Geometry - equation of an arbitrary orientated cylinder

[mathcrazy]

Hi Dan,

I am trying to solve the same problem, I am having numerous xyz data for the surface of cylinder, and cylinder is not parallel to any axis. Can you suggest me some solution to find out axis and radius of the cylinder, if you would like, I can provide you the data which I have, thanks in advance.

[Avni Pllana]

Post by mathcrazy
Hi Dan,
I am trying to solve the same problem, I am having
numerous xyz data for the surface of cylinder, and
cylinder is not parallel to any axis. Can you suggest
me some solution to find out axis and radius of the
cylinder, if you would like, I can provide you the
data which I have, thanks in advance.

Let P be a point through which passes the cylinder axis, and d be a unit length vector parallel to the cylinder axis. Let R be the radius of the cylinder. Then we have

|r-p|^2 - ((r-p)*d)^2 = R^2 ,

where r is the position vector of cylinder points.
So we need at least 7 points to determine the cylinder.

Best regards,
Avni