

I can't believe you still need to buy a shader for that. That bug should have been fixed long time ago....! :(

Quote - Only thing I could think of is to make some kind of invisible shader that picks up the shadow, and apply that to a ground plane. Does that sound right? Is there such an invisible shader included anywhere, or is that something I'm going to have to make up on the fly?

You can use Carrara's standard shadow catcher for your plane's shader.  Then add a distant light with no more than 25% brightness and turn on its soft shadows in its Effects properties.  Works great without buying a plug-in.

yep, I gotta admit it's a tricky problem.  if the only object in the scene is the reflecting sphere,
and there's an hdri background but no ground plane, there's nothing on which to apply the
shadow catcher shader.

Quote - yep, I gotta admit it's a tricky problem.  if the only object in the scene is the reflecting sphere,
and there's an hdri background but no ground plane, there's nothing on which to apply the
shadow catcher shader.

You must create a Infinite Plane or Plane object then apply the shadow catcher on it.

Are you using GI in this image?

Yes.  But I'm not using the DCG GI Shadow Catcher plug-in.

How do you get Shadow Catcher to work with GI without the plugin? I did many tests here and it dont work.

See 7 posts up.

Ahh it works for source lights but not for HDRI light...

Just point the distant light to match the HDRI's bright spot.

shonner, in the above image, why is there a window reflection on the chrome sphere
where it faces the camera, but no light coming from that direction? 
one would also need to blur the sphere to match the general blurriness of the hdri IMVHO.

There is a much much brighter light source to the left than behind the camera.  In theory, I could have added a second distant light behind the camera.  But the sun was coming from the other window.

I could have blurred things.  I could have turned on AA.  I could have turned on Sky Light.  I could have scaled the sphere better for the room.  I could have posted this in the gallery.

But this was just a draft area render from the Assembly Room (I spent only a minute to set up the scene) to show that Carrara can do shadow catching.  The Carrara manual has two pages describing the feature.