An engine that automatically reconstructs a large variety of polyhedral, origami and wire-frame objects from single-view sketched drawings generated in a calligraphic interface is presented. The engine has two stages. An innovative optimisation-based line-drawing beautifier stage is introduced to convert rough sketches into tidied-up line drawings. Optimisation-based 3D reconstruction follows. Solutions are provided with which to overcome the problems associated with earlier approaches to optimisationbased 3D reconstruction. Suitable adjustments in the optimisation algorithms are proposed; simple and efficient tentative models are introduced, and current regularities are categorised in order to allow the objective function to be simplified. All three actions help to prevent local optima and improve the computational efficiency of optimisation-based 3D reconstruction. They all proved to be effective techniques to reduce the typical failure rate of optimisation approaches. A discussion of results that validate the engine is also provided.4

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We aim to reconstruct three-dimensional polyhedral solids from axonometric-like line drawings. A new approach is proposed to make use of planes of mirror symmetry detected in such sketches. Taking account of mirror symmetry of such polyhedra can significantly improve the reconstruction process. Applying symmetry as a regularity in optimisation-based reconstruction is shown to be adequate by itself, without the need for other inflation techniques or regularities. Furthermore, symmetry can be used to reduce the size of the reconstruction problem, leading to a reduction in computing time.

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An education-oriented computer application to draw sketches of polyhedrons that are automatically recognized to reconstructs the suitable three-dimensional models is presented. The users can modify the sketches and see the reaction their modifications have on the models.Earliest classroom tests show that the capacity for spatial vision is improved.