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Handling collision resolution across whole world

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This is in the context a top-down or isometric game like Zelda or Robotron. I don't need or want realistic physics that use forces or acceleration, but I do want different types of collision responses. Moving characters should slide around terrain and around each other. Characters should be knocked back by explosions and powerful attacks. Arcadey bouncy bullets should bounce off walls. Pushable puzzle blocks could exist.

I've read about collision detection, and a little bit about collision resolution between a single pair of colliding objects, but I've seen little about how to prevent a whole group of moving objects from overlapping with each other and the terrain.

Suppose I have a relatively simplistic discrete collision detection scheme, where first I move all objects then check for collisions (my attempts at continuous collision detection always ended in tears). When resolving a pair of colliding objects, how do I make sure that separating them does not create new collisions with other objects?

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