如何在二维矢量场中找到无限循环？
我有一个有限大小的二维矢量场。我想要的是找到这个领域中的任何“循环” - 也就是说，如果这个领域代表流体的流动，并且您将一个物体放在这些循环之一上，则该物体会一圈又一圈，永远不会到达休息。我想我已经找到了一些关于这个问题的学术数学文章，但它们超出了我的理解范围，我无法理解它们。是否有找到此类循环的标准算法？
为什么我要寻找这样的循环？我正在考虑制作一款与《超级马里奥银河》有类似概念的 2D 平台游戏，其中会有几个小的引力体，玩家可以在它们之间跳跃并在其上行走，而不是单个全局重力矢量。静态物体的重力场将在关卡编辑期间静态计算。我确实没有办法解决这个问题，但这将是一个非常好的工具，可以在关卡编辑器中检测不可避免的重力循环，而不必通过游戏测试来发现它们。
I have a finitely-sized 2D vector field. What I want is to find any "cycles" in this field - that is, if this field represented the flow of a fluid, and you placed an object on one of these cycles, the object would go around and around and would never come to rest. I think I've found some scholarly mathematical articles about this problem, but they're so far over my head that I can't make any sense of them. Is there a standard algorithm for finding such cycles?
Why do I want to find cycles like this? I'm considering making a 2D platformer that has a similar concept to Super Mario Galaxy, in that there will be several small gravitating bodies that the player can jump between and walk on, rather than a single global gravity vector. The gravity field for the static bodies would be computed statically during level editing. I don't really have to solve this problem, but it would be a very nice tool for detecting unescapable gravity loops in the level editor rather than having to discover them through playtesting.
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很难想象一个包含循环的“重力场”。然而，玩家的轨迹可能是循环的。我们称之为“轨道”。
一个简单的解决方案可能是加入少量的摩擦或阻尼，以确保轨道衰减。
一个不太容易处理的解决方案：如果空间是离散的，那么您可以测试每个状态（位置、速度）并检查玩家是否重新访问相同的状态。请注意，这还需要有限数量的合法速度值。
从可用性的角度来看，为玩家提供一些推进手段也是解决问题的好方法。
It's hard to imagine a "gravity field" that contains cycles. However, the trajectory of the player might be cyclic. We call this "orbit."
An easy solution might be to include a small amount of friction or dampening to ensure that orbits decay.
A less tractable solution: if the space is discrete, then you can test each state (position,velocity) and check if the player ever re-visits the same state. Note that this would also require a finite number of legal velocity values.
From a usability perspective, giving the player some means of propulsion would also be a nice way to solve the problem.