Rendering effective route maps: improving usability through generalization
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Line Simplification with Restricted Orientations
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Pictorial and Verbal Tools for Conveying Routes
COSIT '99 Proceedings of the International Conference on Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science
A new polynomial-time algorithm for linear programming
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Path simplification for metro map layout
GD'06 Proceedings of the 14th international conference on Graph drawing
Stress majorization with orthogonal ordering constraints
GD'05 Proceedings of the 13th international conference on Graph Drawing
On d-regular schematization of embedded paths
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Automatic generation of route sketches
GD'10 Proceedings of the 18th international conference on Graph drawing
A new method for subdivision simplification with applications to urban-area generalization
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Fast and simple approach for polygon schematization
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
Flexible route guidance through turn instruction graphs
Proceedings of the 1st ACM SIGSPATIAL International Workshop on MapInteraction
On d-regular schematization of embedded paths
Computational Geometry: Theory and Applications
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Motivated from drawing route sketches, we consider the following path schematization problem. We are given a simple embedded polygonal path P=(v1, ..., vn) and a set $\mathcal{C}$ of admissible edge orientations including the coordinate axes. The problem is to redraw P schematically such that all edges are drawn as line segments that are parallel to one of the specified orientations. We also require that the path preserves the orthogonal order and that it remains intersection-free. Finally, we want the drawing to maximize the number of edges having their preferred edge direction and to minimize the path length. In this paper we first present an efficient two-step approach for schematizing monotone paths. It consists of an O(n2)-time algorithm to assign edge directions optimally and a subsequent linear program to minimize the path length. In order to schematize non-monotone paths we propose a heuristic that first splits the input into k monotone subpaths and then combines the optimal embeddings of the monotone subpaths into a single, intersection-free embedding of the initial path in O(k2+n) time.