1. Multi-Layered Navigation Meshes Wouter G. van Toll, Atlas F. Cook IV, Roland Geraerts ICT.OPEN 2011

2. 2 / 18 Motivation Path planning in games and simulations Send virtual characters from start to goal… – …in a smooth an visually convincing way… – …such that they pay attention to other characters – …in real-time, even for large crowds Typical solution: navigation mesh – Subdivision of the walkable space into 2D polygons – Allows smooth, flexible movement – Should be built automatically…

3. 3 / 18 Research is necessary! If you think path planning in games is “solved”…

4. 4 / 18 What to do? What’s the problem? Human error Poor data structures Poor algorithms What do we want? A general framework, as automatic as possible Our framework: path planning with corridors – Automatically built navigation mesh – Global path planning – Local forces Our paper

5. 5 / 18 2D data structure: The medial axis The set of all points with at least two closest obstacle points “The middle” of the walkable space Maximum clearance to obstacles Preserves connectivity  A useful roadmap – “If there’s no path on the medial axis, then there’s no path at all”

6. 6 / 18 The Explicit Corridor Map (ECM) Annotated medial axis (Geraerts, 2010) All event points store a closest obstacle point on both sides Exact subdivision of the walkable space A navigation mesh O(n) storage O(n log n) build time

7. 7 / 18 The Explicit Corridor Map (ECM) - 2 Features of the ECM Global planning – On the MA only: efficient! – Result: path + corridor Indicative Route Method – (Karamouzas et al., 2009) Short paths with clearance Collision avoidance Local updates – “A Navigation Mesh for Dynamic Environments”, submitted to ICRA ‘12  Efficient, flexible path planning & crowd simulation

8. 8 / 18 Multi-layered navigation? Crowd simulation is often a 2D problem Many “3D” environments have a 2D top view (footprint) But what about multi-layered environments? It’s not 2D It’s not 3D  It’s a set of connected 2D problems Existing methods are approximating 3D grid: loss of precision Our method is exact

9. 9 / 18 This paper We extend the ECM to multi-layered environments It is constructed automatically Assumption: layers are given – Can be extracted from 3D data All 2D algorithms will still work  Real-time crowd simulation in multi-layered environments Recall: The ECM is an annotated medial axis Our algorithm first builds the multi-layered medial axis Same annotations: multi-layered ECM

10. 10 / 18 C 01 Multi-layered: Definitions What is a multi-layered environment? A realistic set of layers and connections Layer L i Bounded planar area with a polygonal footprint  2D Connection C AB Line segment connecting L A to L B Half obstacle in L A, half window to L B (access side) Also appears in L B, with flipped sides “Realistic” Layers are logically connected All footprints are taken from 1 top view

11. 11 / 18 Computing the M-L medial axis Construction algorithm 1. Build the 2D medial axis of each layer… – …treating connections as impassable obstacles – Correct, except in influence zones – i.e. the areas with an access side as a closest obstacle – These must be filled in

12. 12 / 18 Computing the M-L medial axis - 2 Construction algorithm 2. Open up the connections one by one – Choose any connection, say C AB between layers L A and L B – Find the connection scene S AB : all obstacles adjacent to C AB – Compute the medial axis of S AB – Merge it with the medial axes of L A and L B – Treat L A and L B as one layer from now on 3. Repeat until all connections are open Result: 1 continuous medial axis of the whole environment LALA LBLB C AB

13. 13 / 18 Computing the M-L medial axis - 3 Example Note: extra vertices on layer transitions Complexity n = #obstacle vertices; k = #connections Storage: O(n) usually O(kn) worst-case Construction: O(n log n) usually O(kn log n) worst-case – Worst case is very uncommon Incremental approach handles every case! Connections may be close together Order of opening does not matter

14. 14 / 18 Result: Multi-layered ECM Add closest-point annotations ECM computed in 46 ms Real-time multi-layered crowd simulation

15. 15 / 18 Experimental results Adding obstacles hardly affects stitching time Connection influence is usually local Running time increases with #connections Improvements are possible We can steer very large crowds in real-time Tens of thousands of characters

16. 16 / 18 Conclusion Our incremental algorithm… builds the medial axis of a multi-layered environment extends this to the multi-layered Explicit Corridor Map Our navigation mesh… is built automatically, given the separate layers is the first exact mesh for polygonal multi-layered environments supports efficient and flexible crowd simulation

17. 17 / 18 Future work What can still be added? Faster automatic layer extraction – Ongoing MSc projects Other game actions and environments – Jumping, 3D surfaces, … There will always be new interesting problems

18. 18 / 18 The End Thank you!