Robustness Issues

1
Street Generationfor City Modeling
Xavier Décoret, François Sillion iMAGIS
GRAVIR/IMAG - INRIA
2
Foreword

• A Computer Graphics point of view
• Graphic artists
• Game developers
• Researchers
• A work in 2 parts
• A framework
• An algorithm

3
Motivations

• City Modeling is a growing field of interest
• Game and Leisure
• Virtual environments are widely used
• Need for larger environments
• Cities are natural and appealing large
  environments
• Analysis and Simulation
• Pedestrians or traffic flow
• Wave transportation

4
Motivations

• Creating the virtual model is a tedious task
• Realistic model
• Model it by hand long and costly
• Reconstruct it automatically not working yet
• Semi-realistic model
• Procedural modelling
• Map is exact, geometry is approximative

5
Motivations

• Creating the virtual model is a tedious task
• Realistic model
• Model it by hand long and costly
• Reconstruct it automatically not working yet
• Semi-realistic model
• Procedural modelling
• Map is exact, geometry is approximative

No existing tool
6
Overview of the tool

• Retrieve the 2D footprints of buildings
• Aerial photographs
• Existing 2D models
• Procedurally generate buildings
• Grammar, library of shapes
• Style information provided by a designer (GIS)
• Generate streets
• Retrieve the street network
• Generate geometry

7
Overview of the tool

• Retrieve the 2D footprints of buildings
• Aerial photographs
• Existing 2D models
• Procedurally generate buildings
• Grammar, library of shapes
• Style information provided by a designer (GIS)
• Generate streets
• Retrieve the street network
• Generate geometry

Our contribution
8
Input Output
Polygonal footprints
Input
Output

9
Principle

• We use a median axis (skeleton)
• Seems natural for roads
• Goes in between 2 buildings
• Goes approximately at equal distance

10
Use of a median axis
Street graph
Polygonal footprints
11
Robustness Issues (1)

• Input sensitivity

Ideal case
Noise effect
Expected result
12
Robustness Issues (2)

• Artefacts

Unwanted branches requiring post-processing
13
Our approach

• A topological phase
• Partition the map into
• Streets
• Crossings

14
Our approach

• A topological phase
• Partition the map into
• Streets
• Crossings

15
Our approach

• A topological phase
• Partition the map into
• Streets
• Crossings

1
2
5
4
6
7
8
3
9
16
Our approach

• A topological phase
• Partition the map into
• Streets
• Crossings
• A geometric phase
• The graph is shaped to a correct position
• Optimisation with constraints

1
2
5
4
6
7
8
3
9
17
Our approach

• A topological phase
• Partition the map into
• Streets
• Crossings
• A geometric phase
• The graph is shaped to a correct position
• Optimisation with constraints

1
2
5
4
6
7
8
3
9
18
Topological Phase

• Sample the footprints with extra vertices

19
Topological Phase

• Sample the footprints with extra vertices

20
Topological Phase

• Sample the footprints with extra vertices
• Delaunay triangulate the samples

21
Topological Phase

• Sample the footprints with extra vertices
• Delaunay triangulate the samples
• Ignore edges joining samples of a same building

22
Topological Phase

• Sample the footprints with extra vertices
• Delaunay triangulate the samples
• Ignore edges joining samples of a same building

23
Topological Phase

• Sample the footprints with extra vertices
• Delaunay triangulate the samples
• Ignore edges joining samples of a same building
• Take the dual of edges (Voronoï diagram)

24
Topological Phase

• Sample the footprints with extra vertices
• Delaunay triangulate the samples
• Ignore edges joining samples of a same building
• Take the dual of edges (Voronoï diagram)
• Construct a graph from the edges

Crossings
Streets
25
Our approach

• A topological phase
• Partition the map into
• Streets
• Crossings
• A geometric phase
• The graph is shaped to a correct position
• Optimisation with constraints

9
26
Geometric Phase

• Place sample median points

27
Geometric Phase

• Place sample median points

28
Geometric Phase

• Place sample median points

29
Geometric Phase

• Place sample median points

30
Geometric Phase

• Place sample median points

31
Geometric Phase

• Place sample median points
• Compute minimum width

32
Geometric Phase

• Place sample median points
• Compute minimum width
• Greedily place a valid polyline in between

33
Geometric Phase

• Place sample median points
• Compute minimum width
• Greedily place a valid polyline in between

34
Geometric Phase

• Place sample median points
• Compute minimum width
• Greedily place a valid polyline in between
• Split the polyline in
• Segments
• Curves

Curve
Segments
35
Robustness

• A topological phase
• Partition the map into
• Streets
• Crossings
• A geometric phase
• The graph is shaped to a correct position
• Optimisation with constraints

- Based on distance - Robust to
footprintsshape - Solves input sensitivity
- Based on optimisation - Robust to
footprintsshape - Solves artefacts
36
Results
37
Street Generation

• Generate streets
• Retrieve the street network
• Topology
• Simple primitives
• Generate geometry
• Match buildings boundaries
• Connect correctly at crossings

38
Workflow

• Generate streets
• Retrieve the street network
• Topology
• Simple primitives
• Generate geometry
• Match buildings boundaries
• Connect correctly at crossings

39
Generating geometry
Use library of parametric modelsto build
segments and curves
Triangulate the remaining border
40
Parametric model
41
Results
42
Conclusion Future Works

• We can generate geometry from a 2D map of
  buildings
• Work in 2D1/2
• Write more parametric modules
• High level features extractions
• Avenues
• Squares
• Generate coherent trafic signs