Parametric Reconstruction of Bent Tube Surfaces

We present a method for parametric reconstruction of a piecewise defined pipe surface, consisting of cylinder and torus segments, from an unorganized point set. Our main contributions are reconstruction of the spine curve of a pipe surface from surface samples, and approximation of the spine curve by G^1 continuous circular arcs and line segments. Our algorithm accurately outputs the parametric data required for bending machines to create the reconstructed tube.