Terminology please

I would like to make a doom-like clone fps. There is something different I want to do, I want it to be 3D graphics AND I would like to make it so the players can go over and under a given spot. Like over and under a bridge. Doom didn’t allow that: What is the style I want called? What is the style that doom was called?

Thanks,

Doom used a BSP tree [binary space partitioning] algorithm to divide a 2D world map design into sectors. Each sector could have a floor height and a ceiling height, but since it was a 2D world, you could never do under-over stuff; there was no way to express multiple floor heights for the same sector, or more than two sectors that met along the same line. This is implied by the “binary” in “binary space partitioning” where every line partitions the world into two spaces, the stuff on this side of the line vs the stuff on that side of the line. Any appearance of 3D was just the altitude of any non-map object relative to the floor or ceiling.

Any actually 3D scene / level / map would not have this limitation. How the engine divides up the 3D space is not really material, there’s no single word for it and many approaches.

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Thank you for the information!