Sort, sweep, and prune: Collision detection algorithms
The sweep-and-prune algorithm enhances collision detection in video games by reducing checks through sorting, achieving an average time complexity of O(n + m), improving performance over naive methods.
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The article discusses the sweep-and-prune algorithm for collision detection in video games, emphasizing its efficiency compared to naive methods. Collision detection is crucial for game mechanics, such as preventing characters from passing through each other or simulating interactions like bouncing. The naive approach, which checks every possible pair of objects for collisions, has a time complexity of O(n²), leading to performance issues as the number of objects increases. The article proposes improvements by leveraging sorting and the transitive property of inequalities to reduce unnecessary checks. By sorting objects based on their minimum x-coordinates, the algorithm can skip pairs that are guaranteed not to collide, significantly enhancing performance. The modified algorithm combines sorting with an early exit strategy in the nested loop, resulting in an average time complexity of O(n + m), where m is the number of overlapping pairs. This approach is particularly effective in scenarios where objects are evenly distributed, making it suitable for many types of games.
- The sweep-and-prune algorithm is an efficient method for collision detection in games.
- Naive collision detection has a time complexity of O(n²), which becomes impractical with many objects.
- Sorting objects by their minimum x-coordinates allows for skipping unnecessary collision checks.
- The modified algorithm achieves an average time complexity of O(n + m), improving performance significantly.
- This method is particularly effective for games with evenly distributed objects.
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- Many commenters appreciate the article's clarity and accessibility, noting its importance for understanding complex systems in game development.
- There is a discussion about the efficiency of different sorting algorithms, with some suggesting that insertion sort may outperform traditional fast algorithms due to the nature of object movement in games.
- Several users mention alternative methods for collision detection, such as spatial hashing and quad-trees, indicating a broader interest in various approaches.
- Commenters express curiosity about the performance comparison between the sweep-and-prune algorithm and other techniques like space partitioning.
- Interactive illustrations in the article are praised for enhancing understanding without overshadowing the content.
22 commentsThe reason is that objects in collision detection systems tend to move relatively small steps between frames, meaning you can keep lists from the previous frame that are already mostly sorted. For sorting these mostly sorted lists, insertion sort tends towards O(n) while Quicksort tends towards O(n^2)!
What’s funny is that I’ve been doing some form of gamedev since late 90s and most of this is abstracted by engines at this point, but this is essential to understanding how complex system simulations work.
Thanks to the author for making a very accessible article
https://github.com/bepu/bepuphysics2/blob/master/Documentati...
The library itself is amazing in terms of performance. It is a bit challenging to integrate with though due to the amount of optimization involved.
Is this true? The naive algorithm's outer loop (i) counts n - 1, while the inner loop (j) begins at i + 1 (so counts progressively less than n - 1).
Not a CS major, is this roughly equivalent (for large values of n) to O(n2) or is it, as it appears, something less?
Sometimes I feel like these articles with interactive illustrations are more like an excuse to put together a bunch of cool demos, like there's a lot of fluff with not much substance (a bit like a TED talk), but this one didn't let the illustrations take over.
Check out his other goodies https://leanrada.com/
I'm curious about this comment, anyone know if the algorithm in the article is generally faster than space partitioning/spatial tree subdivision?
A long time ago I used a spatial tree type of approach which seemed naively to be a pretty good approach, but I never investigated or compared algorithms other people were using (this was 80's, pre-internet).
Also sad that you need all this complexity to test 25 balls in Javascript. 25^2 is a small number in C, especially when your balls fit in cache.
Still a good introduction to various algorithms, though.
Are there other handy 2-d algorithms that are this well explained? I know redblobgames has a treasure trove too, but curious about more.
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