Perlin noise: Difference between revisions
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# Generate a grid of random unit-length vectors | # 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 | #* 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. | # 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. | # Interpolate between these using smoothstep. | ||
#* In improved perlin noise, use smootherstep which has zero first and second derivatives at the boundaries: | |||
#* <math>\operatorname{smootherstep}(x) = 6x^5 - 15x^4 + 10x^3</math> | |||
==Resources== | ==Resources== | ||
* [https://dl.acm.org/doi/10.1145/325165.325247 An image synthesizer (Perlin, SIGGRAPH 1985)] | |||
* [https://www.semanticscholar.org/paper/Improving-noise-Perlin/a6fd5071b73f542c79bd08d409c5f73de38dac5d Improving noise (SIGGRAPH 2002)] | |||
* https://rtouti.github.io/graphics/perlin-noise-algorithm | * https://rtouti.github.io/graphics/perlin-noise-algorithm | ||
Latest revision as of 17:35, 21 April 2023
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:
- \(\displaystyle \operatorname{smootherstep}(x) = 6x^5 - 15x^4 + 10x^3\)