List the coordinates of the known points of the helix, with the “z” coordinates in ascending order. Each point should have an “x,” “y” and “z” coordinate. Typically, the “x” and “y” coordinates represent the radial aspect of the helix, while the “z” coordinates provide its length.
Determine the radius of the circle formed by the “x” and “y” coordinates of the points. If the center of the circle formed by the helix is at the origin, then this is easy, since "x² + y² = r²" when the center is at (0,0). If the center is not at the origin, then this may still be a fairly simple process, provided two of the points share the same “x” coordinate or the same “y” coordinate. In that case, the two points might constitute end points of a diameter of the circle, in which case you can find the radius by calculating the distance between the points and cutting that amount in half. Alternatively, “r” can be determined if any have the points have 0 for the “z” coordinate, since "x = rcos(t)" and the cosine of 0 is 1.0.
Calculate the distance between any points sharing identical pairs of “x” and “y” coordinates. If more than one pair of points share “x” and “y” coordinates, choose the pair with the shortest distance between points. This distance will be a multiple of "2πc."
Divide the shortest distance between parallel “z’s” by "2π." If there is only one loop connecting the two points, that should provide you with the “c” constant in the equations for the helix. Plug the value into the equation "z = c(t)," and the radius value into the “x” and “y” equations, to see if the value works for the coordinates. If the points do not satisfy the equations, there may be one or more loops between the points, so try multiples of the value for “c” until you find one that works.