Abstract
In this paper, the smooth isosurface generation from a set of voxels representing either a volumetric model or a discretization of a given solid is addressed. It is assumed that a certain isosurface value has been already given and that the set of voxels stabbing this value has been extracted from the volumetric model. The goal is to obtain an smooth, C 2, piecewise algebraic surface representing the isosurface. The proposed approach adds one dimension to the problem and works by considering a scalar function with domain coinciding with the octtree (or voxels) universe. An iterative local filtering operator is derived and discussed through several examples.
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References
Andujar, C., Ayala, D., Brunet, P., Joan-Arinyo, R., Sole, J.: Automatic generation of Multiresolution boundary representations. Comput. Graphics 15, 87–96 (1996).
Barnhill, R. E., Opitz, K.: Fat surfaces: a trivariate approach to triangle-based interpolation on surfaces. Comput. Aided Geom. Des. 9, 365–378 (1992).
Brunet, P., Joan-Arinyo, R., Navazo, I., Puig, A., Sole, J., Tost, D.: Modeling and visualization through data compression. In: Data visualization (Earnshaw, R. E., Rosenblumn, L., eds.), pp. 157–169. New York: Academic Press 1994.
Hagen, H., Hahmann, S., Bonneau, G.-P.: Variational surface design and surface interrogation. Comput. Graphics 12, C447–C459 (1993).
Kalvin, A.: A survey of algorithms for constructing surfaces from 3D volume data. Research Report IBM Research Division.
Kaufman, A.: Volume visualization. IEEE Computer Society Press, 1990.
Lorensen, W., Cline, H.: Marching cubes: a high resolution 3D surface reconstruction algorithm. ACM Comput. Graphics 21, 163–169 (1987).
Montani, C., Scateni, R., Scopigno, R.: A modified look-up table for implicit disambiguation of marching cubes. Visual Comput. 10, 353–355 (1994).
Montani, C., Scateni, R., Scopigno, R.: Discretized marching cubes. In: Proc. of IEEE Visualization’ 94, 281–287 (1994).
Patrikalakis, N. M., Kriezis, G. A.: Representation of piecewise continuous algebraic surfaces in terms of B-splines. Visual Comput. 5, 360–374 (1989).
Roulier, J., Rando, T.: Measures of fairness for curves and surfaces. In: Designing fair curves and surfaces: shape quality in geometric modeling and computer-aided design (Spaidis, N., ed.), pp. 75–122. Philadelphia: SIAM, 1995.
Sederberg, T.: Piecewise algebraic surface patches. Comput. Aided Geom. Des. 2, 53–59 (1985).
Van Gelder, A., Wilhems, J.: Interactive animated visualization of flow fields. In: Proceedings of 1992 Workshop on Volume Visualization, 47–54 (1992).
Van Gelder, A., Wilhems, J.: Topological considerations in isosurface generation. ACM Trans. Graphics, 13, 337–375 (1994).
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© 1998 Springer-Verlag Wien
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Vinacua, A., Navazo, I., Brunet, P. (1998). Octtrees Meet Splines. In: Farin, G., Bieri, H., Brunnett, G., De Rose, T. (eds) Geometric Modelling. Computing Supplement, vol 13. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6444-0_18
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DOI: https://doi.org/10.1007/978-3-7091-6444-0_18
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83207-3
Online ISBN: 978-3-7091-6444-0
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