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Developer’s Survey of Polygonal Simplification Algorithms

This article surveys polygonal simplification algorithms based on David Luebke's IEEE CG&A paper, delving into essential questions like why simplification is crucial and what to consider regarding model types. It outlines different models, such as smooth organic shapes and sharp-edged machine parts, emphasizing the need for specific algorithms. Key topics include topology preservation, simplification mechanisms (sampling, adaptive subdivision, decimation, vertex merging), and differing requirements for static, dynamic, and view-dependent approaches. The discussion also highlights trends and the importance of geometric accuracy and visual fidelity in model optimization.

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Developer’s Survey of Polygonal Simplification Algorithms

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  1. Developer’s Survey of Polygonal Simplification Algorithms Based on David Luebke’s IEEE CG&A survey paper

  2. Some questions to ask… • Why simplification? • What are my models like? • What matters to me most?

  3. Why? • Eliminate redundant geometry

  4. Why? (2) • Download models from the web

  5. Why (3) • Improve rendering speed (generating level of details) – produce LODs

  6. What are my models like? • Smooth, organic forms • Machine parts with sharp corners Different models need different simlification algorithms

  7. What are my models like? • Precomputed lighting and textures. • Small number of large complex objects – sci vis • Multiple moderately complex objects- video game • Large number of small objects – CAD models

  8. What’s important for you? • Geometric accuracy? • Hausdorff distance • Volume deviation • Visual fidelity? (how to measure?) • Pre-processing time? • Run-time rendering time? • Automatic?

  9. Taxonomy of SA • Simplification algorithms can be classified into groups based on different criteria: • Topology preservation • Simplification Mechanism • Static/Dynamic/View-dependent

  10. Topology • Refers to the connected polygonal mesh’s structure • Genus : the number of holes (handles) in the object • Sphere and Cube: 0 • Doughnut and Coffee Cup: 1

  11. Topology (cont’d) • 2D manifold (local property) • Exact two triangle share an edge • Every vertex is shared by a ring of triangles to form a surface (local topology is a disc) • Every triangle shares edges with exact three triangles

  12. Topology (cont’d) • Examples of manifold and non-manifold

  13. Topology and SA • Topology-preserving algorithms • Preserve manifold connectivity at every step (don’t close up or create holes) Yes Yes No

  14. Topology and SA (cont’d) •  Good visual fidelity •  Limited simplification •  Often require the model to be a manifold to begin with (less robust) Topology-preserving algorithms

  15. Topology and SA (cont’d) Opposite: Topology-modifying algorithms •  Permit drastic simplification •  Poor visual quality/Popping effect •  Often insensitive to topological features • Work best when drastic simplification is needed (visualization or complex scenes)

  16. Topology and SA Summary • Topology-preserving or Topology-modifying? • Topology-tolerant or Topology-sensitive? Questions to ask before using the algorithm:

  17. Mechanism • Strategies used to remove polygons • Sampling • Adaptive Subdivision • Decimation • Vertex Merging

  18. (1) Sampling • Sample the surface: • Embedding a 3D volumetric grid around the surface • Remove high-frequency (fine) features • Applying image processing to perform low-pass filter • Recover the surface from filtered samples: • Recover the simplified surface from the low-passed volume

  19. Sampling (cont’d) •  High frequency features are gradually removed •  high frequency features are hard to sample • Work best for smooth objects

  20. (2) Adaptive Subdivisoin • Find a base mesh • Recursively subdivide the base mesh to approach the initial mesh • Example: Terrain simplification (rectangle as the base mesh)

  21. Adaptive Subdivision • Work best when the base mesh is easily found (can be very hard) • Preserve topology • Multi-resolution editing (low level feature naturally propagate to finer level)

  22. (3) Decimation • Iteratively remove vertices from the mesh • Remove the associated triangles • Retriangulate the resulting holes at each step

  23. Decimation (cont’d) • Simple to code and very fast • Topology preserving • No drastic simplification • Topology tolerant

  24. (4) Vertex Merging • Collapsing two or more vertices into a single vertex • Reconnecting the points with the remaining adjacent vertices • Different algorithms have varying sophistication in which vertices to merge in what order

  25. Vertex Merging (cont’d)

  26. Mechanism Summary • Sampling • Adaptive Subdivision • Decimation • Vertex Merging

  27. Static/Dynamic/View-dependt • Static: Compute a fixed set of simplifications or LODs offline • Dynamic: Encoding a continuous spectrum of LODs as opposed to a fixed set • Better granularity • Support progressive transmission

  28. Static/Dynamic/View-dependt • View-dependent: Extending Dynamic methods – LOD selections are based on view dependent criteria: • Distance to the eye • Silhouette regions •  better fidelity for a given polygon count •  increase the run time CPU load for choosing the LODs

  29. Issues and Trends • Converge on vertex merging as the underlying mechanism • Hierarchical vertex merging provides general framework • Still lack an agree-upon definition of fidelity • Perceptual metric is hard to get

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