Dear all, I misinterpreted the original question, thinking the spiral involved was a helix! The bitmap certainly helps formulate the problem, albeit a hugh file!
The solution below is not quite as requested - the length was required from information only on the line spacing and the overall diameter of the spiral. Owing to the maths involved, a more practical component is the angle the spiral has swept through, measured in radians (2 pi radians = 360 degrees, i.e. one revolution). If the spiral has gone through 2 revolutions then the angle you will need to use is 4 pi etc. Let A be the angle swept through in radians Let w be the width apart of the lines Then Length = (w / 4 * pi) * [(arc sinh A) + (A * sqrt (1 + A*A))] A*A is the angle squared, sqrt is the square root, and arc sinh is the inverse hyperbolic sine function. As you can see, this is a bit of a mouthful and may be more exact than you require! For any point on the spiral to the same point one line out, an approximation based on the circumference of the circle half way between them may be close enough. ie if the radii of the inner point is r and that of the outer point one revolution further out is R, then what I guess to be a reasonable approximation would be 2 * pi * (R - r) Unfortunately I don't have a scientific calculator at work to be able to do some trial calculations to see if this is true. Perhaps someone else would be kind enough to oblige... Hope this helps, whatever you need it for! David Higgon London
