Multi-Layered Navigation MeshesWouter G. van Toll, Atlas F. Cook IV, Roland GeraertsICT.OPEN 2011

2 / 18Motivation

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 / 18Research is necessary!

If you think path planning in games is “solved”…

4 / 18What 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 / 182D 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 / 18The Explicit Corridor Map (ECM)

Annotated medial axis (Geraerts, 2010)• All event points store

a closest obstacle pointon both sides

• Exact subdivision of the walkable space

A navigation mesh• O(n) storage• O(n log n) build time

7 / 18The 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 / 18Multi-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 / 18This 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 / 18

C01

Multi-layered: Definitions

What is a multi-layered environment?• A realistic set of layers and connections

Layer Li

• Bounded planar area with a polygonal footprint 2D

Connection CAB

• Line segment connecting LA to LB

• Half obstacle in LA, half window to LB (access side)

• Also appears in LB, with flipped sides

“Realistic”• Layers are logically connected• All footprints are taken from 1 top view

11 / 18Computing the M-L medial axis

Construction algorithm1. 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 / 18Computing the M-L medial axis - 2

Construction algorithm2. Open up the connections one by one

– Choose any connection, say CAB between layers LA and LB

– Find the connection scene SAB: all obstacles adjacent to CAB

– Compute the medial axis of SAB

– Merge it with the medial axes of LA and LB

– Treat LA and LB as one layerfrom now on

3. Repeat until all connections are open

Result: 1 continuous medial axis of the whole environmentLA

LB

CAB

13 / 18Computing 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 / 18Result: Multi-layered ECM

Add closest-point annotations• ECM computed in 46 ms• Real-time multi-layered crowd simulation

15 / 18Experimental 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 / 18Conclusion

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 / 18Future 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 / 18The End

Thank you!