Abstract
A combinatorial algorithm to find the intersection of an axis-parallel slicing plane with the orthogonal cover of a digital object is presented in this paper. The orthogonal cover is the smallest-volume 3D orthogonal polyhedron containing the object and stored in a doubly connected edge list (DCEL). Its intersection with the slicing plane consists of one or more isothetic polygons that provide topological information about the cover. The algorithm traverses the vertices on the polyhedron boundary and lying on the slicing plane, and the direction of next move from a vertex is determined by a set of linear equations in the integer domain. Results for few objects with successive slicing planes are presented to demonstrate the effectiveness and elegance of the algorithm.
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.
References
Aguilera, A.: Orthogonal Polyhedra: Study and Application. PhD Thesis, Universitat Politécnica de Catalunya (April 1998)
AutoCAD, http://docs.autodesk.com
Berg, M.D., Cheong, O., Kreveld, M.V., Overmars, M.: Computational Geometry—Algorithms and Applications. Springer (1997)
Biswas, A., Bhowmick, P., Bhattacharya, B.B.: Construction of Isothetic Covers of a Digital Object: A Combinatorial Approach. Journal of Visual Communication and Image Representation 21, 295–310 (2010)
CarveWright, http://www.carvewright.com
Colak, S.B., Papaioannou, D.G., Hooft, G.W., van der Mark, M.B., Schomberg, H., Paasschens, J.C.J., Melissen, J.B.M., van Asten, N.A.A.J.: Tomographic image reconstruction from optical projections in light-diffusing media. Appl. Opt. 36, 180–213 (1997)
Costa, J.M., Venetsanopoulos, A.N., Trefler, M.: Digital Tomographic Filtering of Radiographs. IEEE Trans. Medical Imaging 2(2), 76–88 (1983)
Defrise, M.: A short reader’s guide to 3D tomographic reconstruction. Comput. Med. Imaging Graph. 25(2), 113–116 (2001)
Karmakar, N., Biswas, A., Bhowmick, P., Bhattacharya, B.B.: Construction of 3D Orthogonal Cover of a Digital Object. In: Aggarwal, J.K., Barneva, R.P., Brimkov, V.E., Koroutchev, K.N., Korutcheva, E.R. (eds.) IWCIA 2011. LNCS, vol. 6636, pp. 70–83. Springer, Heidelberg (2011)
Klette, R., Rosenfeld, A.: Digital Geometry: Geometric Methods for Digital Picture Analysis. Morgan Kaufmann, San Francisco (2004)
My CAD Site, http://www.we-r-here.com
Preparata, F.P., Shamos, M.I.: Computational Geometry—An Introduction. Spinger, New York (1985)
The Official Google Sketchup Blog, http://sketchupdate.blogspot.in
Trussell, H.J.: Processing of X-ray images. Proc. IEEE 69(5), 615–627 (1981)
Ziedses des Plantes, B.G.: Body-section radiography: History, image information, various techniques and results. Australasian Radiology XV(1), 57–64 (1971)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Karmakar, N., Biswas, A., Bhowmick, P. (2012). Fast Slicing of Orthogonal Covers Using DCEL. In: Barneva, R.P., Brimkov, V.E., Aggarwal, J.K. (eds) Combinatorial Image Analaysis. IWCIA 2012. Lecture Notes in Computer Science, vol 7655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34732-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-34732-0_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34731-3
Online ISBN: 978-3-642-34732-0
eBook Packages: Computer ScienceComputer Science (R0)