One solution is to calculate the horizontal distance from each block to the center of the island, e.g. the coordinate (0, 0, 0). Then subtract that distance from the height. That way the island will be taller in the center and get lower and lower further away until it finally goes below the water line.
One improvement is to not just use the distance. Here’s a 2D from-the-side plot of how the height of the island would behave:
It has a sharp corner in the middle where it suddenly stops going up and starts going down in an instant, which might look ugly in the generated map. If we use a different curve than a straight line we can get smoother results. One curve that’s pretty smooth is the smoother-step function
As you can see it starts perfectly flat at x=0 and ends up perfectly flat at x=1. If we put the distance from the center of the island in place of x then we can use that as a multiplier for the height. If we divide the distance by the radius of the island we get some control over the size of the island.
The smootherstep function is -2 x³ + 3x². If we flip it and scoot it over a bit we get the function that is shown with the orange graph: -2 (-x+1)³ + 3(-x+1)². Which looks like this in code:
function smootherStep(x)
return 2 * math.pow(x, 3) + 3 * math.pow(x, 2)
end
function smootherStep1To0(x)
return smootherStep(-x + 1)
end
If you have some function for calculating the height of the terrain at a given (X, Z) coordinate, you can modify it to use this function like so:
local ISLAND_RADIUS = 100
function coordinateHeightMultiplier(x, z)
local dist = math.clamp( Vector3.new(x, 0, z).Magnitude, 0, ISLAND_RADIUS )
return smootherStep1To0(dist / ISLAND_RADIUS)
end
function coordinateHeight(x, z)
--- whatever code you have for calculating the height of the island...
-- height = height of the terrain before applying the modifier
return height * coordinateHeightMultiplier(x, z)
end
If you don’t all this smootherstep stuff you can replace the multiplier function with this instead:
local ISLAND_RADIUS = 100
function coordinateHeightMultiplier(x, z)
local dist = math.clamp( Vector3.new(x, 0, z).Magnitude, 0, ISLAND_RADIUS )
return 1 - (dist / ISLAND_RADIUS)
end
