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For one of my games, I need an enemy that pursues the player in a sort of "lazy" way, where they don't exactly follow the player's movement and instead have somewhat slippery movement. Example: the player does a sharp turn to the right, the enemy will go to that direction too, but it will slightly "overshoot" the distance and go beyond the point where the player turned to the right before going to the new direction. Here is an example:

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Some examples from games:

  • Missiles (Super Meat Boy)
  • Phanto (Super Mario Bros. 2, the USA one)

Is there a term for this kind of "lazy" movement for homing enemies?

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I'd just say your enemy entity has momentum.

Usually this means the steering function can only affect the acceleration but not the velocity, so it cannot stop on a dime.

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