I want to create terrain that has sharply defined features, but still has the flexibility of a height map. Though a height map must be defined by a grid, I don't want to terrain to look like a grid. All my previous approaches to this problem tend to look like grids, so now I'm aiming to allow for completely arbitrary discontinuities in the height map. It should be possible to split a cell of the grid between two or more elevations and along curved boundaries. The discontinuities should be independent of the height map grid. Here is a hand-made illustration of the kind of terrain we're aiming for:
On the left is a curve of discontinuity that has been drawn onto a height map grid. On the right is a rendering of height map terrain that has been split along the same discontinuity curve. Wherever a discontinuity is found, the terrain represents a difference in elevation by a vertical wall instead of the usual slope. The idea is to get an automated system for putting this sort of terrain into a game.
I have considered allowing the discontinuities to be an unrestrained set of line segments with floating-point 2D vertices. We'd have total freedom to draw any discontinuities we could imagine, such as splitting a single grid cell into a dozen pieces. This introduces many complexities, such as forcing us to use procedural triangulation to determine how each cell should be rendered. Here is a link to a pdf guide to the Ear Clipping algorithm which we might use for this triangulation: Triangulation By Ear Clipping
It also makes navigating the terrain tricky. At a minimum we need to determine if one of the player's moves would cross a discontinuity. That in itself is not too hard, but we wouldn't want the player to be stopped dead just by brushing a discontinuity. We want the player to slide along these barriers when appropriate, and the math behind doing that is not at all obvious. We also need a way for computer-controlled enemies to navigate this world, perhaps by automatically generating a navigation mesh.
Perhaps the problem should be simplified by restricting the discontinuities in ways that have no significant impact on the resulting terrain. We don't particularly want a cell to be split into a dozen pieces, so maybe there should be a limit to how many discontinuities can pass through a single cell. We might be limited to certain vertices within each cell, such as a vertex on each corner, a vertex somewhere on each edge, and a 9th vertex floating somewhere in the interior of the cell. With that sort of restriction, triangulation should be greatly simplified.
What sort of algorithms and approaches would you use to create this effect? Are there any other ways to simplify the problem?
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