Abstract
The “discrete approach” of volume graphics (that is, the one using internal model, which is a set of voxels) has various advantages over surface graphics [1]. In particular, it is helpful for ensuring the use of exact arithmetic and thus avoiding rounding errors. This may also help to raise significantly the computational efficiency of some computer graphics algorithms, in particular, of the ray-tracing algorithm [2]. Based on a detailed analysis of the matter, Kaufman et al. prognosticated that “… volume graphics will develop into a major trend in computer graphics” [1]. For additional arguments and experience supporting the above thesis, the reader is referred to Chapters 4, 6 and 10.
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.
Similar content being viewed by others
References
Kaufman A, Cohen D, Yagel R. Volume graphics. IEEE Computer, 1993; 26 (7): 51 - 64.
Yagel R, Cohen D, Kaufman A. Discrete ray tracing. IEEE Computer Graphics and Applications, 1992; 22 (5): 19–28.
Kaufman A, Shimony E. 3D scan-conversion algorithms for voxel-based graphics. In: Proc. 1986 Workshop on Interactive 3D Graphics, Chapel Hill, NC, ACM, New York, 1986; 45–75.
Kaufman A. An algorithm for 3D scan-conversion of polygons. In: Proc. Eurographics ’87; 197–208.
Cohen D, Kaufman A. Scan-conversion algorithms for linear and quadratic objects. In: Proc. IEEE Symposium on Volume Visualization, Los Alamos, CA, 1991; 280–301.
Cohen D, Kaufman A. 3D Line voxelization and connectivity control. IEEE Computer Graphics and Applications, 1997; 17(6).
Andres E, Nehlig P, Fran?on J. Tunnel-free supercover 3D polygons and polyhedra. In: Proc. Eurographics ’97; 16(3): C3-C13.
Françon J. On recent trends in discrete geometry in computer imagery. In: Proc. the 6th Workshop on Discrete Geometry for Computer Imagery, Lyon, France, Lecture Notes in Computer Sciences No 1176, Springer-Verlag, November 1996; 141–150.
Andres E, Nehlig P, Fran?on J. Supercovers of straight lines, planes and triangles. In: Proc. the 7th International Workshop DGCI, Montpelier, France, Lecture Notes in Computer Science No 1347, Springer Verlag, 1997; 243–254.
Andres E, Achatya R, Sibata C. The discrete analytical hyperplane. Graphical Models and Image Processing, 1997; 59 (5): 302–309.
Barneva RP, Brimkov VE, Nehlig P. Thin discrete triangular meshes. To appear in Theoretical Computer Science, Elsevier.
Debled-Rennesson I, Reveilles J-P. A new approach to digital planes. In: Spie’s International Symposium on Photonics for Industrial Applications, Technical Conference Vision Geometry 3, Boston, USA, 1994.
Brimkov VE, Barneva RP. Graceful planes and thin tunnel-free meshes. In: Proc. of the 8th Conference on Discrete Geometry for Computer Imagery, March 17–19, 1999, Marne-la-Vallee, France, Lecture Notes in Computer Sciences No 1568, Springer-Verlag, March 1999; 53–64.
Figueiredo O, Reveilles J-P. A contribution to 3D digital lines. In: Proc. the 5th International Workshop on Discrete Geometry for Computer Imagery, Clermont- Ferrand, France, September 25–27, 1995; 187–198.
Rosenfeld A. Three-dimensional digital topology. Computer Science Center, Univ. of Maryland, Tech. Rep. 963, 1980.
Srihari SN. Representation of three-dimensional digital images. Computing Surveys, 1981; 4 (13): 399–424.
Pavlidis T. Algorithms for Graphics and Image Processing. Computer Science Press, Rockville, MD, 1982.
Reveilles J-P. Geometrie Discrete, Calcul en Nombres Entiers et Algorithmique, these d’etat, Universite Louis Pasteur, Strasbourg, 1991.
Bresenham JE. Algorithm for computer control of a digital plotter. ACM Transaction on Graphics, 1965; 4 (l): 25–30.
Cohen D, Kaufman A. Fundamentals of surface voxelization. CVGIP-GMIP, 1995; 57 (6): 453–461.
Kaufman A, Cohen D, Yagel R. Normal estimation in 3D discrete space. The Visual Computer, 1992; 8: 278–291.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag London
About this chapter
Cite this chapter
Brimkov, V.E., Barneva, R.P., Nehlig, P. (2000). Minimally Thin Discrete Triangulation. In: Chen, M., Kaufman, A.E., Yagel, R. (eds) Volume Graphics. Springer, London. https://doi.org/10.1007/978-1-4471-0737-8_3
Download citation
DOI: https://doi.org/10.1007/978-1-4471-0737-8_3
Publisher Name: Springer, London
Print ISBN: 978-1-85233-192-4
Online ISBN: 978-1-4471-0737-8
eBook Packages: Springer Book Archive