Real-Time Scalable Motion Planning for Crowds

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 spline curve of a pipe surface from surface samples, and approximation of the spline curve by G¹ continuous circular arcs and line segments. Our algorithm accurately outputs the parametric data required for bending machines to create the reconstructed tube.