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 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 Augmentations Future Work 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)

Coral to go here

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

Future Directions 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