Street Generation for City Modeling

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 Polygonal footprints Street graph

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 footprints’shape - Solves input sensitivity - Based on optimisation - Robust to footprints’shape - 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