Undine

Liquids for design, games, 3D and .NET. Water first.

A pool that moves on the GPU and is lit the way water is lit. The surface is the long-wave equation with the liquid's own viscosity; the light through it is Caustikon's optics for that liquid, one refractive index per colour channel and absorption from its measured k table; the lamp's caustics on the floor come from refracted rays, not from a texture. Nine liquids, water to carbon disulfide, each with its handbook density, viscosity and surface tension.

The site at https://undine.levvs.cc is the pool: touch it, change the liquid, take the shaders. The surface runs at the liquid's own ripple speed from its dispersion relation, the light is Caustikon's, and the caustics on the floor and walls are refracted rays.

What is in the repository

Path	What
src/Undine	The .NET package: Liquid and Liquids, Surface (height field with viscous damping), LiquidOptics (indices, Fresnel, absorption from Caustikon), CausticMap.
shaders/	GLSL ES 3.00 for the spectral surface step (FFT pass, mode evolution, forces), the caustics and the pool render, for the shallow-water flow step and the table render, and for the particle liquid (the whole position-based scheme, and its screen-space rendering) (what the site runs); an HLSL file for Unity and Unreal; a Godot 4 shader.
site/Undine.Site/	The site: Blazor WebAssembly in the Caustikon format. The WebGL2 pool, the liquid table, one "Give Me!" page per craft with the numbers and the shaders. wwwroot/data/liquids.json is baked by tools/Undine.Bake.
tests/	What the physics must keep doing: water's index and its blue over metres, wave speed, a drop spreading, glycerol dying, a flat surface lighting the floor evenly and a ripple focusing it.
external/caustikon	Caustikon as a submodule, the source of every optical number.

Install

git clone --recurse-submodules https://github.com/levvs-one/undine.git
dotnet build Undine.slnx -c Release
dotnet test --project tests/Undine.Tests/Undine.Tests.csproj -c Release -f net10.0
dotnet run --project tools/Undine.Bake -c Release     # site/Undine.Site/wwwroot/data/liquids.json

Use

using System.Numerics;
using Undine;

Liquid water = Liquids.Water;                       // optics from Caustikon, mechanics from the CRC Handbook
LiquidOptics optics = new(water);
Vector3 n = optics.IndexRgb;                        // 1.3327, 1.3347, 1.3387 at 610, 550, 465 nm
Vector3 tenMetres = optics.Transmittance(10);       // what white becomes after ten metres: blue

Surface pool = new(cells: 256, sizeMetres: 4, depthMetres: 1.2, water);
pool.Disturb(xMetres: 2, yMetres: 2, radiusMetres: 0.05, amountMetres: -0.01);   // a drop
pool.Step(1 / 60d);                                 // substeps as stability requires
Vector3 normal = pool.NormalAt(128, 128);

CausticMap floor = new(256);
floor.Build(pool, optics, lightDirection: new Vector3(0.3f, -1f, 0.2f), raysPerSide: 512);

What is modelled, and what is not

The surface is a height field: v += c²∇²h·dt + ν∇²v·dt, h += v·dt, with c = √(g·depth) and ν = η/ρ. The substep is bounded by both the wave and the diffusion stability limits. Light: exact Fresnel per channel, Snell's law per channel, Beer–Lambert absorption over the path, caustics by ray counting.

Not modelled yet: dispersive gravity–capillary waves (Liquid.PhaseSpeed gives the true phase speed, the height field runs at one speed), breaking, splashes, foam, floating bodies, light reflected off the floor back up through the surface. The next stages are viscous liquids on particles (oil, honey) and slime as a viscoelastic material.

Data

Optics: Caustikon's liquids, generated from the RefractiveIndex.INFO database (CC0 1.0), each with its citation. Mechanics: CRC Handbook of Chemistry and Physics, 97th ed., values at 20 °C, rounded.

License

MIT. Copyright (c) 2026 levvs-one.