authoring hierarchical road networks eric galin :: adrien peytavie :: eric guerin :: bedřich beneš
TRANSCRIPT
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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?
ü
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Motivation
Roads in Cities?
Roads over Landscape?
ü
ü
![Page 6: Authoring Hierarchical Road Networks Eric Galin :: Adrien Peytavie :: Eric Guerin :: Bedřich Beneš](https://reader036.vdocuments.us/reader036/viewer/2022062620/551b57345503465c7e8b5d6e/html5/thumbnails/6.jpg)
Motivation
Roads in Cities?
Roads over Landscape?
Road Hierarchies!
CitiesTowns
Villages
ü
üHighways
Major roadsMinor 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. 2010 Interesting graph theory Some 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. 2010 Interesting graph theory Some topology
![Page 10: Authoring Hierarchical Road Networks Eric Galin :: Adrien Peytavie :: Eric Guerin :: Bedřich Beneš](https://reader036.vdocuments.us/reader036/viewer/2022062620/551b57345503465c7e8b5d6e/html5/thumbnails/10.jpg)
Find a road over terrain…
Isolines
Lattice
1. Generate graph2. Find shortest path3. Account for curvature, elevation,
environment, “other”
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…for each city pair
A B
C D E
F G
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. 2010 Interesting graph theory Some topology
![Page 13: Authoring Hierarchical Road Networks Eric Galin :: Adrien Peytavie :: Eric Guerin :: Bedřich Beneš](https://reader036.vdocuments.us/reader036/viewer/2022062620/551b57345503465c7e8b5d6e/html5/thumbnails/13.jpg)
Discard Redundant Roads
• Complete Graph – too dense• MST – too sparse• Some candidates:
β-skeleton, 1983 Relative NeighbourGraph, 1980
Gabriel Graph, 1969
Is a kind of
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Relative Neighbour and Gabriel Graphs
Contains edge (pi,pj) no other point in Ω
Relative Neighbour Gabriel
Ω Ω
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 = 1Continuum 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. 2010 Interesting graph theory Some topology
![Page 19: Authoring Hierarchical Road Networks Eric Galin :: Adrien Peytavie :: Eric Guerin :: Bedřich Beneš](https://reader036.vdocuments.us/reader036/viewer/2022062620/551b57345503465c7e8b5d6e/html5/thumbnails/19.jpg)
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 MinorDon’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 Corsica Our Corsica
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Results
512x512 ~ 380 m resolution Grid size of 256x256
FAST - O(n3) w/o heuristic
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Future Work
Urban fringe
Highway intersections
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Thank you!