Abstract
We propose Inflate-Paste – a new technique for generating orthogonal polygons with a given number of vertices from a unit square based on gluing rectangles. It is dual to Inflate-Cut – a technique we introduced in [12] that works by cutting rectangles.
Partially funded by LIACC through Programa de Financiamento Plurianual, Fundaçã o para a Ciência e Tecnologia (FCT) and Programa POSI, and by CEOC (Univ. of Aveiro) through Programa POCTI, FCT, co-financed by EC fund FEDER.
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
Aichholzer, O., Cortés, C., Demaine, E.D., Dujmovic, V., Erickson, J., Meijer, H., Overmars, M., Palop, B., Ramaswawi, S., Toussaint, G.T.: Flipturning polygons. Discrete Comput. Geom. 28, 231–253 (2002)
Bajuelos, A.L., Tomás, A.P., Marques, F.: Partitioning orthogonal polygons by extension of all edges incident to reflex vertices: lower and upper bounds on the number of pieces. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds.) ICCSA 2004. LNCS, vol. 3045, pp. 127–136. Springer, Heidelberg (2004)
Erdös, P.: Problem number 3763. American Mathematical Monthly 42, 627 (1935)
Joe, B., Simpson, R.B.: Corrections to Lee’s visibility polygon algorithm. BIT 27, 458–473 (1987)
Lee, D.T.: Visibility of a simple polygon. Computer Vision, Graphics, and Image Processing 22, 207–221 (1983)
Meisters, G.H.: Polygons have ears. Am. Math. Mon. 82, 648–651 (1975)
O’Rourke, J.: An alternate proof of the rectilinear art gallery theorem. J. Geometry 21, 118–130 (1983)
O’Rourke, J., Pashchenko, I., Tewari, G.: Partitioning orthogonal polygons into fat rectangles. In: Proc. 13th Canadian Conference on Computational Geometry (CCCG 2001), pp. 133–136 (2001)
Overmars, M., Wood, D.: On rectangular visibility. J. Algorithms 9, 372–390 (1988)
Sz.-Nagy, B.: Solution of problem 3763. Am. Math. Mon. 46, 176–177 (1939)
Tomás, A.P., Bajuelos, A.L., Marques, F.: Approximation algorithms to minimum vertex cover problems on polygons and terrains. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003. LNCS, vol. 2657, pp. 869–878. Springer, Heidelberg (2003)
Tomás, A.P., Bajuelos, A.L.: Generating Random Orthogonal Polygons. In: Postconference Proc. of CAEPIA-TTIA 2003. LNCS (LNAI), Springer, Heidelberg (2003) (to appear)
Toussaint, G.T.: Polygons are anthropomorphic. Am. Math. Mon. 122, 31–35 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tomás, A.P., Bajuelos, A.L. (2004). Quadratic-Time Linear-Space Algorithms for Generating Orthogonal Polygons with a Given Number of Vertices. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-24767-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22057-2
Online ISBN: 978-3-540-24767-8
eBook Packages: Springer Book Archive