Artificial Intelligence in Game Design

Map Representation and Path Finding

Path Creation

Strategy “Where to move to” Path Planning “How to get there” Movement “Get there” Current location Idea: Specify goal location and let AI find path from current position to goal

Waypoints

• Path = graph structure • Vertices = waypoints on path • Edges between waypoints directly reachable from one another Current location

Waypoints and Costs

• Goals: – Provide waypoints that let characters reach all locations on level • Can

SEEK

any location from some waypoint – Minimize number of waypoints • Cost of path planning =

O

(number of waypoints) 2 • Key idea: – Waypoint creation done offline (during game design) – Path planning done many times during gameplay

Defining Waypoints

• Defining waypoints manually – Usually at points where direction change necessary • Corners • Intersections • Doors – Character must be able to directly seek waypoint from any adjacent waypoint – Character must be able to directly seek all points in map from some waypoint

Defining Waypoints Manually

Defining Waypoints

• Convenient to generate waypoints automatically • Simplest case: simple 2D grid (square or hex) – Some points impassible (water, mountains, etc.)

Defining Waypoints Automatically

• Can often use floor tiles – Used by level designer to create level – Used to define visibility, lighting areas, where sounds can be heard, etc.

– Usually triangular or rectangular

Defining Waypoints Automatically

• One waypoint per tile – Usually in center • Link waypoints in adjacent tiles • May still need to tweak manually – Make sure all points directly reachable from a waypoint – Add strategic waypoints (cover, shadow, etc.) – Make special waypoints for door entry, exit, etc.

Triangular Mesh Generation

• Automatically generating triangular tiles that cover level – Connect some two adjacent walls to form a triangle – Continue connecting adjacent walls and/or adjacent borders – Continue until all walls are part of some triangle

Waypoint Cleanup

• Can automatically remove some “redundant” waypoints – Not an endpoint (degree > 1) – All adjacent points can directly reach each other without using that waypoint – Often based on visibility (ray tracing)

Path Creation

• Path = list of adjacent waypoints 73 27 21 45 • Move along path using

FollowPath

steering – Seek “close enough” to next path waypoint 45 73 Desired path 27 21

Path Creation

• • Initial waypoint = – Waypoint in same tile as character – Closest waypoint to character • May need to test each – Avoid going backward initially – Less of a problem with small tiles

Seek

that first waypoint Goal: ATM Should seek this first

Path Creation

• • Reaching goal = – Character in same tile as goal – Character at waypoint nearest goal

Arrive

at goal from that last waypoint Goal

Hierarchical Paths

• Simple maps at different levels of detail – Better than single map with thousands of points – Single best solution to minimizing pathfinding costs • Connect points on high-level maps to entrances/exits on low level maps

Hierarchical Paths

• Requires hierarchical representation of location Me At podium Room 301 Meshel Hall Holy Grail Under seat D001 Computer Lab Kilcawley Center Path to room 301 exit Path from 301 exit to Meshel Hall exit Path from Meshel Hall exit to Kilcawley Center entrance Path from Kilcawley Center entrance to Computer Lab entrance Path from Computer Lab entrance to seat D001

Path Planning

• May have several possible paths from current location to goal • Need to find “best” path – Otherwise character does not look intelligent!

Goal Bad path Good path

Edge Costs

• “Best” path defined by edge costs – Time to travel path – Distance, etc.

• Best path = path with smallest total cost 4 3 6 Goal 5 4 Good path Cost = 22 4 5 7 Bad path Cost = 47 4 4 5 5 3 4 4 2

Terrain-based Costs

• Can base cost on terrain type – Grass = 1 – Desert = 2 – Forest = 3 – River = 20 • Often multiply by edge distance – 5 miles of desert = cost of 10 – 8 miles of grass with ¼ mile river = cost of 8 + 5 = 13

Other Edge Costs

•

Danger

– Cost of traveling through enemy territory = 5 * normal cost – Important part of tactical movement

Other Edge Costs

•

Visibility

– –

Dark = factor of 3 Fog = factor of 2

– Can also add to danger Long path now best

Character Edge Costs

• Different characters may have different edge costs – Grass = 2 – Desert = 2 – Forest = 10 – River = 30 – Grass = 1 – Desert = 3 – Forest = 2 – River = 10 • Squad cost = max(individual costs)

Non-Symmetric Edge Costs

• Often harder to go one direction than another – Stairs – Jumping from one level to lower level • Will have different costs in each direction – Two directed edges instead of one directed edge – No second edge in “one way” path 4 2 1

Turning Costs

• Some characters require time to realistically make a direction change – Part of edge cost – Separate edge from location to same location Align Arrive 3 5 4 Seek

Inflection Points

• Waypoints often near convex corners – Shortest path in wide areas – Better than putting waypoint in center of area Path given by floor tiles Faster path

Inflection Points

• Put waypoint at each convex corner • Move out some safeRadius from corner • Connect waypoints visible from one another safeRadius safeRadius

Inflection Points

• Potential problem: “jagged” areas could create too many waypoints • Solution: Only add waypoints for obstacles between critical areas (such as doors) – Recursively add waypoints until critical areas connected Irrelevant inflection points

Inflection Points

• Automatic creation of waypoints on arbitrary racing track

Path Smoothing

• Problem: Grid-based floor tiles with waypoints at center – Jagged” paths – Too many unnecessary turns – Better to create path using non adjacent nodes

Path Smoothing

• Recursive algorithm: – Draw line between start and goal – Stop at obstacle – Continue