1. 1 Street Generation for City Modeling Xavier Décoret, François Sillion iMAGIS GRAVIR/IMAG - INRIA

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

3. 3 Motivations City Modeling is a growing field of interest 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. 4 Motivations Creating the virtual model is a tedious task 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. 5 Motivations Creating the virtual model is a tedious task 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. 6 Overview of the tool Retrieve the 2D footprints of buildings Retrieve the 2D footprints of buildings –Aerial photographs –Existing 2D models Procedurally generate buildings Procedurally generate buildings –Grammar, library of shapes –Style information provided by a designer (GIS) Generate streets Generate streets –Retrieve the street network –Generate geometry

7. 7 Overview of the tool Retrieve the 2D footprints of buildings Retrieve the 2D footprints of buildings –Aerial photographs –Existing 2D models Procedurally generate buildings Procedurally generate buildings –Grammar, library of shapes –Style information provided by a designer (GIS) Generate streets Generate streets –Retrieve the street network –Generate geometry Our contribution

8. 8 Input & Output Input Output Polygonal footprints +

9. 9 Principle We use a median axis (skeleton) We use a median axis (skeleton) Seems natural for roads Seems natural for roads –Goes in between 2 buildings –Goes approximately at equal distance

10. 10 Use of a median axis Street graphPolygonal footprints

11. 11 Robustness Issues (1) Input sensitivity Input sensitivity Ideal caseNoise effectExpected result

12. 12 Robustness Issues (2) Artefacts Artefacts Unwanted branches requiring post-processing

13. 13 Our approach A topological phase A topological phase –Partition the map into »Streets »Crossings

14. 14 Our approach A topological phase A topological phase –Partition the map into »Streets »Crossings

15. 15 Our approach A topological phase A topological phase –Partition the map into »Streets »Crossings 1 2 3 9 4 5 6 7 8

16. 16 Our approach A topological phase A topological phase –Partition the map into »Streets »Crossings A geometric phase A geometric phase –The graph is shaped to a correct position –Optimisation with constraints 1 2 3 4 5 6 7 8 9

17. 17 Our approach A topological phase A topological phase –Partition the map into »Streets »Crossings A geometric phase A geometric phase –The graph is shaped to a correct position –Optimisation with constraints 1 2 3 4 5 6 7 8 9

18. 18 Topological Phase Sample the footprints with extra vertices Sample the footprints with extra vertices

19. 19 Topological Phase Sample the footprints with extra vertices Sample the footprints with extra vertices

20. 20 Topological Phase Sample the footprints with extra vertices Sample the footprints with extra vertices Delaunay triangulate the samples Delaunay triangulate the samples

21. 21 Topological Phase Sample the footprints with extra vertices Sample the footprints with extra vertices Delaunay triangulate the samples Delaunay triangulate the samples Ignore edges joining samples of a same building Ignore edges joining samples of a same building

22. 22 Topological Phase Sample the footprints with extra vertices Sample the footprints with extra vertices Delaunay triangulate the samples Delaunay triangulate the samples Ignore edges joining samples of a same building Ignore edges joining samples of a same building

23. 23 Topological Phase Sample the footprints with extra vertices Sample the footprints with extra vertices Delaunay triangulate the samples Delaunay triangulate the samples Ignore edges joining samples of a same building Ignore edges joining samples of a same building Take the dual of edges (Voronoï diagram) Take the dual of edges (Voronoï diagram)

24. 24 Topological Phase Sample the footprints with extra vertices Sample the footprints with extra vertices Delaunay triangulate the samples Delaunay triangulate the samples Ignore edges joining samples of a same building Ignore edges joining samples of a same building Take the dual of edges (Voronoï diagram) Take the dual of edges (Voronoï diagram) Construct a graph from the edges Construct a graph from the edges Crossings Streets

25. 25 Our approach A topological phase A topological phase –Partition the map into »Streets »Crossings A geometric phase A geometric phase –The graph is shaped to a correct position –Optimisation with constraints 9

26. 26 Geometric Phase Place sample median points Place sample median points

27. 27 Geometric Phase Place sample median points Place sample median points

28. 28 Geometric Phase Place sample median points Place sample median points

29. 29 Geometric Phase Place sample median points Place sample median points

30. 30 Geometric Phase Place sample median points Place sample median points

31. 31 Geometric Phase Place sample median points Place sample median points Compute minimum width Compute minimum width

32. 32 Geometric Phase Place sample median points Place sample median points Compute minimum width Compute minimum width Greedily place a valid polyline in between Greedily place a valid polyline in between

33. 33 Geometric Phase Place sample median points Place sample median points Compute minimum width Compute minimum width Greedily place a valid polyline in between Greedily place a valid polyline in between

34. 34 Place sample median points Place sample median points Compute minimum width Compute minimum width Greedily place a valid polyline in between Greedily place a valid polyline in between Split the polyline in Split the polyline in –Segments –Curves Geometric Phase Segments Curve

35. 35 Robustness A topological phase A topological phase –Partition the map into »Streets »Crossings A geometric phase 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. 36 Results

37. 37 Street Generation Generate streets Generate streets –Retrieve the street network »Topology »Simple primitives –Generate geometry »Match buildings boundaries »Connect correctly at crossings

38. 38 Workflow Generate streets Generate streets –Retrieve the street network »Topology »Simple primitives –Generate geometry »Match buildings boundaries »Connect correctly at crossings

39. 39 Generating geometry Use library of parametric models to build segments and curves Triangulate the remaining border

40. 40 Parametric model

41. 41 Results

42. 42 Conclusion & Future Works We can generate geometry from a 2D map of buildings We can generate geometry from a 2D map of buildings –Work in 2D1/2 Write more parametric modules Write more parametric modules High level features extractions High level features extractions –Avenues –Squares Generate coherent trafic signs Generate coherent trafic signs