combinational vector field pathfindinganima/408/notes/crowds/vectorfield.pdfuniversity of regina ....

J O H A N N E S M O E R S C H & H O W A R D H A M I L T O N

U N I V E R S I T Y O F R E G I N A

Hybrid Vector Field Pathfinding

The Problem

The Method

A* for Long-Range Pathfinding

Crowd Continuum for Medium-Range Pathfinding

Waypoint Graph

A way of planning routes for characters that is not used much any more

NavMesh

Short for Navigational Mesh

Constructing NavMesh

A navmesh can be constructed by starting with one polygon (typically a rectangle) representing the overall area. This is the initial open area.

Add the obstacles, each modeled by a polygon, one by one.

When an obstacle is added it is either completely inside the open area or overlaps part of it (otherwise it wouldn’t be an obstacle!).

Split the open area into more polygons by drawing a line segment “out” from the obstacle all the way across the open area (example follows)

Constructing NavMesh

Suppose a white obstacle is placed overlapping the blue open area. Draw lines outward to form new polygons. Remove area covered by obstacle.

Constructing NavMesh

Four cases for consecutive vertices of the obstacle polygon were identified, as shown below.

Traversing NavMesh

To measure the lengths of a path through a navmesh, go from the center of one connecting side to the center of the other connecting side.

Density Map

Velocity Map

Legend for Directions

+x −x

−y

+y

Speed Map

Cost Map

Potential Field

Fast Marching Method

Vector Field

Legend for Directions

+x −x

−y

+y

Lane Formation Results

Congestion Avoidance Results

Maze Results

Performance Results

64x64 128x128 192x192 256x256

4 ms 18 ms 37 ms 65 ms

References

Cui, Xiao. “A*-based Pathfinding in Modern Computer Games” IJCSNS January 2011. <http://paper.ijcsns.org/07_book/201101/20110119.pdf> Gas Powered Games. “Supreme Commander 2 ‘Flowfield Pathfinding’ Trailer” Youtube 2010.

<http://www.youtube.com/watch?v=bovlsENv1g4> Shopf, Jeremy. “Crowd Simulation in Froblins” SIGGRAPH 2008.

<http://s08.idav.ucdavis.edu/shopf-crowd-simulation-in-froblins.pdf> Tozour, Paul. “Fixing Pathfinding Once and For All” ai-blog.net 2008. <http://www.ai-blog.net/archives/2008_07.html> Treuille, Adrien. “Continuum Crowds” SIGGRAPH 2006.

<http://grail.cs.washington.edu/projects/crowd-flows/continuum-crowds.pdf>