aarg:
You have to pass through the arguments to the constructor, as I have done with an LCD class:
class sevenSegment : public HT1621
{
public:
sevenSegment(byte selectPin, byte rwPin, byte dataPin);
//..........
}; // end class
// then the implementation...
// constructor:
sevenSegment::sevenSegment(byte selectPin, byte rwPin, byte dataPin)
: HT1621(selectPin, rwPin, dataPin) {}
Thanks, I didn't remember the colon trick 
Okay, maybe not what you wanted exactly. But it's a start. Unless I misunderstand you, you wish to internalize the constructor parameters. In my case, the result of that would be losing the ability to define multiple displays.
As I'm using a shield, that can be stacked only once (on top), only one instance is ever required.
RayLivingston:
But not the best way to handle it. See the link I posted...
I've moved everything into the class declaration, now it works as expected.
But I'm not sure what you mean with "best way". Which way would you prefer?
And another question:
Since I want a singleton, can I move the instance variable also into the header file?
How do I prevent multiple variables then?
I'd guess that then I have to duplicate the declaration in the related cpp file, so that the variable is allocated in that module?