The Journal of Supercomputing

, Volume 75, Issue 3, pp 1241–1255 | Cite as

Geometry-based methods for general non-planar perspective projections on curved displays

  • Mariano Pérez
  • Silvia Rueda
  • Juan M. OrduñaEmail author


Curved monitors are getting more and more popular nowadays, due to the immersive sensation they provide to users in front of planar monitors. The display in curved monitors is cylindrical surfaces with significant curvatures, which must be taken into account for an accurate projection of the rendered scene. In this paper, we propose new geometry-based methods for nonlinear projections over cylindrical surfaces (corresponding to the geometry of the curved monitor displays) instead of the traditional planar projections, which produce incorrect results on this kind of screens. The proposed methods allow accurate projections on curved screens, even in the case of non-symmetric view frustum, which is the typical view volume obtained either when stereoscopic techniques are used for creating the illusion of depth or when head-tracking is used and the projection equations must be adapted to the relative position of the user eyes. The proposed methods are designed to be implemented on modern programmable GPUs, and the performance evaluation results show that they easily achieve interactive refresh rates even with complex scenes, while they do not significantly reduce the system performance with respect to the case of planar projection.


Non-planar projections Non-symmetric view frustum Curved monitors Fish Tank VR 


  1. 1.
    Ardouin J, Lcuyer A, Marchal M, Marchand E (2014) Stereoscopic rendering of virtual environments with wide Field-of-Views up to 360. In: Proceedings of IEEE Virtual Reality, pp 3–8Google Scholar
  2. 2.
    Bayarri S (2009) Computing non-planar perspectives in real time. Comput Graph 19(3):431–440CrossRefGoogle Scholar
  3. 3.
    Boustila S, Capobianco A, Gnevaux O, Bechmann D (2016) New hybrid projection to widen the vertical field of view with large screen to improve the perception of personal space in architectural project review. In: Proceedings of IEEE Virtual Reality (VR), pp 159–160Google Scholar
  4. 4.
    Brosz J, Samavati FF, Carpendale MST, Sousa MC (2007) Single camera flexible projection. In: Proceedings of the 5th ACM International Symposium on Non-Photorealistic Animation and Rendering, pp 33–42Google Scholar
  5. 5.
    Gascuel J-D, Holzschuch N, Fournier G, Proche B (2008) Fast non-linear projections using graphics hardware. In: Proceedings of the Symposium on Interactive 3D Graphics and Games (I3D) ACM, pp 107–114Google Scholar
  6. 6.
    Lorenz H, Dollner J (2009) Real-time Piecewise Perspective Projections. In: Proceedings of GRAPP, pp 147–155Google Scholar
  7. 7.
    Mulder JD, Van Liere R (2000) Enhancing fish tank VR. In: Proceedings IEEE Virtual Reality, pp 91–98Google Scholar
  8. 8.
    Pérez M, Rueda S, Orduña JM (2017) Enabling the use of fish tank virtual reality systems with curved monitors. In: Proceedings of Computational and Mathematical Methods in Science and Engineering, pp 1665–1675Google Scholar
  9. 9.
    Petkov K, Papadopoulos C, Zhang M, Kaufman AE, Gu X (2012) Interactive visibility retargeting in vr using conformal visualization. IEEE Trans Vis Comput Graphcs 18(7):1027–1040CrossRefGoogle Scholar
  10. 10.
    Shreiner D, Sellers G, Kessenich J, Licea-Kane B (2013) OpenGL(R) programming guide: the official guide to learning OpenGL(R), versions 4.3, 8th edn. Addison-Wesley, BostonGoogle Scholar
  11. 11.
    Simon A, Smith RC, Pawlicki RR (2004) Omnistereo for panoramic virtual environment display systems. In: Proceedings of IEEE Virtual Reality, pp 67–73Google Scholar
  12. 12.
    Spindler M, Bubke M, Germer T, Strothotte T (2006) Camera textures. In: Proceedings of the 4th ACM International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia, pp 295–302Google Scholar
  13. 13.
    Trapp M, Lorenz H, Dllner J (2009) Interactive stereo rendering for non-planar projections of 3d virtual environments. In: Proceedings of GRAPP, pp 199–204Google Scholar
  14. 14.
    Ware C, Arthur K, Booth KS (1993) Fish tank virtual reality. In: Proceedings of the INTERACT’93 and CHI’93 Conference on Human Factors in Computing Systems, pp 37–42Google Scholar
  15. 15.
    Yang Y, Chen JX, Beheshti M (2005) Nonlinear perspective projections and magic lenses: 3D view deformation. IEEE Comput Graph Appl 25(1):76–84CrossRefGoogle Scholar
  16. 16.
    Zhao X, Zeng W, Gu XD, Kaufman AE, Xu W, Mueller K (2012) Conformal magnifier: a focus+ context technique with local shape preservation. IEEE Trans Vis Comput Graph 18(11):1928–1941CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de InformáticaUniversidad de ValenciaValenciaSpain

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