Abstract: 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. Once the optimized model is available, a variety of compelling rendering effects can be applied to the impossible figure.