I developed an Ocean Wave function that uses a multi-layer Gerstner wave sum algorithm, voxelized into a height field.

After a few attempts, I obtained these results. What’s interesting is how the foam forms—it’s not like a classic simulation where foam forms on the crests of the waves, but rather an approximation based on noise.



* It generates a spectrum of waves in several layers: swell, medium chop, ripples.
* Each wave has a direction, a wavelength, an amplitude, a random phase, and a frequency.
* The dominant wavelength comes from a Pierson-Moskowitz approximation based on wind speed : lambda\_peak \~= 2π \* wind\_speed² / gravity
* The amplitude is also inspired by Pierson-Moskowitz : H\_s \~= 0.21 \* wind\_speed² / gravity
* Then each point (x, z) samples a height : height = sum(amplitude \* sin(kx\*x + kz\*z - omega\*time + phase))
* The Choppiness parameter modifies the shape of the sine wave with a signed power term to make the peaks sharper.
* Foam is added when the local slope of the height field exceeds Foam Slope, within a band controlled by Foam Thickness.

As a reference, I looked at what the Houdini Ocean Spectrum node produced.

I used a ray tracer to display the render.

Developed on PC and Mac in Rust.



Feel free to give me your feedback, see you soon \^\^

Ocean wave voxel generation