1. Modeling Dendritic Structures Using 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 Augmentations Future Work 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

13. 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

22. real DLA
imitated DLA

23. 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

24. real DLA
imitated DLA

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

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

29. Coral to go here

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

33. Future Directions Procedural endpoint placement Additional phenomena
Path smoothing
Path extrusion

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