Midpoint Displacement Algorithm

The midpoint displacement algorithm is a simple algorithm used for basic heightmaps on a square base. It is used for simple heightmaps only. Overhangs, and creased terrain are impossible for it to generate, as are true vertical cliffs.
The midpoint displacement algorithm leads to a somewhat blocky look to the heightmap created, which is why it has been superseded in most uses by an improved version called the diamond square algorithm.

The midpoint displacement algorithm makes calculating a new random heightmap rather easy. You start with a basic rectangle of any size, as the area to be shaped. Either assign random height values to the corners, or take the height values from existing terrain. Divide the rectangle into four other rectangles, of equal or very different volumes, does not matter. They do not however, overlap one another. Let the height values of unspecified corners of these rectangles be calculated from the mean values of the four corners of the parent rectangle divided by the mean of whichever corners of the parent fall along the edge of the subdivided rectangle, plus or minus one standard deviation.
Each subdivided rectangle is then further subdivided and the process is repeated again and again until no more subdivisions are possible. Your finished terrain is now ready to use.

The blocky nature comes from the fact that in many if not most instances, the subdivided rectangles share at least one corner with their parents. As the generations pass you often find many generations are sharing the same corner, which gives the heightmap that blocky look the algorithm is infamous for.

Like all random heightmap algorithms, midpoint displacement cannot be used to create specific terrain features. It's only real use is in truly random terrain within specified parameters, for procedually generated raw landscapes.

See Also: Diamond Square Algorithm, Heightmap, Procedural Content Generation

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Diamond Square Algorithm Midpoint Displacement Algorithm

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