Geometry Processing AlgorithmsGeometry Processing Algorithms

CSCS468468htt //htt // 468468 t f d d /t f d d /http://cshttp://cs468468.stanford.edu/.stanford.edu/

ObjectiveObjectiveObjectiveObjective

• Theory and algorithms for efficient• Theory and algorithms for efficient analysis and manipulation of complex 3D modelsmodels

• Hands‐on experience

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RequirementsRequirementsqq

Prerequisites:I t d ti t C t G hi‐ Introduction to Computer Graphics

‐ Experience with C++ programming‐ Background in geometry or computational geometry 

helpful, but not necessary.

Grade (3 units):‐ Programming exercisesProgramming exercises

‐ OpenMesh intro (10%)‐ Surface smoothing (20%)‐ Simplification (20%)Simplification (20%)‐ Parameterization (25%)‐ Remeshing (25%)

k i i O hWork in pairs. Use OpenMesh API

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ReferencesReferencesReferencesReferences

• Book“Polygon Mesh Processing”by Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, Bruno Levy

• Eurographics 2008 course notes“Geometric Modeling Based onGeometric Modeling Based on Polygonal Meshes”by Mario Botsch, Mark Pauly, Leif Kobbelt, Pierre Alliez, Bruno Levy Stephan Bischoff Christian RösslBruno Levy, Stephan Bischoff, Christian Rössl

• More links on web site

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What is Geometry Processing About?What is Geometry Processing About?What is Geometry Processing About?What is Geometry Processing About?

• Acquiring

• Analyzing

• ManipulatingManipulating

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ApplicationsApplications

MedicalMedical SimulationSimulationEE CommerceCommerceMedicalMedical

EngineeringEngineeringSimulationSimulation

CultureCultureEE‐‐CommerceCommerce

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Games & MoviesGames & Movies ArchitectureArchitectureCreatingCreating

ArchitectureArchitectureReverse EngineeringReverse Engineering

A Geometry Processing PipelineA Geometry Processing PipelineLow Level AlgorithmsLow Level Algorithms

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A Geometry Processing PipelineA Geometry Processing PipelineA Geometry Processing PipelineA Geometry Processing Pipeline

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A Geometry Processing PipelineA Geometry Processing PipelineHigh Level AlgorithmsHigh Level Algorithms

Deformation and editingDeformation and editing

Extracting shape structure

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Acquiring Acquiring 33D GeometryD GeometryR SR SRange ScannersRange Scanners

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Acquiring Acquiring 33D GeometryD GeometryR SR SRange ScannersRange Scanners

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Acquiring Acquiring 33D GeometryD GeometryTomographyTomography

Mesh ConstructionMesh Construction

fromfrom contourscontours from from point cloudspoint clouds

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from from contourscontours

SimplificationSimplificationSimplificationSimplification

DDDemoDemo

20,000 2,0008,000

ApplicationsApplicationsApplicationsApplicationsMulti‐resolution hierarchies for 

– efficient geometry processing

– level‐of‐detail (LOD) rendering( ) g

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SizeSize--Quality TradeoffQuality TradeoffSizeSize Quality TradeoffQuality Tradeoff

errorerror

ii

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sizesize

CompressionCompressionCompressionCompression

VRML = VRML = 200200K, zipped VRML = K, zipped VRML = 7070K, compressed = K, compressed = 1515KK

demodemo

GeometrySurface Connectivity

ParameterizationParameterization3D space (x,y,z)

2D parameter domain (u,v)

1818boundaryboundary

Application Application ‐‐ Texture Texture MappingMapping

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RemeshingRemeshingRemeshingRemeshing

More More RemeshingRemeshinggg

2121demodemo

QuadQuad RemeshingRemeshingQuad Quad RemeshingRemeshing

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Symmetry DetectionSymmetry DetectionSymmetry DetectionSymmetry Detection

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DeformationDeformationDeformationDeformation

Deformation TransferDeformation Transfere o a o a s ee o a o a s e

Deformation TransferDeformation Transfer

TargetTarget SourceSourceTargetTarget SourceSource

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What’s Next?What’s Next?What s Next?What s Next?

• Learn about geometry data structuresLearn about geometry data structures

• Go into detail of a few representative• Go into detail of a few representative algorithms

• Code them up!

• Have fun with geometry ☺

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