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Graph."],"published-print":{"date-parts":[[2010,3]]},"abstract":"<jats:p>This article introduces an optimization approach for modeling and rendering impossible figures. Our solution is inspired by how modeling artists construct physical 3D models to produce a valid 2D view of an impossible figure. Given a set of 3D locally possible parts of the figure, our algorithm automatically optimizes a view-dependent 3D model, subject to the necessary 3D constraints for rendering the impossible figure at the desired novel viewpoint. A linear and constrained least-squares solution to the optimization problem is derived, thereby allowing an efficient computation and rendering new views of impossible figures at interactive rates. 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