\(
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Algorithm
- Generate a grid of random unit-length vectors
- In improved perlin noise, vectors which only contain +=1 and 0 such as (1, 1, 0) are used
- For each point, find the closest corners in the grid and compute the dot product between the vector from the corner and the corner's random vector. This results in 4 values for each pixel, one for each corner.
- Interpolate between these using smoothstep.
- In improved perlin noise, use smootherstep which has zero first and second derivatives at the boundaries:
- \(\displaystyle \operatorname{smootherstep}(x) = 6x^5 - 15x^4 + 10x^3\)
Resources
