问题
I'm building a simple 2D grid based game and am looking for a way to calculate the "threat" area that each character can exert on the game board. Threat from the current spot is easy to calculate - this is the red diamond below. But I'm looking to combine this information with an arbitrary "can walk here" area (orange).
Together the algorithm will give me a combination of all tiles that my character can attack from all available moves and current position.
Of course I can just iterate over all possible moves, apply the diamond shape there and create a set of all threat squares. Is there a better way?
回答1:
The problem you are solving here is analogous to 2D Convolution:
--------------- --------------- -------XX------
-------X------- --------------- ------XXXX-----
------XXX------ -------XX------ -----XXXXXX----
-----XXXXX----- * ------XXX------ = ----XXXXXXX----
------XXX------ --------X------ -----XXXXXX----
-------X------- --------------- ------XXXX-----
--------------- --------------- --------X------
In your case where an element is only either covered or uncovered (versus containing a scalar or vector value), this reduces to the Dilation operation in morphology. There are many papers and code samples on efficient implementations of dilation - this one looks particularly applicable to your problem.
来源：https://stackoverflow.com/questions/20624202/is-there-an-algorithm-for-combining-threat-range-with-arbitrary-move-range-on-2d