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Modeling Dendritic Structures Using Path Planning

Modeling Dendritic Structures Using Path Planning. Ling Xu, David Mould. Importance of Dendrites. trees, lichens, coral, lightning, venation, river systems. Man-made dendrites. mazes networks. Existing Methods. Diffusion-Limited Aggregation. L-systems. Ontogenetic Modeling.

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Modeling Dendritic Structures Using Path Planning

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  1. Modeling Dendritic StructuresUsing Path Planning Ling Xu, David Mould

  2. Importance of Dendrites • trees, lichens, coral, lightning, venation, river systems

  3. Man-made dendrites • mazes • networks

  4. Existing Methods Diffusion-Limited Aggregation L-systems

  5. Ontogenetic Modeling • Ontogenetic modeling: approach appearance of model without regard for underlying process • Seek lightweight means of mimicking appearance of dendritic objects • Path planning: • irregular curves • paths from root never cross

  6. Path planned dendrites

  7. Overview • Implementation • Results • timing • model gallery • Augmentations • Future Work

  8. Basic Idea • Geodesics in a weighted graph • Control: • weights in graph influence path shape • endpoint choice affects dendrite’s appearance • generator shape, likewise

  9. Implementation • Dijkstra’s algorithm used to get costs from root to all other nodes in graph • O(N) to cover graph • O(n) for path from arbitrary endpoint to root • endpoints placed by hand or procedurally

  10. Fractal Dendrites • Real objects often exhibit fractal (multiscale) detail • Explicitly introduce hierarchical detail: • Create low-frequency detail • Add structure at higher frequency • Repeat previous step

  11. real DLA imitated DLA

  12. Timing Comparison • Previously reported methods: minutes to hours, depending on complexity • Random walker DLA: 25k sites, 7.5 min • Our method: • simple 2D: about 1 second • simple 3D: about 3 seconds • fractal 2D: about 7.5 seconds

  13. real DLA imitated DLA

  14. “Rocks” • Multi-source path planning partitions space – can be used to produce irregular 3D objects

  15. Model Creation • Extrusion around path • Isosurface within 3D graph • distance values known • choose isovalue, use isosurface extraction to get mesh (marching cubes)

  16. Limitations • Resolution bound to fixed resolution of graph • in 3D, adding diagonal edges costly (26-connected vs. 6-connected) • Solution? • path smoothing • multiresolution graph

  17. Future Directions • Procedural endpoint placement • Additional phenomena • Path smoothing • Path extrusion

  18. Acknowledgements • Thanks to Jeremy Long for fruitful discussions regarding path planned models • This work was supported by NSERC RGPIN 299070-04 and by the University of Saskatchewan

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