Radio Psychedelica

I have become mesmerized by the Reprap and by the CandyFab. Sure, I'll admit it.
I can imagine printing things - useful things, like dino skulls and monstrously expanded ants.
I made the mistake of mentioning this to RenegadeMime, who was eating popcorn and jeering at Alvin Toffler.
He held up a popcorn kernal. "This would look good the size of a baseball." he said, "But how would you deal with the pixelization? If I wanted to look at voxels, I'd build popcorn out of Lego."
Vectors. I suggested.
"Hah." he said. And went back to reciting Future Shock in reverse, which he claims is the equivelent to time travel.
Most printers are built with stepper moters and a x-y ( and sometimes z) cartesian grids because they are conceptually simple and easy to manipulate.

But an extruder is basically a pen, with 'solid' ink. If I am drawing with a marker, I don't have pixelization problems - because I can draw real curves without staircasing.
Without the dreaded 'jaggies'.
If I used polar co-ordinates rather than cartesian, I could draw any arc - including the 'arc of infinite radius' AKA the 'straight' line.

Limits do arise; for a polar plotter, viz;
'Pen Width'...which dictates the narrowest line,
'Stroke Length'...which dictates the shortest line,
'Angular Resolution'...which dictates how similar two dis-similar lines can be,
'Integerization'...which forces all endpoints to snap to an intrinsic grid.