Single-View 3D Reconstruction of Curves

This paper describes a method to generate a 3D curve from a planar polygonal curve. One application of such method is the modeling of trajectories of moving objects in 3D using sketches. Given a planar polygonal curve \(C_{2D}\) , our algorithm computes a 3D curve \(C_{3D}\) such that its orthogonal projection matches the input curve. The algorithm aims at minimizing the variation of the curvature along the reconstructed curve. The driving idea is to fit a set of ellipses to the input curve; these ellipses enable us to determine the osculating circles and thus the tangent at every point of the curve to reconstruct in 3D. The reconstruction of 3D curve using these tangents is then straightforward. The method is demonstrated with several examples.