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I was browsing some lecture slides by Eric Anderson for his Cornell course CS 4154 (Analytics-driven Game Design). In a series of slides he mentions discretizing space as a way of paper prototyping action games. As an example he illustrates with a screen shot of Super Mario with a grid overlay (shown below). Unfortunately the slides do not expound on how this technique is used.

How is discretizing space used to prototype platform games or action games generally?

enter image description here

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    \$\begingroup\$ It hurts that the grid on the image is not along the sprite boundaries, which is the discrete foundation of the game. \$\endgroup\$ Commented Mar 20, 2015 at 8:47

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Discretization in general means to split a while into discrete parts. Discrete parts refers to the notion that they have a size -- as opposed to differential parts which do not have a finite size in math.

Often, people use discretizing space to refer to splitting the region into a regular grid which can be indexed in 2d or 3d.

In this paper it appears that each discretization's behavior is evaluated independently of what is around it. In the picture, the pipe is considered as a pipe and its functionality is tested without regard to what is around it. Only the player and the pipe would be tested without regards to the coins or other platforms.

My 2 cents.

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He may have had something like movement in mind. In discrete space and time, the player would move from one grid square to the next in "turns." Each turn can be thought of as a span of time. This idea of playing the game with turns helps create the logic required to move the character and interact with the environment.

This seems to be a very abstract, high level presentation.

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  • \$\begingroup\$ Doesn't seem to necessitate the use of a grid, especially one misaligned. I think the author had something else on his mind. \$\endgroup\$ Commented Mar 19, 2015 at 21:10
  • \$\begingroup\$ He may have had something like movement in mind. In discrete space and time, the player would move from one grid square to the next in "turns." Each turn can be thought of as a span of time. This idea of playing the game with turns helps create the logic required to move the character and interact with the environment. \$\endgroup\$ Commented Mar 19, 2015 at 21:35
  • \$\begingroup\$ @RusselTrahan Yes, that seems a much more likely reason, I would edit that into the answer. \$\endgroup\$ Commented Mar 19, 2015 at 21:44
  • \$\begingroup\$ yes but, HOW does it work? Move one square per turn? what about diagonals? thats much further is that OK in a prototype. What about gravity. What about collisions? If I were prototyping super Mario with this technique, how exactly would it work? Sorry @RussellTrahan I'm not attacking your answer, you're just the first answer and I felt I needed to specify my question. \$\endgroup\$ Commented Mar 19, 2015 at 23:36
  • \$\begingroup\$ I would treat it as such. I'm at square A and wish to move to square B. Check what is square B. Is it a walkway? Yes: move, No: compute gravity influence. Is square B a pipe? Yes: change to new map, No: do nothing. Is square B a coin? Yes: change coin balance, No: do nothing. See? You play the game one action at a time by looking at all of the logic & decision making the game must make. This mindset when making your game logic will help you make the logic efficient by only considering POSSIBLE decisions to make and access the causality of all events. \$\endgroup\$ Commented Mar 20, 2015 at 19:28

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