Abstract
The extraction of feature lines on surfaces approximated by dense polygon meshes provides an effective one dimensional visual cue for the understanding of 3D shapes. Detection of directions over meshes is a crucial prerequisite for the extraction of such feature lines as it determines where and how the lines should be generated on meshes. While the majority of the feature lines proposed so far are defined based on classical definition of curvature in a discrete differential geometry context, extraction of curvature information from an integral invariant viewpoint has been proposed comparatively recently. This paper provides a systematic discussion over various critical directions including but not limited to principal directions of curvature, based on integral invariants defined over local neighborhoods on meshes. We categorize the critical directions with our framework, address their implementation, and present the result of implementation and observation from the viewpoints of effectiveness, robustness and computational costs.
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References
Ohtake, Y., Belyaev, A., Seidel, H.: Ridge-valley lines on meshes via implicit surface fitting. In: Proceedings of ACM SIGGRAPH, pp. 609–612 (2004)
DeCarlo, D., Finkelstein, A., Rusinkiewicz, S., Santella, A.: Suggestive contours for conveying shape. In: Proceedings of ACM SIGGRAPH, pp. 848–855 (2003)
Judd, T., Durand, F., Adelson, E.: Apparent ridges for line drawing. ACM Trans. Graph. 26(3) (2007)
Xie, X., He, Y., Tian, F., Seah, H.-S., Gu, X., Qin, H.: An effective illustrative visualization framework based on photic extremum lines (PELs). IEEE Trans. Vis Comput. Graph. 13, 1328–1335 (2007)
Kolomenkin, M., Shimshoni, I., Tal, A.: Demarcating curves for shape illustration. ACM Trans. Graph. 27(5) (2008)
Rusinkiewicz, S.: Estimating curvatures and their derivatives on triangle meshes. In: Proceedings of 3D PVT, pp. 486–493 (2004)
Manay, S., Hong, B.-W., Yezzi, A.J., Soatto, S.: Integral invariant signatures. In: Pajdla, T., Matas, J. (eds.) Computer Vision—ECCV 2004, vol. 3024, pp. 87–99. Springer, Heidelberg (2004)
Connolly, M.: Measurement of protein surface shape by solid angles. J. Mol. Graph. 4(1), 3–6 (1986)
Yang, Y.-L., Lai, Y.-K., Hu, S.-M., Pottmann, H.: Robust principal curvatures on multiple scales. In: Polthier, K., Sheffer, A. (eds.) Eurographics Symposium on Geometry Processing (2006)
Pottmann, H., Wallner, J., Yang, Y.-L., Lai, Y.-K., Hu, S.-M.: Principal curvatures from the integral invariant viewpoint. Comput. Aided Geom. Des. 24(8–9), 428–442 (2007)
Clarenz, U., Rumpf, M., Telea, A.: Robust feature detection and local classification for surfaces based on moment analysis. IEEE TVCG 10 (2004)
Yasuda, Y.: Surrounded lines. Master’s thesis, The University of Tokyo (2009)
Max, N.L.: Horizon mapping: shadows for bump-mapped surfaces. Vis. Comput. 4(2), 109–117 (1988)
Hill, S.: Hardware accelerating art production. https://www.gamasutra.com/view/feature/130455/hardware_accelerating_art_.php. Last accessed 2018/05/13
Jylanki, J.: An exact algorithm for finding minimum oriented bounding boxes. http://clb.demon.fi/minobb/minobb.html. Last accessed 2018/05/11
Raskin, R.G.: Spatial analysis on the sphere: a review (94–7). https://escholarship.org/uc/item/5748n2xz. Last accessed 2018/05/11
Yaglom, I.M., Boltyanskii, V.G.: Convex figures, p. 9. Holt, Rinehart and Winston (1961)
Toussaint, G.: Solving geometric problems with the rotating calipers. In: Proceedings of IEEE MELECON, Athens (1983)
Suggestive Contours Homepage. http://gfx.cs.princeton.edu/proj/sugcon/. Last accessed 2018/05/14
Acknowledgements
We would like to thank Prof. Yong-Liang Yang, Dr. Yu-Kun Lai and Prof. Johannes Wallner for sharing the details of their implementation, Prof. Otto Röschel and Prof. Hans-Peter Schröcker for valuable discussions and anonymous reviewers for their constructive feedback.
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Gao, Q., Yamaguchi, Y. (2019). Detection of Critical Direction for Feature Line Extraction on Meshes Based on Local Integral Invariants. In: Cocchiarella, L. (eds) ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics. ICGG 2018. Advances in Intelligent Systems and Computing, vol 809. Springer, Cham. https://doi.org/10.1007/978-3-319-95588-9_20
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DOI: https://doi.org/10.1007/978-3-319-95588-9_20
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