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Is there a way I can "Weight" a noise generation algorithm to a specific point i.e the center of the generated "image" or one of its corners, assuming the generated "image" is square?

I have been working with Unity5 for around a month, but recently got interested in Noise Generation and Procedural Terrains, which lead me to Perlin Noise, which has lead me to using noise generation for the heightmap of the terrain.

I have implemented Perlin Noise which works fine, however the two versions implemented give different effects:

  1. Each tile shares an entire heightmap cut into sections
  2. Each tile has its own heightmap

1 - When the entire heightmap is shared, you get an unexpected end to the terrain, which in extreme cases might be 300m up a mountain. eg: Shared Heightmap Seperated Terrain Pieces sharing a single heightmap

2 - When each tile has an individual heightmap, the ability to get a much more "organic" feel is possible, however it is nearly impossible to achieve an "island" effect with the blending, I end up with some tiles at huge heights and some at the lowest points, however the lowest points might actually be in the center of the map eg:

Seperate Heightmap per Tile Seperate Heightmap per Tile

This is remedied by taking the overall dimensions of a tile (512x513x512 - WxHxD) and taking a sampled point and interpolating the heightmap values between the two neighbouring tiles, in this case the value is 1/3rd of the width = 171 eg: Sampled blending

I want to Weight the noise to the center of a square thus giving an "island" effect on the generated heightmap - for example, this image represents how the terrain currently looks from the side (sorry for SumoPaint..): - Top is current generation where you can get a peak anywhere on the map, which is annoying - Bottom is how I would like the generation to work, having greater weighted peaks in the middle of the terrain with the edges feathering out to near flat where the water would be.

Badly Drawn representation

If anyone could point me in the correct direction for weighting noise generation, I would be extremely greatful!

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