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
L-systems
Diffusion-Limited
Aggregation
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
Path planned dendrites
Overview
• Implementation
• Results
– timing
– model gallery
• Augmentations
• Future Work
Basic Idea
• Geodesics in a weighted graph
• Control:
– weights in graph influence path shape
– endpoint choice affects dendrite’s appearance
– generator shape, likewise
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
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
real DLA
imitated DLA
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
real DLA
imitated DLA
“Rocks”
• Multi-source path
planning partitions
space – can be used
to produce irregular
3D objects
Model Creation
• Extrusion around path
• Isosurface within 3D graph
– distance values known
– choose isovalue, use isosurface extraction to get
mesh (marching cubes)
Limitations
• Resolution bound to fixed resolution of
graph
– in 3D, adding diagonal edges costly (26connected vs. 6-connected)
• Solution?
– path smoothing
– multiresolution graph
Future Directions
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Procedural endpoint placement
Additional phenomena
Path smoothing
Path extrusion
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