Polygon Soup for Polygon Soup for the the
Programmer’s Programmer’s Soul: 3D Soul: 3D
PathfindingPathfindingPatrick Smith ([email protected])
Greg Hjelstrom ([email protected])
IntroductionIntroduction
AI is an important contributor to the AI is an important contributor to the realism of games.realism of games. Pathfinding is a major component of Pathfinding is a major component of
convincing AI.convincing AI.
Problem DomainProblem Domain
Pathfinding requires connectivity.Pathfinding requires connectivity. A streetmap is a real-life example.A streetmap is a real-life example. Given this connectivity graph, paths can Given this connectivity graph, paths can
be found using well known algorithms be found using well known algorithms such as A*.such as A*.
How do we get this connectivity How do we get this connectivity data?data?
Connectivity SolutionsConnectivity Solutions
In grid-based games the grid inherently In grid-based games the grid inherently provided the connectivity data.provided the connectivity data. RTS games.RTS games.
Many 3D games use manual Many 3D games use manual connectivity.connectivity. Manually placed points and connections Manually placed points and connections
between points.between points. Automatic connectivity.Automatic connectivity.
How?How?
Floodfilling to the Floodfilling to the Rescue!Rescue!
We’ll reuse old 2D paint program We’ll reuse old 2D paint program technology – the recursive floodfill.technology – the recursive floodfill.
For our purposes the floodfill is For our purposes the floodfill is really a recursive physics simulation really a recursive physics simulation of an AI moving between points.of an AI moving between points.
The goal: given a seed point, detect The goal: given a seed point, detect all traversable locations in a level.all traversable locations in a level.
The Floodfill AlgorithmThe Floodfill Algorithm
Simulate the AI moving in each of Simulate the AI moving in each of the 4 cardinal directions.the 4 cardinal directions.
Add each successful “position” to a Add each successful “position” to a list.list. Mark this “position” as traversable.Mark this “position” as traversable. Store the connection between positions.Store the connection between positions.
Pop the head of the list and recurse Pop the head of the list and recurse into it.into it.
Movement SimulationMovement Simulation
The character is represented by an The character is represented by an axis aligned collision box.axis aligned collision box.
Our collision code uses swept boxes.Our collision code uses swept boxes. The floodfill algorithm performs tens The floodfill algorithm performs tens
of millions of swept box queries so of millions of swept box queries so we need to make them fast.we need to make them fast.
Colliding with the WorldColliding with the World
We use a hierarchical bounding volume We use a hierarchical bounding volume tree to quickly determine what meshes tree to quickly determine what meshes in the world need to be checked for in the world need to be checked for collision.collision.
Each mesh contains an internal Each mesh contains an internal bounding volume tree to quickly bounding volume tree to quickly determine which of its triangles need to determine which of its triangles need to be checked for collision.be checked for collision.
For speed and space, we use axis aligned For speed and space, we use axis aligned bounding boxes.bounding boxes.
Swept Box CollisionSwept Box Collision
Separating axis theoremSeparating axis theorem Given two convex polyhedra, if they are not Given two convex polyhedra, if they are not
intersecting at least one separating plane will intersecting at least one separating plane will exist.exist.
The plane normal will be defined by either:The plane normal will be defined by either: One of the faces of either objectOne of the faces of either object The cross product of two edges, one from each objectThe cross product of two edges, one from each object
Early rejection.Early rejection. Once you find a separating plane, you can reject the Once you find a separating plane, you can reject the
triangle.triangle. This algorithm can be extended to support “swept” This algorithm can be extended to support “swept”
convex primitives, providing “time of collision”.convex primitives, providing “time of collision”.
Making a MoveMaking a Move
During the floodfill, to move one “unit” in During the floodfill, to move one “unit” in any given direction, we must successfully any given direction, we must successfully complete the following steps:complete the following steps: Move up the maximum height the AI can step Move up the maximum height the AI can step
over.over. Sweep the collision box one “unit” in the Sweep the collision box one “unit” in the
movement direction at an angle equal to the movement direction at an angle equal to the steepest slope the AI can climb.steepest slope the AI can climb.
Finally, sweep the collision box back down to Finally, sweep the collision box back down to the ground to see if we have a place to stand.the ground to see if we have a place to stand.
Of Units and PositionsOf Units and Positions
Our pathfinding system will make Our pathfinding system will make good use of the AI’s collision box.good use of the AI’s collision box.
Unit of Distance:Unit of Distance: A unit is ¼ of the AI’s collision box.A unit is ¼ of the AI’s collision box.
Position:Position: A position is the volume defined by A position is the volume defined by
splitting the collision box into four splitting the collision box into four equal pieces.equal pieces.
Visualizing the DataVisualizing the Data
Each “position” is a box.Each “position” is a box. Each unit moves one box length Each unit moves one box length
away.away. This forms a sort of grid.This forms a sort of grid. However, since the floodfill can However, since the floodfill can
travel over and under overpasses travel over and under overpasses there can be more then one “cell” there can be more then one “cell” for every x,y position on the grid.for every x,y position on the grid.
What the Data Gives UsWhat the Data Gives Us
Each cell “knows” which directions Each cell “knows” which directions it can travel (up, down, left, right).it can travel (up, down, left, right).
This linkage forms a connectivity This linkage forms a connectivity graph of all possible traversable graph of all possible traversable locations in the level.locations in the level.
Given this connectivity graph we can Given this connectivity graph we can now use our favorite shortest path now use our favorite shortest path algorithm to pathfind between any algorithm to pathfind between any two points in the level. two points in the level.
Too Much Data!Too Much Data!
A “typical” level might require in A “typical” level might require in excess of 2 million cells.excess of 2 million cells.
This can require upwards of 128 MB This can require upwards of 128 MB of RAM just to store the graph.of RAM just to store the graph.
This is way too much data for a real This is way too much data for a real time game.time game.
CompressionCompression
The goal is to combine cells into The goal is to combine cells into largest possible rectangular regions.largest possible rectangular regions.
SectorsSectors
Compressed “cells” become sectors.Compressed “cells” become sectors. Sectors are 3D axis-aligned boxes Sectors are 3D axis-aligned boxes
that the pathfind system can use to that the pathfind system can use to determine where an AI is in the determine where an AI is in the connectivity graph.connectivity graph.
Sectors need connection data to Sectors need connection data to other sectors.other sectors.
PortalsPortals
Portals are connections between sectors.Portals are connections between sectors. Portals can be one-way or two-way.Portals can be one-way or two-way. Portals have a physical location in the Portals have a physical location in the
world.world. Because of this, an AI simple needs to “walk” to Because of this, an AI simple needs to “walk” to
the portal, at which point they are at the the portal, at which point they are at the destination sector.destination sector.
This allows us to easily integrate “teleporters” This allows us to easily integrate “teleporters” such as doors, ladders, elevators, or even star-such as doors, ladders, elevators, or even star-trek like teleporters.trek like teleporters.
How do we generate these portals?How do we generate these portals?
Portal GenerationPortal Generation
During the compression stage, we During the compression stage, we store a list of edge cells with each store a list of edge cells with each sector.sector.
Each edge cell also stores which Each edge cell also stores which sector it belongs to.sector it belongs to.
Portal GenerationPortal Generation
Once all sectors have been Once all sectors have been generated, the edge cells can then generated, the edge cells can then be converted into portals.be converted into portals. These portals know what sector they These portals know what sector they
are coming from and which sector they are coming from and which sector they are going to.are going to.
Data SummaryData Summary
Floodfill the world by simulating the Floodfill the world by simulating the AI walking in a recursive pattern.AI walking in a recursive pattern.
Compress the millions of floodfill Compress the millions of floodfill cells into sectors.cells into sectors.
Use the edge cells of a sector to Use the edge cells of a sector to generate portals between sectors. generate portals between sectors.
Floodfill DemoFloodfill Demo
Extending the PathsolveExtending the Pathsolve
Lets consider a few pieces of Lets consider a few pieces of information we can “bake” into our information we can “bake” into our pathfind data that will allow us to pathfind data that will allow us to easily path solve across “teleporters” easily path solve across “teleporters” such as doors, elevators, and ladders.such as doors, elevators, and ladders.
A teleporter is a “feature” of the level A teleporter is a “feature” of the level that, when activated, will transport a that, when activated, will transport a game object from one part of the game object from one part of the world to the other.world to the other.
Floodfilling across Floodfilling across TeleportersTeleporters
Consider a building with roof access Consider a building with roof access via elevator only.via elevator only. Currently, the pathsolve will never Currently, the pathsolve will never
reach the roof.reach the roof. To solve this:To solve this:
During floodfill, check each cell to see if its During floodfill, check each cell to see if its inside an “entrance zone”.inside an “entrance zone”.
Create a cell inside the “exit zone” for the Create a cell inside the “exit zone” for the elevator and continue floodfilling from this elevator and continue floodfilling from this cell. cell.
Pathsolving Across Pathsolving Across TeleportersTeleporters
Incorporate teleporters post floodfill. Incorporate teleporters post floodfill. Each teleporter has an entrance and exit “zone”. Each teleporter has an entrance and exit “zone”. For each teleporter in the level, check to see if For each teleporter in the level, check to see if
both the entrance and exit zones intersect a both the entrance and exit zones intersect a pathfind sector.pathfind sector.
Create a “teleporter” portal and add it to the Create a “teleporter” portal and add it to the portal list for the entrance sector.portal list for the entrance sector.
Create a portal and add it to the portal list for Create a portal and add it to the portal list for the exit sector.the exit sector.
Link the entrance portal to the exit portal as a Link the entrance portal to the exit portal as a one-way transition.one-way transition.
Teleport Portal DataTeleport Portal Data
Embed as much information about Embed as much information about the teleporter as necessary into the the teleporter as necessary into the entrance portal.entrance portal. Flag specifying teleporter type.Flag specifying teleporter type.
Door, elevator, ladder, etc.Door, elevator, ladder, etc. Teleporter mechanism ID.Teleporter mechanism ID. Keys needed to operate mechanism.Keys needed to operate mechanism.
Solving the PathSolving the Path
Given our connectivity graph, solving Given our connectivity graph, solving the path is now straightforward.the path is now straightforward. Given an AI’s current position and a Given an AI’s current position and a
destination position we can lookup the destination position we can lookup the pathfind sectors that contain these points. pathfind sectors that contain these points.
Path is unsolvable if either sector cannot be Path is unsolvable if either sector cannot be found.found.
We now have a start position and end We now have a start position and end position within our connectivity graph.position within our connectivity graph.
The Pathsolve AlgorithmThe Pathsolve Algorithm
Most traditional shortest path Most traditional shortest path algorithms can be used.algorithms can be used.
A modified A* worked pretty good for A modified A* worked pretty good for Renegade.Renegade. First, loop over all the portals for the First, loop over all the portals for the
starting sector.starting sector. Each portal has a destination sector.Each portal has a destination sector. Each of these destination sectors has a list Each of these destination sectors has a list
of portals.of portals. Continue traversing sectors until you’ve Continue traversing sectors until you’ve
reached the destination sector.reached the destination sector.
Path DemoPath Demo
Time to SolveTime to Solve
Short paths can solve quickly.Short paths can solve quickly. Long paths take a bit longer.Long paths take a bit longer. 20 AI’s solving long paths at the 20 AI’s solving long paths at the
same time can tax even the most same time can tax even the most efficient pathsolver.efficient pathsolver.
Distributing the SolveDistributing the Solve
If an AI takes 15 frames to solve a If an AI takes 15 frames to solve a path in a 30 FPS game, they will path in a 30 FPS game, they will only pause for ½ a second.only pause for ½ a second.
In most cases, this short pause is not In most cases, this short pause is not noticeable.noticeable.
This means we can devote a set This means we can devote a set amount of time each frame to amount of time each frame to pathfinding and simply solve as pathfinding and simply solve as much of each path as possible.much of each path as possible.
The Distributed The Distributed AlgorithmAlgorithm
The pseudo-algorithm:The pseudo-algorithm:
while (Time_Left () && PathSolver != NULL) {
if (PathSolver->Process (Time_Left_This_Frame)) {
RELEASE (PathSolver);
PathSolver = Get_Next_Path_Solver (); }
}
The Distributed The Distributed AlgorithmAlgorithm
The pseudo-algorithm:The pseudo-algorithm:
while (Time_Has_Not_Elapsed) {
CPathfindSector * sector = Get_Least_Cost_Sector ();
if (sector == NULL) {
Handle_No_Path ();
} else if (sector == DestinationSector) {
Hande_Path_Found ();
} else {
CPathfindPortal *portal = NULL;
while (portal = sector->Get_Next_Portal (portal)) {
Process_Portal (portal);
}
}
}
Robotic PathsRobotic Paths
The results of this path solve will The results of this path solve will often look robotic.often look robotic. Straight lines connecting points in the Straight lines connecting points in the
portals along the path.portals along the path. This path can be made more organic This path can be made more organic
by creating a spline which goes by creating a spline which goes through its points.through its points.
Smoothing the PathSmoothing the Path
We chose to use a natural spline whose We chose to use a natural spline whose control points are points along the path. control points are points along the path.
Unfortunately this can cause the path to stray Unfortunately this can cause the path to stray outside of valid pathfind sectors; causing outside of valid pathfind sectors; causing characters to get stuck against walls for characters to get stuck against walls for example.example.
To solve this problem, we convert the spline To solve this problem, we convert the spline into a series of Bezier curves and constrain into a series of Bezier curves and constrain the control points to our pathfind sectors.the control points to our pathfind sectors. A Bezier curve is guaranteed to be contained by A Bezier curve is guaranteed to be contained by
the convex shape defined by its control points.the convex shape defined by its control points.
Visualizing the SplineVisualizing the Spline
Innate WaypathsInnate Waypaths
Waypaths are hand-placed paths Waypaths are hand-placed paths consisting of a series of points.consisting of a series of points. Waypaths can be linear or splined, one-Waypaths can be linear or splined, one-
way, two-way, and looping.way, two-way, and looping. Each point on the waypath can encode Each point on the waypath can encode
specific information such as speed up, specific information such as speed up, slow down, jump, crouch, slide, crawl, slow down, jump, crouch, slide, crawl, etc.etc.
The path solver can bias towards these The path solver can bias towards these waypaths to achieve complex results.waypaths to achieve complex results.
Using Innate WaypathsUsing Innate Waypaths Create a pathfind sector without position or size.Create a pathfind sector without position or size. Intersect each point on the waypath with sectors Intersect each point on the waypath with sectors
that already exist in the world.that already exist in the world. Create portals at each intersection point that exit Create portals at each intersection point that exit
from the real-world sectors onto the “imaginary” from the real-world sectors onto the “imaginary” innate waypath sector.innate waypath sector.
Intersect each segment of the waypath with Intersect each segment of the waypath with sector boundaries that already exist in the sector boundaries that already exist in the world.world. Create portals at these intersections as well.Create portals at these intersections as well.
Flag these portals so the shortest path heuristic Flag these portals so the shortest path heuristic can make them “cheaper” to follow.can make them “cheaper” to follow.
Waypath DemoWaypath Demo
Learning From the Learning From the PlayerPlayer
Players can conceive of more Players can conceive of more complicated actions than AI.complicated actions than AI.
By allowing the AI to “copy” some of By allowing the AI to “copy” some of the player’s moves, they appear the player’s moves, they appear more intelligent.more intelligent.
Implementing LearningImplementing Learning
Everytime the player jumps and lands:Everytime the player jumps and lands: Lookup the pathfind sector the player Lookup the pathfind sector the player
jumped from and landed in.jumped from and landed in. Record the player’s orientation and Record the player’s orientation and
velocity at jump time.velocity at jump time. Add a temporary “jump” portal from the Add a temporary “jump” portal from the
start sector to the land sector.start sector to the land sector. The AI will now seamlessly incorporate The AI will now seamlessly incorporate
this move into its pathsolve.this move into its pathsolve.
Learning DemoLearning Demo
Vehicle PathfindingVehicle Pathfinding
Vehicles are intrinsically more Vehicles are intrinsically more difficult.difficult. Vehicles are bigger than characters.Vehicles are bigger than characters. Vehicles have turn radius.Vehicles have turn radius. Vehicles do not stop on a dime.Vehicles do not stop on a dime. Vehicles can roll over.Vehicles can roll over. Vehicles behave differently in forwards Vehicles behave differently in forwards
and reverse.and reverse.
Re-using DataRe-using Data
Vehicles can reuse bipedal data.Vehicles can reuse bipedal data. Take into consideration the vehicle’s Take into consideration the vehicle’s
turn radius when evaluating portals.turn radius when evaluating portals. If a vehicle cannot make a turn, coming If a vehicle cannot make a turn, coming
from its current portal to the from its current portal to the destination portal, then skip the destination portal, then skip the destination portal. destination portal.
Vehicle CurvesVehicle Curves
Vehicles need to “turn out” to make sharp Vehicles need to “turn out” to make sharp corners.corners.
By creating a vehicle curve that is based By creating a vehicle curve that is based on the turn radius of the vehicle, the on the turn radius of the vehicle, the vehicle will seamlessly follow its path.vehicle will seamlessly follow its path.
Vehicle curve is composed of three parts:Vehicle curve is composed of three parts: The exit curve from the previous point.The exit curve from the previous point. A straight line from the exit curve to the A straight line from the exit curve to the
entrance curve of the next point.entrance curve of the next point. The entrance curve to the next point.The entrance curve to the next point.
Vehicle Curve AnatomyVehicle Curve Anatomy
Here you can see the 3 distinct parts Here you can see the 3 distinct parts of the vehicle curve.of the vehicle curve.
Vehicle Curve ResultsVehicle Curve Results
Here is a comparison of a linear Here is a comparison of a linear (unsplined) vehicle path and the (unsplined) vehicle path and the post-processed vehicle curve.post-processed vehicle curve.
Vehicle DemoVehicle Demo
ConclusionConclusion Floodfill solves “static” pathfinding.Floodfill solves “static” pathfinding.
““Kinks” in the path arise due to the non-Kinks” in the path arise due to the non-uniform nature of the sectors.uniform nature of the sectors.
Does not address dynamic objects.Does not address dynamic objects. Innate waypaths and jump portals Innate waypaths and jump portals
increase intelligence.increase intelligence. Arbitrary vehicle pathfinding is difficult.Arbitrary vehicle pathfinding is difficult.
Reusing data is possible, but not optimal.Reusing data is possible, but not optimal. Vehicle curves simplify the path following Vehicle curves simplify the path following
logic.logic.
Q & AQ & A
