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Abstract: This paper presents an intuitive, freehand sketching application for Computer Aided Design (CAD) that can reconstruct a 3D object from a single, flat, freehand sketch. A pen is used to draw 2D sketches consisting of straight and curved strokes connected at vertices. The sketches are processed by a reconstruction algorithm that uses the angular distribution of the strokes and their connectivity to determine an orthogonal 3D axis system whose projection correlates with the observed stroke orientations. The axis system is used to determine a plausible depth for each vertex. This approach works well for drawings of objects whose edges predominantly conform to some overall orthogonal axis system. A second, independent optimization procedure is then used to reconstruct each curved stroke in the original sketch, assuming that the curve is planar. New strokes can be attached to the 3D object, or drawn directly onto the object''s faces. An implementation of the reconstruction algorithm based on Levenberg–Marquardt optimization allows objects with over 50 strokes to be reconstructed in interactive time. [Copyright &y& Elsevier]