Abstract
The performance of shading and ray-tracing algorithms depends heavily on the quality of the surface normal information. As a result, in many visual applications normal information turns out to be more important than spatial information. This paper proposes a logistic model for the degradation of the normal information resulting from the quantisation of the vertex coordinates. The mesh is degraded by the randomization of each vertex coordinate after its t-th significant bit. The normal degradation is computed as a weighted average of the angle differences between the normals of the original triangles and the corresponding degraded triangles. The proposed model is validated experimentally. As an application, we use the proposed logistic model to estimate suitable levels of quantisation for 3D triangle meshes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gouraud, H.: Continuous Shading of Curved Surfaces. IEEE Transactions on Computers 20, 623–629 (1971)
Phong, B.T.: Illumination for Computer Generated Pictures. ACM Commun. 18, 311–317 (1975)
Walter, B., Zhao, S., Holzschuch, N., Bala, K.: Single Scattering in Refractive Media with Triangle Mesh Boundaries. In: SIGGRAPH, pp. 1–8. ACM Press, New York (2009)
Jin, S., Lewis, R.R., West, D.: A Comparison of Algorithms for Vertex Normal Computation. The Visual Computer 21, 71–82 (2005)
Meyer, Q., Susharpmuth, J., Susharpner, G., Stamminger, M., Greiner, G.: On Floating-Point Normal Vectors. Computer Graphics Forum 29, 1405–1409 (2010)
Pauly, M., Mitra, N.J., Guibas, L.J.: Uncertainty and Variability in Point Cloud Surface Data. In: Symposium on Point-Based Graphics, pp. 77–84. Eurographics Press, Aire-la-Ville (2004)
Kalaiah, A., Varshney, A.: Statistical Geometry Representation for Efficient Transmission and Rendering. ACM Transactions on Graphics 24, 348–373 (2005)
Gray, R., Stockham, T.: Dithered quantizers. IEEE Transactions on Information Theory 39, 805–812 (1993)
Touma, C., Gotsman, C.: Triangle Mesh Compression. In: Graphics Interface, pp. 26–34. Canadian Human-Computer Communications Society, Waterloo (1998)
Alliez, P., Desbrun, M.: Progressive Compression for Lossless Transmission of Triangle Meshes. In: SIGGRAPH, pp. 195–202. ACM Press, New York (2001)
Choe, S., Kim, J., Lee, H., Lee, S.: Random Accessible Mesh Compression Using Mesh Chartification. IEEE Transactions on Visualization and Computer Graphics 15, 160–173 (2009)
Isenburg, M., Ivrissimtzis, I., Gumhold, S., Seidel, H.-P.: Geometry Prediction for High Degree Polygons. In: 21st Spring Conference on Computer Graphics (SCCG 2005), pp. 147–152. ACM Press, New York (2005)
Yoon, M., Ivrissimtzis, I., Lee, S.: Variational Bayesian Noise Estimation of Point Sets. Computers & Graphics 33, 226–234 (2009)
Ivrissimtzis, I.: Effects of Noise on Quantized Triangle Meshes. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, J.-L., Mørken, K., Schumaker, L.L. (eds.) MMCS 2008. LNCS, vol. 5862, pp. 274–284. Springer, Heidelberg (2010)
Pham, H.: Springer Handbook of Engineering Statistics. Springer, London (2006)
Chao, M.-W., Lin, C.-H., Yu, C.-W., Lee, T.-Y.: A High Capacity 3D Steganography Algorithm. IEEE Transactions on Visualization and Computer Graphics 15, 274–284 (2009)
Yang, Y., Ivrissimtzis, I.: Polygonal Mesh Watermarking Using Laplacian Coordinates. Computer Graphics Forum (Eurographics/ACM SIGGRAPH Symposium on Geometry Processing 2010) 29, 1585–1593 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yang, Y., Ivrissimtzis, I. (2012). A Logistic Model for the Degradation of Triangle Mesh Normals. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_46
Download citation
DOI: https://doi.org/10.1007/978-3-642-27413-8_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27412-1
Online ISBN: 978-3-642-27413-8
eBook Packages: Computer ScienceComputer Science (R0)