polygonal meshes - princeton university computer science · polygonal mesh processing storage o...

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Polygonal Meshes

Thomas Funkhouser

Princeton University

COS 526, Fall 2010

Digital Geometry Processing

Processing of 3D surfaceso Creation, acquisitiono Storage, transmissiono Editing, animation, simulationo Manufacture

Applicationso Movies, gameso Computer-aided designo Medicine, biologyo Art, history

Sweldens


Many possible surface representationso Polygonal mesheso Parametric surfaceso Subdivision surfaceso Implicit surfaceso etc.


Let’s focus on 3D polygonal mesheso Simple, common representationo Rendering with hardware supporto Output of many acquisition toolso Input to many simulation/analysis tools

Stanford Graphics Lab

3D Polygonal Meshes

Set of polygonal faces representing a 2D surface embedded in 3D

Zorin & Schroeder, SIGGRAPH 99, Course Notes

3D Polygonal Meshes

Set of polygonal faces representing a 2D surface embedded in 3D

Zorin & Schroeder, SIGGRAPH 99, Course Notes

Face

Vertex

Edge

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Outline

Acquisition

Processing

Representation

Outline

Acquisition

Processing

Representation

Polygonal Mesh Acquisition

Interactive modelingo Polygon editorso Interchange formats

Scannerso Laser range scannerso CAT, MRI, etc. (isosurfaces)

Simulationso Physical processes


Interactive modelingØ Polygon editorso Interchange formats



Sketchup

Blender


Interactive modelingo Polygon editorsØ Interchange formats



Princeton Shape Benchmark



ScannersØ Laser range scannerso CAT, MRI, etc. (isosurfaces)


Digital Michelangelo ProjectStanford

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Large Geometric Model RepositoryGeorgia Tech




SimulationsØ Physical processes

MIT

Outline

Acquisition

Processing

Representation

Polygonal Mesh Processing

Storageo Compressiono Transmission

Analysiso Parameterizationo Differential geometryo Feature detectiono Segmentation

Editingo Smoothing, sharpening, etc.o Deformationo Completion


StorageØ Compressiono Transmission



Lossy Compression(Simplification)

Garland


Storageo CompressionØ Transmission



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AnalysisØ Parameterizationo Differential geometryo Feature detectiono Segmentation

Editingo Smoothing, sharpening, etc.o Deformationo Completion Sheffer



Analysiso ParameterizationØ Differential geometryo Feature detectiono Segmentation

Editingo Smoothing, sharpening, etc.o Deformationo Completion Sheffer



Analysiso Parameterizationo Differential geometryØ Feature detectiono Segmentation

Editingo Smoothing, sharpening, etc.o Deformationo Completion Novatnek et al.



Analysiso Parameterizationo Differential geometryo Feature detectionØ Segmentation

Editingo Smoothing, sharpening, etc.o Deformationo Completion Katz & Tal




EditingØ Smoothing, sharpening, etc.o Deformationo Completion Desbrun

Smoothing

Sharpening




Editingo Smoothing, sharpening, etc.Ø Deformationo Completion Sheffer

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Editingo Smoothing, sharpening, etc.o DeformationØ Completion Podolak

Outline

Acquisition

Processing

Representation

Polygon Mesh Representation

Data structures determine algorithmso Data structure must support key operations of

algorithm efficiently

Examples:o Drawing a mesho Removing a vertexo Computing per-vertex normals

Different data structures for different algorithms


Important properties of mesh representation?


Important properties of mesh representation?o Efficient traversal of topologyo Efficient use of memory


Possible data structureso List of independent faceso Vertex and face tableso Adjacency listso Winged edgeo Half edgeo etc.

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Independent Faces

Each face lists vertex coordinateso Redundant verticeso No topology information

Vertex and Face Tables

Each face lists vertex referenceso Shared verticeso Still no topology information

Adjacency Lists

Store all vertex, edge, and face adjacencies o Efficient topology traversalo Extra storage

Partial Adjacency Lists

Can we store only some adjacency relationshipsand derive others?

Winged Edge

Adjacency encoded in edgeso All adjacencies in O(1) timeo Little extra storage (fixed records)o Arbitrary polygons

Winged Edge

Example:

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Half Edge

Adjacency encoded in edgeso All adjacencies in O(1) timeo Little extra storage (fixed records)o Arbitrary polygons

Similar to winged-edge,except adjacency encoded in half-edges

e heinv

vbegin

Fleft

henext

Summary

Polygonal mesh overviewo Acquisitiono Processingo Representation

Summary

Do polygonal mesh reps have these properties?o Easy to acquireo Accurateo Conciseo Efficient displayo Efficient intersectionso Efficient deformationso Efficient topology changeso Guaranteed validityo Guaranteed smoothnesso Intuitive editing controls

Summary

Next time: Laplacian Surface Editing

polygonal meshes - princeton university computer science · polygonal mesh processing storage o...

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