Abstract
In this paper, we describe a new algorithm to compute in linear time a 3D planar polygonal curve from a planar digital curve, that is a curve which belongs to a digital plane. Based on this algorithm, we propose a new method for converting the boundary of digital volumetric objects into polygonal meshes which aims at providing a topologically consistent and invertible reconstruction, i.e. the digitization of the obtained object is equal to the original digital data. Indeed, we do not want any information to be added or lost. In order to limit the number of generated polygonal faces, our approach is based on the use of digital geometry tools which allow the reconstruction of large pieces of planes.
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References
Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3D surface construction algorithm. In: SIGGRAPH, Computer Graphics (ACM), Anaheim, USA, vol. 21, pp. 163–169 (1987)
Lewiner, T., Lopes, H., Vieira, A.W., Tavares, G.: Efficient implementation of marching cubes’ cases with topological guarantees. JGT 8, 1–15 (2003)
Nielson, G.M.: Dual marching cubes. In: IEEE Visualization, pp. 489–496. IEEE Computer Society, Los Alamitos (2004)
Montani, C., Scateni, R., Scopigno, R.: Discretized marching cubes. In: Proceedings of the Conference on Visualization, Los Alamitos, CA, USA, pp. 281–287 (1994)
Lachaud, J.O., Montanvert, A.: Continuous analogs of digital boundaries: A topological approach to iso-surfaces. Graph. Mod. and Im. Proc. 62, 129–164 (2000)
Françon, J., Papier, L.: Polyhedrization of the boundary of a voxel object. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 425–434. Springer, Heidelberg (1999)
Klette, R., Sun, H.J.: Digital planar segment based polyhedrization for surface area estimation. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, pp. 356–366. Springer, Heidelberg (2001)
Sivignon, I., Dupont, F., Chassery, J.-M.: Reversible polygonalization of a 3D planar discrete curve: Application on discrete surfaces. In: Andrès, É., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 347–358. Springer, Heidelberg (2005)
Andres, E.: Discrete linear objects in dimension n: the Standard model. Graphical Models 65, 92–111 (2003)
Buzer, L.: A linear incremental algorithm for Naive and Standard digital lines and planes recognition. Graphical models 65, 61–76 (2003)
Gerard, Y., Debled-Rennesson, I., Zimmermann, P.: An elementary digital plane recognition algorithm. Discrete Applied Mathematics 151, 169–183 (2005)
Vittone, J., Chassery, J.-M.: Recognition of digital naive planes and polyhedrization. In: Nyström, I., Sanniti di Baja, G., Borgefors, G. (eds.) DGCI 2000. LNCS, vol. 1953, pp. 296–307. Springer, Heidelberg (2000)
Dexet, M., Andrès, É.: A generalized preimage for the standard and supercover digital hyperplane recognition. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 639–650. Springer, Heidelberg (2006)
Cœurjolly, D., Zerarga, L.: Supercover model, digital straight line recognition and curve reconstruction on the irregular isothetic grids. Computer and Graphics 30, 46–53 (2006)
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Dexet, M., Cœurjolly, D., Andres, E. (2006). Invertible Polygonalization of 3D Planar Digital Curves and Application to Volume Data Reconstruction. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2006. Lecture Notes in Computer Science, vol 4292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11919629_52
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DOI: https://doi.org/10.1007/11919629_52
Publisher Name: Springer, Berlin, Heidelberg
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