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billmo
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Would that result in a seamless transition though in regards to the level background? I would have the camera following the player so I'm just not sure how the actual tilemap's end point would connect back to the tilemap's beginning point.  Imagine it as a 2 dimensional view of the earth but unraveled so that it doesn't appear that you're walking on actual circle.

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The easiest way to do that would be to continually append a viewport's width-worth of content at the end of the level each time the player traverses through it.

* - - - * - - - * - - - *|       |       |       || P     |       |       |* - - - * - - - * - - - ** - - - * - - - * - - - *|       |       |       ||     P |       |       |* - - - * - - - * - - - ** - - - * - - - * - - - *|       |       |       ||       |P      |       |* - - - * - - - * - - - *        * - - - * - - - * - - - *        |       |       |       |        |  P    |       |       |        * - - - * - - - * - - - *  |                          ^  | _ _ _ _ _ _ _ _ _ _ _ _ _|
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I would suggest going the way @Skeptron suggested. If you append map to the end of it, you still need the type of map which will assure seamless transition. Given such map it matters not whether you append the map or reset players position to the symmetric opposite point. This is pretty all you need for this:

 

...if the player continues to walk right, eventually they end up back at the beginning of the stage...

 

And it is better from the memory usage perspective, than appending the map to the end.

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