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Street GenerationStreet Generationfor City Modelingfor City Modeling

Xavier Décoret, François SillionXavier Décoret, François Sillion

iMAGIS GRAVIR/IMAG - INRIAiMAGIS GRAVIR/IMAG - INRIA

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A Computer Graphics point of viewA Computer Graphics point of view– Graphic artistsGraphic artists

– Game developersGame developers

– ResearchersResearchers

A work in 2 partsA work in 2 parts– A frameworkA framework

– An algorithmAn algorithm

ForewordForeword

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MotivationsMotivations

City Modeling is a growing field of interestCity Modeling is a growing field of interest– Game and LeisureGame and Leisure

» Virtual environments are widely usedVirtual environments are widely used

» Need for larger environmentsNeed for larger environments

» Cities are natural and appealing large environmentsCities are natural and appealing large environments

– Analysis and SimulationAnalysis and Simulation» Pedestrians or traffic flowPedestrians or traffic flow

» Wave transportationWave transportation

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MotivationsMotivations

Creating the virtual model is a tedious taskCreating the virtual model is a tedious task– Realistic modelRealistic model

» Model it by hand: long and costlyModel it by hand: long and costly

» Reconstruct it automatically: not working yetReconstruct it automatically: not working yet

– Semi-realistic modelSemi-realistic model» Procedural modellingProcedural modelling

» Map is exact, geometry is approximativeMap is exact, geometry is approximative

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MotivationsMotivations

Creating the virtual model is a tedious taskCreating the virtual model is a tedious task– Realistic modelRealistic model

» Model it by hand: long and costlyModel it by hand: long and costly

» Reconstruct it automatically: not working yetReconstruct it automatically: not working yet

– Semi-realistic modelSemi-realistic model» Procedural modellingProcedural modelling

» Map is exact, geometry is approximativeMap is exact, geometry is approximative

No existing tool

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Overview of the toolOverview of the tool

Retrieve the 2D footprints of buildingsRetrieve the 2D footprints of buildings– Aerial photographsAerial photographs

– Existing 2D models Existing 2D models

Procedurally generate buildingsProcedurally generate buildings– Grammar, library of shapesGrammar, library of shapes

– Style information provided by a designer (GIS)Style information provided by a designer (GIS)

Generate streetsGenerate streets– Retrieve the street networkRetrieve the street network

– Generate geometryGenerate geometry

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Overview of the toolOverview of the tool

Retrieve the 2D footprints of buildingsRetrieve the 2D footprints of buildings– Aerial photographsAerial photographs

– Existing 2D models Existing 2D models

Procedurally generate buildingsProcedurally generate buildings– Grammar, library of shapesGrammar, library of shapes

– Style information provided by a designer (GIS)Style information provided by a designer (GIS)

Generate streetsGenerate streets– Retrieve the street networkRetrieve the street network

– Generate geometryGenerate geometry

Our contribution

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Input & OutputInput & Output

Input

Output

Polygonal footprints

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PrinciplePrinciple

We use a median axis (skeleton)We use a median axis (skeleton)

Seems natural for roadsSeems natural for roads– Goes in between 2 buildingsGoes in between 2 buildings

– Goes approximately at equal distanceGoes approximately at equal distance

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Use of a median axisUse of a median axis

Street graphPolygonal footprints

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Robustness Issues (1)Robustness Issues (1)

Input sensitivityInput sensitivity

Ideal case Noise effect Expected result

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Robustness Issues (2)Robustness Issues (2)

ArtefactsArtefacts

Unwanted branches requiring post-processing

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Our approachOur approach

A topological phaseA topological phase– Partition Partition the map intothe map into

» StreetsStreets

» CrossingsCrossings

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Our approachOur approach

A topological phaseA topological phase– Partition Partition the map intothe map into

» StreetsStreets

» CrossingsCrossings

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Our approachOur approach

A topological phaseA topological phase– Partition Partition the map intothe map into

» StreetsStreets

» CrossingsCrossings

11 22

3399

44

55

6677

88

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Our approachOur approach

A topological phaseA topological phase– Partition Partition the map intothe map into

» StreetsStreets

» CrossingsCrossings

A geometric phaseA geometric phase– The graph is shaped to a The graph is shaped to a

correct positioncorrect position

– Optimisation with constraintsOptimisation with constraints

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33

44

55

6677

8899

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Our approachOur approach

A topological phaseA topological phase– Partition Partition the map intothe map into

» StreetsStreets

» CrossingsCrossings

A geometric phaseA geometric phase– The graph is shaped to a The graph is shaped to a

correct positioncorrect position

– Optimisation with constraintsOptimisation with constraints

11 22

33

44

55

6677

8899

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Topological PhaseTopological Phase

Sample the footprints with extra verticesSample the footprints with extra vertices

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Topological PhaseTopological Phase

Sample the footprints with extra verticesSample the footprints with extra vertices

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Topological PhaseTopological Phase

Sample the footprints with extra verticesSample the footprints with extra vertices

Delaunay triangulate the samplesDelaunay triangulate the samples

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Topological PhaseTopological Phase

Sample the footprints with extra verticesSample the footprints with extra vertices

Delaunay triangulate the samplesDelaunay triangulate the samples

Ignore edges joining samples of a same buildingIgnore edges joining samples of a same building

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Topological PhaseTopological Phase

Sample the footprints with extra verticesSample the footprints with extra vertices

Delaunay triangulate the samplesDelaunay triangulate the samples

Ignore edges joining samples of a same buildingIgnore edges joining samples of a same building

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Topological PhaseTopological Phase

Sample the footprints with extra verticesSample the footprints with extra vertices

Delaunay triangulate the samplesDelaunay triangulate the samples

Ignore edges joining samples of a same buildingIgnore edges joining samples of a same building

Take the dual of edges (Voronoï diagram)Take the dual of edges (Voronoï diagram)

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Topological PhaseTopological Phase

Sample the footprints with extra verticesSample the footprints with extra vertices

Delaunay triangulate the samplesDelaunay triangulate the samples

Ignore edges joining samples of a same buildingIgnore 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 edgesConstruct a graph from the edges

Crossings

Streets

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Our approachOur approach

A topological phaseA topological phase– Partition Partition the map intothe map into

» StreetsStreets

» CrossingsCrossings

A geometric phaseA geometric phase– The graph is shaped to a The graph is shaped to a

correct positioncorrect position

– Optimisation with constraintsOptimisation with constraints

99

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Geometric PhaseGeometric Phase

Place sample Place sample medianmedian points points

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Geometric PhaseGeometric Phase

Place sample Place sample medianmedian points points

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Geometric PhaseGeometric Phase

Place sample Place sample medianmedian points points

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Geometric PhaseGeometric Phase

Place sample Place sample medianmedian points points

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Geometric PhaseGeometric Phase

Place sample Place sample medianmedian points points

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Geometric PhaseGeometric Phase

Place sample Place sample medianmedian points points

Compute minimum widthCompute minimum width

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Geometric PhaseGeometric Phase

Place sample Place sample medianmedian points points

Compute minimum widthCompute minimum width

Greedily place a Greedily place a validvalid polyline in between polyline in between

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Geometric PhaseGeometric Phase

Place sample Place sample medianmedian points points

Compute minimum widthCompute minimum width

Greedily place a Greedily place a validvalid polyline in between polyline in between

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Place sample Place sample medianmedian points points

Compute minimum widthCompute minimum width

Greedily place a Greedily place a validvalid polyline in between polyline in between

Split the polyline inSplit the polyline in– SegmentsSegments

– CurvesCurves

Geometric PhaseGeometric Phase

Segments

Curve

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RobustnessRobustness

A topological phaseA topological phase– Partition Partition the map intothe map into

» StreetsStreets

» CrossingsCrossings

A geometric phaseA geometric phase– The graph is shaped to a The graph is shaped to a

correct positioncorrect position

– Optimisation with constraintsOptimisation with constraints

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

- Based on optimisation- Robust to footprints’shape- Solves artefacts

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ResultsResults

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Street GenerationStreet Generation

Generate streetsGenerate streets– Retrieve the street networkRetrieve the street network

» TopologyTopology

» Simple primitivesSimple primitives

– Generate geometryGenerate geometry» Match buildings boundariesMatch buildings boundaries

» Connect correctly at crossingsConnect correctly at crossings

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WorkflowWorkflow

Generate streetsGenerate streets– Retrieve the street networkRetrieve the street network

» TopologyTopology

» Simple primitivesSimple primitives

– Generate geometryGenerate geometry» Match buildings boundariesMatch buildings boundaries

» Connect correctly at crossingsConnect correctly at crossings

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Generating geometryGenerating geometry

Use library of parametric modelsto build segments and curves

Triangulate the remaining border

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Parametric modelParametric model

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ResultsResults

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Conclusion & Future WorksConclusion & Future Works

We can generate geometry from a 2D map of We can generate geometry from a 2D map of buildingsbuildings

– Work in 2D1/2Work in 2D1/2

Write more parametric modulesWrite more parametric modules

High level features extractionsHigh level features extractions– AvenuesAvenues

– SquaresSquares

Generate coherent trafic signsGenerate coherent trafic signs