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Authoring Hierarchical Road Networks Eric Galin :: Adrien Peytavie :: Eric Guerin :: Bedřich Beneš

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Outline Motivation Previous work Algorithm – Overview – Road generation – Removing redundant roads – Mergin roads Results

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Motivation Roads in Cities?

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Motivation Roads in Cities? Roads over Landscape?

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Motivation Roads in Cities? Roads over Landscape?

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Motivation Roads in Cities? Roads over Landscape? Road Hierarchies! Cities Towns Villages Highways Major roads Minor roads

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Previous work

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Algorithm - Overview 1)For each city pair, find a road over terrain 2) Discard some of the roads as redundant 3) Merge nearby pieces of road Basically, Galin et al. 2010Interesting graph theorySome topology

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Algorithm - Overview 1)For each city pair, find a road over terrain 2) Discard some of the roads as redundant 3) Merge nearby pieces of road Basically, Galin et al. 2010Interesting graph theorySome topology

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Find a road over terrain… Isolines Lattice 1.Generate graph 2.Find shortest path 3.Account for curvature, elevation, environment, “other”

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…for each city pair A B C D E FG H i.e. AB, AC, AD, …, FG, FH, GH => Complete Graph over Cities Road type depends on city size

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Algorithm - Overview 1)For each city pair, find a road over terrain 2) Discard some of the roads as redundant 3) Merge nearby pieces of road Basically, Galin et al. 2010Interesting graph theorySome topology

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Discard Redundant Roads Complete Graph – too dense MST – too sparse Some candidates: β-skeleton, 1983 Relative Neighbour Graph, 1980 Gabriel Graph, 1969 Is a kind of

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Relative Neighbour and Gabriel Graphs Contains edge (p i,p j ) no other point in Ω Relative Neighbour Gabriel ΩΩ Both Contain MST as subgraph; Euclidean Dist.

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Our Version 1)Road length Euclidean distance Changes the shape of neighborhood balls 2) Parameterize graph density by γ

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Our Version, cont. Gabriel Ω γ = 2 Ω Relative Neighbour γ -> ∞ γ = 1 Continuum of densities

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Density Continuum A little sparse, γ = 2 Quite sparse, γ = 8 Rather dense, γ = 1,2

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Algorithm - Overview 1)For each city pair, find a road over terrain 2) Discard some of the roads as redundant 3) Merge nearby pieces of road Basically, Galin et al. 2010Interesting graph theorySome topology

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Merge nearby roads Distance between curves – Length of leash? Frechet distance – (over all reparameterizations)

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Road Merging, cont. Roads are close AND road types allow it => MERGE Merge: e.g. Highways and Highways, Major and Minor Don’t Merge: e.g. Highways and Major

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And more.. Waypoints User steering Road interaction

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Results We generate realistic road networks

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Results We generate realistic road networks Real-life CorsicaOur Corsica

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Results 512x512 ~ 380 m resolutionGrid size of 256x256 FAST - O(n 3 ) w/o heuristic

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Future Work Urban fringe Highway intersections

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Thank you!

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