Fast Screen Space Curvature Estimation on GPU

Martin Prantl, Libor Váša, Ivana Kolingerová

2016

Abstract

Curvature is an important geometric property in computer graphics that provides information about the behavior of object surfaces. The exact curvature can only be calculated for a limited set of surfaces description. Most of the time, we deal with triangles, point sets or some other discrete representation of the surface. For those, curvature computation is problematic. Moreover, most of existing algorithms were developed for static geometry and can be slow for interactive modeling. This paper proposes a screen space method which estimates the mean and Gaussian curvature at interactive rates. The algorithm uses positions and normals to estimate the curvature from the second fundamental form matrix. Using the screen space has advantages over the classical approach: low-poly geometry can be used and additional detail can be added with normal and bump maps. The screen space curvature can be easily added to existing rendering pipelines. The proposed algorithm was tested on several models and it outperforms current state-of-the-art GPU approaches.

References

  1. Boschiroli, M., Fünfzig, C., Romani, L., and Albrecht, G. (2012). {G1} rational blend interpolatory schemes: A comparative study. Graphical Models, 74(1):29 - 49.
  2. Fünfzig, C., Müller, K., Hansford, D., and Farin, G. (2008). Png1 triangles for tangent plane continuous surfaces on the gpu. In Proceedings of Graphics Interface 2008, GI 7808, pages 219-226, Toronto, Ont., Canada, Canada. Canadian Information Processing Society.
  3. Gray, A. (1997). Surfaces in 3-dimensional space via mathematica. In Modern Differential Geometry of Curves and Surfaces with Mathematica, chapter 17, pages 394-401. CRC Press, Inc., Boca Raton, FL, USA, 2nd edition.
  4. Griffin, W., Wang, Y., Berrios, D., and Olano, M. (2012). Real-time gpu surface curvature estimation on deforming meshes and volumetric data sets. IEEE TVCG, 18(10):1603-1613.
  5. Hattori, T., Kubo, H., and Morishima, S. (2011). Real time ambient occlusion by curvature dependent occlusion function. In SIGGRAPH Asia 2011 Posters, SA 7811, pages 48:1-48:1, New York, NY, USA. ACM.
  6. Magid, E., Soldea, O., and Rivlin, E. (2007). A comparison of gaussian and mean curvature estimation methods on triangular meshes of range image data. Computer Vision and Image Understanding, 107(3):139 - 159.
  7. Mellado, N. (2015). Screen space curvature using cuda/c++ (algorithm implementation from patate library).
  8. Mellado, N., Barla, P., Guennebaud, G., Reuter, P., and Duquesne, G. (2013). Screen-space curvature for production-quality rendering and compositing. In ACM SIGGRAPH 2013 Talks, SIGGRAPH 7813, pages 42:1-42:1, New York, NY, USA. ACM.
  9. Meyer, M., Desbrun, M., Schröder, P., and Barr, A. (2003). Discrete differential-geometry operators for triangulated 2-manifolds. In Hege, H.-C. and Polthier, K., editors, Visualization and Mathematics III, Mathematics and Visualization, pages 35-57. Springer Berlin Heidelberg.
  10. Razdan, A. and Bae, M. (2005). Curvature estimation scheme for triangle meshes using biquadratic bzier patches. CAD, 37(14):1481 - 1491.
  11. Rusinkiewicz, S. (2004). Estimating curvatures and their derivatives on triangle meshes. In Proceedings of the 3DPVT 7804, 2Nd International Symposium, pages 486-493, Washington, DC, USA. IEEE Computer Society.
  12. Theisel, H., Rossi, C., Zayer, R., and Seidel, H.-P. (2004). Normal based estimation of the curvature tensor for triangular meshes. In CG&A, 2004. PG 2004. Proceedings. 12th Pacific Conference on , pages 288-297.
  13. Yang, P. and Qian, X. (2007). Direct computing of surface curvatures for point-set surfaces. In Botsch, M., Pajarola, R., Chen, B., and Zwicker, M., editors, Eurographics Symposium on Point-Based Graphics. The Eurographics Association.
  14. Zhihong, M., Guo, C., Yanzhao, M., and Lee, K. (2011). Curvature estimation for meshes based on vertex normal triangles. CAD, 43(12):1561 - 1566.
Download


Paper Citation


in Harvard Style

Prantl M., Váša L. and Kolingerová I. (2016). Fast Screen Space Curvature Estimation on GPU . In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016) ISBN 978-989-758-175-5, pages 151-160. DOI: 10.5220/0005676801490158


in Bibtex Style

@conference{grapp16,
author={Martin Prantl and Libor Váša and Ivana Kolingerová},
title={Fast Screen Space Curvature Estimation on GPU},
booktitle={Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016)},
year={2016},
pages={151-160},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005676801490158},
isbn={978-989-758-175-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016)
TI - Fast Screen Space Curvature Estimation on GPU
SN - 978-989-758-175-5
AU - Prantl M.
AU - Váša L.
AU - Kolingerová I.
PY - 2016
SP - 151
EP - 160
DO - 10.5220/0005676801490158