(Barely) Plausible Wave Displacement

I’m on holiday on the South coast this week, and after amazing weather, this morning it’s had the audacity to rain, so I thought I’d see how difficult it would be to make a fake-but-sometimes-plausible procedural texture for emulating waves on the sea via displacement.

Jerry Tenssendorf’s paper “Simulating Ocean Water” is essentially the way to do it accurately, using a discrete Fourier Transform, which allows very accurate modelling of wave peaks and troughs based on the wind interaction and gravity, and indeed other waves around them.

I only had a couple of hours I wanted to devote to it, and couldn’t get into that level of detail, so I tried to fake it by just using Simplex noise modulated by the sine of the texture coordinates.

Basically, at a very simple level (ignoring wind which is pretty important for accurate simulation), the peaks and troughs of waves on the sea closely resemble a trochoid, which can be emulated with the sin() function. I ended up modulating two different resolutions of these waves (major primary waves and smaller secondary waves) on top of each other along with noise, which at least for non-open-water waves (open water waves crests tend to have angled peaks when it’s windy and when the number of waves increases) with moderate wind, gives reasonable results. It’s certainly better than just random noise. But it’s very rigid and consistent even with the noise modulation, so for large areas it basically looks like a tiled texture.

At some point, I’d like to investigate implementing Jerry Tenssendorf’s paper to do it accurately.

Displacement

I’ve now added initial support for displacement of geometry after subdivision using displacement maps. It’s far from perfect yet - it’s quite slow when subdividing to the number of levels required for decent results (the two cubes above are 6.2m faces, subdivided 10 times), and the Half-Edge data structures I’m using for subdivision use a fair amount of memory, and there’s a very slight amount of faceting that doesn’t look normal.

The first two issues (speed and memory consumption) I can probably fix quite easily by making my Half Edge data structures more compact and efficient - currently, each Half Edge Vertex, Half Edge Edge and Half Edge Face store pointers to each other which while easy, consumes more memory than required. Converting them to using offset indexes (like my KDTree does) should bring memory usage down by half (instead of storing an 8-byte pointer, it’s possible to store a 4-byte uint_32 for an offset into a table).

It’s also not on-the-fly micro-polygon displacement - that’s more difficult (and slower while rending), can only be done on triangles (loop SubD is the normal variant) but uses much less memory and allows easy adaptive stopping criteria by checking each edge length in camera-space to see whether it’s smaller than a pixel yet.

There’s also vector displacement (displacement in three dimensions, as opposed to simply along the vertex’s normal), which should be pretty trivial to implement.