If you go with one of the suggestions to use a graphics package to draw
the arc, you can then take the resulting bitmap image and iterate over
it to see which pixels are black and which are white.
But, I'm wondering about your comment that, "Using trigonometry is too
expensive". Trig is cheaper than you think, because it's all done down
in the C libraries, and I wouldn't be surprised if it's not pushed all
the way down to the hardware on most modern machines. Compared to your
Python application code, I suspect the amount of trig needed for this
problem isn't going to be a major factor in timing.
Are you guessing that trig is too slow, or have you actually done some
profiling to measure whether it is or not?
What's the resolution required? Let's assume a 1k x 1k image with the
sensor in the center and you need 1 degree angular resolution. There's
about 2200 pixels in each 1-degree sector. You could pre-compute those
and store 360 sets of 2200 pixels each (about 800k points total). For
any given 30 degree sector, just "or" together the 30 1-degree slices
and you've got your set of pixels for that sector.
Will it be fast enough? Beats me, but it's easy to test.
A side comment here if I may. Your 1 degree assumption is, generally
speaking, an extremely coarse answer in terms of the accuracy needed, as we
need accuracies a lot closer to an arc-second than to a whole degree in
robotics.
To get an idea, assume a pick-n-place arm that has to retrieve the part
from whatever method delivers it to within reach of the arm, the arms total
joint to joint to joint length is 4 feet, and that the part is being
delivered hot as in 700F, while the piece it will be installed on is fresh
from contact with a block of dry ice. So its a shrink fit, a one time
assembly because once the temps equalize, the part will be shrunk into
place so tightly that it can only be removed by a lathe.
So the accuracy needed to place this part properly at the start of the push
to set it in place is .01mm, and the push into position must be done to a
..01mm accuracy before the parts freeze together.
I know, this is a bit like asking if that persimmon branch will hold 2
opossums, but what is the accuracy needed in arc seconds per joint
(counting the arms pivot joint, and an articulated wrist for part
orientation, makes at least 5 joints, to pull this motion off every 15
seconds on some GM part assembly line at Delphi?
Real world problem guys. My own experience with machine vision says that
without cameras and video processing running at 1000x the speeds of what I
can buy on fleabay, its way to slow (see camview-emc for an example) to
actually be used in a production line environment, they don't have time for
the arm to stop just short of where its going, take a closeup pix & wait
3-5 seconds for the video to be processed, and then apply the corrective
moves to 'get it right'.
This isn't even worth a reply, its even off-topic, but when an OP posits a
problem, he should posit it in terms of his real world targets, as should
the answers proposed. The correct answer may well help your parent company
sell Delphi some new machines at 5 mil/copy.
Cheers, Gene
--
"There are four boxes to be used in defense of liberty:
soap, ballot, jury, and ammo. Please use in that order."
-Ed Howdershelt (Author)
Wedding is destiny, and hanging likewise.
-- John Heywood
A pen in the hand of this president is far more
dangerous than 200 million guns in the hands of
law-abiding citizens.
