Someone refresh my memory about cannons?

[Blutsauger]

They need to be able to see the base of the target they are shooting at, yes?

 

[Hanblack Nagash]

Yes they do. They have to see the point in the ground they want to land the shot.

 

[Vipoid]

They need to be able to see the base of the target they are shooting at, yes?

Only if they're actually shooting at its base.

If they're aiming in front of it (i.e. at a point on the table) then they only need to be able to see that point.

 

[Demian]

Or they can also see the model they want to shoot at (ie: Terrorgheist's face / body for example, but not the wings).

Shooting "at bases" is more common, to calculate the cannonball's bounce and such, and it is a very good idea to obscure such point with anything (monstruous things work best for this) to make the shot more difficult to strike their intended target.

But if they cannot see the terrain, they can also risk it a bit and nominate the one thing they can see as a first target point (true line of sight here) and just hope to roll low on the first artillery dice.