Abstract
We consider the problem of labeling point objects in interactive maps where the user can pan and zoom continuously. We allow labels to slide along the point they label. We assume that each point comes with a priority; the higher the priority the more important it is to label the point. Given a dynamic scenario with user interactions, our objective is to maintain an occlusion-free labeling such that, on average over time, the sum of the priorities of the labeled points is maximized. Even the static version of the problem is known to be NP-hard. We present an efficient and effective heuristic that labels points with sliding labels in real time. Our heuristic proceeds incrementally; it tries to insert one label at a time, possibly pushing away labels that have already been placed. To quickly predict which labels have to be pushed away, we use a geometric data structure that partitions screen space. With this data structure we were able to double the frame rate when rendering maps with many labels.
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Notes
- 1.
http://bahn.de/zugradar, accessed Feb. 6, 2014.
- 2.
http://www.u2.com/gigapixelfancam/, accessed Feb. 7, 2014.
- 3.
- 4.
http://www.openscenegraph.org/, accessed Nov. 24, 2013.
- 5.
http://www.naturalearthdata.com/, accessed Nov. 28, 2013.
References
Adamaszek A, Wiese A (2013) Approximation schemes for maximum weight independent set of rectangles. In: Proceedings of 54th annual IEEE symposium on foundations of computer science (FOCS’13), pp 400–409
Agarwal PK, van Kreveld M, Suri S (1998) Label placement by maximum independent set in rectangles. Comput Geom Theory Appl 11:209–218
Alinhac G (1962) Cartographie Théorique et Technique, chapter IV. Institut Géographique National, Paris
Been K, Daiches E, Yap C (2006) Dynamic map labeling. IEEE Trans Visual Comput Graphics 12(5):773–780
Been K, Nöllenburg M, Poon SH, Wolff A (2010) Optimizing active ranges for consistent dynamic map labeling. Comput Geom Theory Appl 43(3):312–328. http://dx.doi.org/10.1016/j.comgeo.2009.03.006
Chalermsook P, Chuzhoy J (2009) Maximum independent set of rectangles. In: Proceedings of 20th annual ACM-SIAM symposium on discrete algorithms (SODA’09), pp 892–901
de Berg M, Cheong O, van Kreveld M, Overmars M (2008) Computational geometry: algorithms and applications, chapter 6, 3rd edn. Springer, Berlin
Erlebach T, Jansen K, Seidel E (2005) Polynomial-time approximation schemes for geometric intersection graphs. SIAM J Comput 34(6):1302–1323
Erlebach T, Hagerup T, Jansen K, Minzlaff M, Wolff A (2009) Trimming of graphs, with application to point labeling. Theory Comput Syst 47(3):613–636. http://dx.doi.org/10.1007/s00224-009-9184-8
Fowler RJ, Paterson MS, Tanimoto SL (1981) Optimal packing and covering in the plane are NP-complete. Inform Process Lett 12(3):133–137
Gemsa A, Niedermann B, Nöllenburg M (2013) Trajectory-based dynamic map labeling. In: Cai L, Cheng SW, Lam TW (eds) Proceedings of 24th annual international symposium on algorithms computation (ISAAC’13). Lecture notes in computer science, vol 8283. Springer, pp 413–423. http://dx.doi.org/10.1007/978-3-642-45030-3_39
Gemsa A, Nöllenburg M, Rutter I (2011a) Consistent labeling of rotating maps. In: Dehne F, Iacono J, Sack JR (eds) Proceedings of 12th international symposium on algorithms and data structures (WADS’11). Lecture notes in computer science, vol 6844. Springer, pp 451–462. http://dx.doi.org/10.1007/978-3-642-22300-6_38
Gemsa A, Nöllenburg M, Rutter I (2011b) Sliding labels for dynamic point labeling. In: Proceedings of 23th Canadian conference on computational geometry (CCCG’11), pp 205–210
Goralski R, Gold CM, Dakowicz M (2007) Application of the kinetic Voronoi diagram to the real-time navigation of marine vessels. In: Proceedings of 6th international conference on computer information systems and industrial management applications (CISIM’07), pp 129–134
Harrie L, Stigmar H, Koivula T, Lehto L (2005) An algorithm for icon labelling on a real-time map. In: Fisher PF (ed) Proceedings of 11th international symposium on spatial data handling (SDH’05), pp 493–507
Imhof E (1975) Positioning names on maps. Am Cartogr 2(2):128–144
Luboschik M, Schumann H, Cords H (2008) Particle-based labeling: fast point-feature labeling without obscuring other visual features. IEEE Trans Visual Comput Graphics 14(6):1237–1244. http://dx.doi.org/10.1109/TVCG.2008.152
Maass S, Döllner J (2006) Efficient view management for dynamic annotation placement in virtual landscapes. In: Butz A, Fischer B, Krüger A, Oliver P (eds) Proceedings of 6th international symposium on smart graphics (SG’06). Lecture notes in computer science, vol 4073. Springer, Berlin, pp 1–12
Mote KD (2007) Fast point-feature label placement for dynamic visualizations. Inf Visual 6(4): 249–260. http://dx.doi.org/10.1057/palgrave.ivs.9500163
Ooms K, Kellens W, Fack V (2009) Dynamic map labelling for users. In: Cartwright W, Lopez P (eds) Proceedings of the 24th international cartographic conference (ICC’09)
Poon SH, Shin CS, Strijk T, Uno T, Wolff A (2003) Labeling points with weights. Algorithmica 38(2):341–362. http://dx.doi.org/10.1007/s00453-003-1063-0
van Kreveld M, Strijk T, Wolff A (1999) Point labeling with sliding labels. Comput Geom Theory Appl 13:21–47. http://dx.doi.org/10.1016/S0925-7721(99)00005-X
Zhang Q, Harrie L (2006) Real-time map labelling for mobile applications. Comput Environ Urban Syst 30(6):773–783
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Schwartges, N., Haunert, JH., Wolff, A., Zwiebler, D. (2014). Point Labeling with Sliding Labels in Interactive Maps. In: Huerta, J., Schade, S., Granell, C. (eds) Connecting a Digital Europe Through Location and Place. Lecture Notes in Geoinformation and Cartography. Springer, Cham. https://doi.org/10.1007/978-3-319-03611-3_17
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