The Is-It-A-Circle Question
Given a finite set of points (say, around 15 points) in 3 dimensions, determine if those
points all lie on a circle (to within a certain degree of accuracy).
In general, you must come up with an algorithm for testing the points. The points may be
completely and utterly noncircular in nature (in which case your algorithm should say
“not a circle”), the points may be almost a circle but not quite, such as being bent out of
shape by 20% or curved a little out of a plane (in which case your algorithm should still
say “not a circle”) or it may be almost a perfect circle, in which case I very much hope
your algorithm will say “yes a circle, thank you.”
You should use linear algebra as part of the algorithm. In general, it is a good idea to
split the problem into two parts:
1) try to put all the 3d points into a single 2D plane
2) given points in 2d, determine if those are all in a circle
If you write an actual computer program, that would be awesome. At the very least, you
will have to use some computer program (such as Matlab or Mathematica) to help out
since otherwise it will be too much work to do by hand.
I will give you a few sets of data points, and you must demonstrate that your algorithm
correctly classifies each set.