Abstract
A new class of so-called pseudo-starshaped polygons is introduced. A polygon is pseudo-star-shaped if there exists a point from which the whole interior of the polygon can be seen, provided it is possible to see through single edges. We show that the class of pseudo-star-shaped polygons unifies and generalizes the well-known classes of convex, monotone and pseudostar-sphaped polygons. We give algorithms for testing whether a polygon is pseudostar-shaped from a given point in linear time, and for constructing all regions from which the polygon is pseudo-star-shaped in quadratic time. We show the latter algorithm to be worst-case optimal. Also, we give efficient algorithms solving standard geometrical problems such as point-location and triangulation for pseudo-starshaped polygons.
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References
Dean JA (1985) Structural properties of polygons. Master's Thesis, Carleton Univ Ottawa, Canada
Dean JA, Sack J-R (1985) Efficient hidden-line elimination by capturing winding information. Proc 23rd Allerton Conf Commun Control Comput, Monticello, Ill, pp 496–505
ElGindy H, Avis D (1981) A linear algorithm for computing the visibility polygon from a point. J Algorithms 2(2):186–197
Keil JM (1985) Decompositions of polygons into simpler components. SIAM J Comput 14:799–817
Lee DT (1983) Visibility of a simple polygon. Comput Vision, Graph Image Proc 22:207–221
Lee DT, Preparata FP (1979) An optimal algorithm for finding the kernel of a simple polygon. J ACM 26(3):415–421
Newman W, Sproull R (1978) Principles of interactive computer graphics, Mcgraw Hill, New York
O'Rourke J (1987) Art Gallery Theorems and Algorithms. Oxford Univ Press, New York Oxford
Preparata FP, Supowit KJ (1981) Testing a simple polygon for monotonicity. Inf Proc Lett 12:161–164
Preparata FP, Shamos MI (1985) Computational geometry: an introduction. Springer, Berlin Heidelberg New York Tokyo
Sack, J-R, Toussaint GT (1985) Translating polygons in the plane. Proc STACS85, Saarbrücken FRG, Lect Notes Comput Sci 182, Springer, Berlin Heidelberg New York Tokyo, pp 310–321; also (1987) Robotica 5:55–63
Toussaint GT (1985a) Movable separability of sets. In: Toussaint GT (ed) Computational geometry, North-Holland, Amsterdam New York Oxford, pp 335–376
Toussaint GT (1985b) Shortest path solves translation separability of polygons. Tech Rep SOCS-85.27, School Comput Sci, McGill Univ, Montréal, Canada
Toussaint GT (1983) A new linear algorithm for triangulating monotone polygons. Tech Rep SOCS-83.9, School Comput Sci, McGill Univ, Montréal, Canada
Toussaint GT, Avis D (1982) On a convex hull algorithm for polygons and its applications to triangulation. Pattern Recognition 15(1):23–29
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Research for this paper was done while the author was at Carleton University
Research for this paper was done in part while the author was visiting Carleton University
This research was supported in part by NSERC and by Carleton University
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Dean, J.A., Lingas, A. & Sack, JR. Recognizing polygons, or how to spy. The Visual Computer 3, 344–355 (1988). https://doi.org/10.1007/BF01901192
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DOI: https://doi.org/10.1007/BF01901192