Modeling and Rendering of Impossible Figures

Tai-Pang WU, Chi-Wing FU, Sai-Kit Yeung, Jiaya Jia, and Chi-Keung Tang

ACM Transactions on Graphics (ACM TOG), vol. 29, No. 2, Article 13, March 2010.
to be presented in SIGGRAPH 2010.


This paper 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-square 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.


Click the following link to download:
  • Paper: pdf (20.7MB)
  • Presentation video:


    author = {Tai-Pang Wu and Chi-Wing Fu and Sai-Kit Yeung and Jiaya Jia and Chi-Keung Tang},
    title = {Modeling and Rendering of Impossible Figures},
    journal = {ACM Transactions on Graphics},
    month = {August},
    year = {2010},
    volume = {29},
    number = {2},
    pages = {13:1--13:15},