Abstract
It is an effective method to use isosurface expressing inhomogeneous attribute field of solid objects inside. Due to the shortcomings such as topological ambiguity and segmentation ambiguity of the widely used isosurface algorithms (moving cube and moving tetrahedral), this paper presents an isosurface extraction algorithm based on generalized tri-prism voxel, which is called moving generalized triangular prism (MGTP) algorithm. The triangular patches are extracted from each generalized triangular prism (GTP) to establish the isosurface in this algorithm. In this paper, the linear interpolation algorithm is used to calculate the equivalent points and subdivision points, which can eliminate isosurface cracks. The topological structure of the equivalent patches is determined according to the number of GTP equivalent points. If there is topology ambiguity in GTP, isosurface is extracted after using the subdivision method to eliminate it. The MGTP algorithm can effectively solve the problem of topological ambiguity and segmentation ambiguity.
Foundation Support: National Natural Science Foundation of China (41272367).
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References
Simov, W.: Holding 3D Geoscientific Modeling Computer Technique for Geological Characterization. South Sea in Press, Hong Kong (1994)
Royse, K.R.: Combining numerical and cognitive 3D modelling approaches in order to determine the structure of the Chalk in the London Basin. J. Comput. Geosci. 36(2), 500–511 (2010)
Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. J. Comput. Graph. 21(4), 163–169 (1987)
Liu, S., Yang, X., Chen, K.: Segmentation MC algorithm-based method of ultrasound image 3D reconstruction. J. Tsinghua Univ. Sci. Technol. 50(8), 1214–1218 (2010). (in Chinese)
Liu, H., Wang, S., Lu, X.: The multi-storey medical image reconstruction based on marching cube algorithm. J. South-Central Univ. Nationalities Nat. Sci. Ed. 28(3), 79–84 (2009). (in Chinese)
Li, S., Tang, J., Wu, G.: Algorithm of geology mesh surface reconstruction based on constraints. J. Comput. Eng. 35(1), 253–254 (2009). (in Chinese)
Yang, H., Liu, M., Zhao, Y.: 3D geological modelling based on kriging and marching cube algorithm. J. Image Graph. 13(3), 531–535 (2008). (in Chinese)
Doi, A., Koide, A.: An Efficient method of triangulating qqui-valued surfaces by using tetrahedral cells. J. IEICE Trans. E 74(1), 214–224 (1991)
Nielson, G.M., Hamann, B.: The asymptotic decider: resolving the ambiguity in marching cubes. In: IEEE Visualization, San Diego, CA, pp. 83–91 (1992)
Lixin, W., Ruixin, Z., Yixin, Q., et al.: 3D Geoscience modelling and virtual mine system. J. Acta Geodaetica et Cartographica Sinica. 31(1), 28–33 (2002). (in Chinese)
Cheng, P., Gong, J., Shi, W., et al.: Geological object modeling based on quasi tri-prism volume and its application. J. Geomatics Inform. Sci. Wuhan Univ. 29(7), 607–607 (2004). (in Chinese)
Wu, L.: Topological relations embodied in a generalized tri-prism (GTP) model for A 3D geo-science modeling system. J. Comput. Geosci. 30(4), 405–418 (2005)
Cheng, P.G., Shi, W.Z., Gong, J.Y., et al.: QTPV data model and algorithm and its application to geological exploration engineering. J. Geo. Spat. Inform. Sci. 5(1), 64–71 (2005)
Zou, Y., He, J.: A spatial shape simulation method for three-dimensional geological body based on marching cubes algorithm. J. Acta Geodaetica et Cartographica Sinica. 41(6), 910–917 (2012). (in Chinese)
Durst, M.J: Letters: additional reference to “Marching Cubes”. J. Comput. Graph. 22(2), 72–73 (1988)
Natarajan, B.K.: On generating topologically consistent isosurfaces from uniform samples. J. Vis. Comput. 11(1), 52–62 (1994)
Nielson, G.M.: On marching cubes. J IEEE Trans. Vis. Comput. Graph. 9(3), 283–297 (2003)
Liang, X., Zhang, C.: A Topology complexity based method to approximate isosurface with trilinear interpolated triangular patch. J. Comput. Res. Dev. 43(3), 528–535 (2006). (in Chinese)
Li, C.: Geological data rendering based on MT algorithm. J. Digital Commun. 41(4), 35–38 (2014). (in Chinese)
Cignoni, P., Ganovelli, F., Montani, C., et al.: Reconstruction of topologically correct and adaptive trilinear surfaces. J Comput. Graph. 24(3), 399–418 (2000)
Cheng, L.: Research on the Surface Rendering Algorithm Based on Delaunay Tetrahedral Subdivision. Chengdu University of Technology, Chengdu (2015). (in Chinese)
Zhou, Y., Tang, Z.: Adaptive trilinear approximation to isosurfaces of data sets in 3D space. J. Chinese Comput. 17, 1–10 (1994). (in Chinese)
Li, Q., Cui, Y., Sun, L., Chen, C., Dong, Q.: Interpolation for layered ore considering difference of variation rate in along and through layer directions and application in the description of shale gas reservoir. In: 2015 Conference of Geological Society of China, p. 257 (2015) (in Chinese)
Xin, Z.: Research on 3D Geological Modeling and Visualization Use GTP method based on VTK. Liaoning Technical University, Fuxin (2012). (in Chinese)
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The authors gratefully acknowledge support from the National Natural Science Foundation of China (41272367).
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Li, Q., Li, Q., Liu, X., Wei, Z., Dong, Q. (2018). Isosurface Algorithm Based on Generalized Three Prism Voxel. In: Wang, Y., et al. Advances in Image and Graphics Technologies. IGTA 2017. Communications in Computer and Information Science, vol 757. Springer, Singapore. https://doi.org/10.1007/978-981-10-7389-2_3
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DOI: https://doi.org/10.1007/978-981-10-7389-2_3
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