I’m working on an AI system for a territory capture game (think games like Paper.io or similar area control games). The AI needs to find the best spots to create enclosures and claim territory.
In my game, there are owned areas (represented in blue) and unclaimed spaces (shown in black). The AI should identify strategic points where it can draw a path to surround and capture the maximum amount of empty territory with minimal movement.
Basically I need an algorithm that can answer: what’s the most efficient route to surround the largest possible unclaimed area?
I’ve been thinking about edge detection or boundary tracing methods, but I’m not sure if that’s the right approach. Has anyone tackled similar pathfinding problems for territory control games? Any suggestions for algorithms or techniques that work well for this type of spatial analysis would be really helpful.
I tackled this with convex hull algorithms plus potential field analysis. Basically, I treat unclaimed areas as attractive forces and existing boundaries as constraints. My modified Graham scan evaluates potential enclosure polygons by their area-to-perimeter ratio - you want max area with minimal exposure. The algorithm samples key points along your territory’s edge and calculates the convex hull that’ll grab the most area without overextending. I preprocess the grid to find ‘capture candidates’ using connected component analysis on empty regions, then score each one based on how accessible it is from where you are now. Purely greedy approaches kept leading to overextension, so I added a territorial density metric that favors enclosures near your existing strongholds. The computational overhead isn’t bad since you only recalculate when major territory changes happen.
voronoi diagrams are perfect for this. use your territory edges as seeds and generate the cells - the biggest ones show your best expansion spots. i combine it with dijkstra but weight by area/perimeter ratio instead of distance. way faster than brute forcing every enclosure path.
Hit this exact problem building an AI for a zone control game three years ago. Best solution was treating it like a shortest enclosing loop problem with value density mapping.
First, find “hotspots” using morphological operations on your grid. Dilation and erosion show you where small moves grab big territory chunks. Then use a modified traveling salesman approach to find the shortest path back to your existing boundary.
Key insight: don’t go for biggest area - go for highest value per distance traveled. Score each potential enclosure by dividing captured area by path length squared. The squared part penalizes risky long paths opponents can easily cut.
For performance, cache potential enclosure zones and only recalculate when the territory map changes 5%+. Add early termination when scanning - if a partial path already costs more than your best complete path, dump it.
One gotcha: always simulate one opponent move ahead. Perfect-looking enclosures might be trivial to block. I added opponent movement prediction using simple line of sight checks from their current positions.
Built something like this for a mobile strategy game last year. The best approach was mixing flood fill with modified A* pathfinding. Instead of just finding the shortest path, I weighted the scoring based on how much area could actually be enclosed. First, use flood fill to identify ‘pockets’ of unclaimed territory, then calculate the enclosure paths for each pocket by finding routes back to your existing territory. My heuristic factored in both path length and pocket size. I learned the hard way that it’s important to account for risk as well; sometimes a smaller, secure enclosure is better than going for maximum area if it leaves you exposed. I added a safety buffer that checks if opponents could easily block your proposed path. Performance was solid even on larger grids, and I optimized the calculations to only run when the game state changed significantly, rather than every frame.
Ran into this exact problem while building tactical AI for a client’s area control game. Instead of using standard pathfinding, I went with contour analysis plus cost-benefit math.
The key insight was treating it like finding optimal enclosure boundaries using image processing. I used Canny edge detection to spot territory boundaries, then contour approximation to find the minimum points needed to close gaps between owned regions. This gives you enclosure shapes without expensive path calculations.
For each potential contour, I scored it using enclosed area divided by boundary cost, plus a stability factor for how defensible the new boundary would be. Natural chokepoints and existing partial boundaries scored way higher than open spaces.
The real performance boost came from hierarchical processing. I’d analyze large territorial chunks first, then zoom in on promising candidates at higher resolution. Cut computational overhead massively while keeping strategic accuracy.
One crucial thing: implement rollback simulation. Before the AI commits to an enclosure path, it simulates completing it and checks if that creates new vulnerabilities elsewhere in its territory.