Reconstruction of helices from their orthogonal projection

We describe a method for modeling helices from planar curves. Given a polygonal curve in the (x,y) plane, the method computes a helix such that its orthogonal projection onto the (x,y) plane fits the polygonal curve. The helix curve is first sampled and the transformation matrix that best aligns points of the sampled helix to those of the polygonal curve is calculated. This transformation matrix is then used to estimate the parameters of the helix whose projection fits the polygonal curve.