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Ocean Rendering, Part 1 - Simulation

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Robert Ryan

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Ocean Rendering, Part 1 - Simulation is an October 2025 technical blog post by Robert Ryan on the theory and mathematics of real-time FFT ocean surface simulation using oceanographic spectra.

It covers Tessendorf-style spectral oceans with modern spectra, finite-depth dispersion, JONSWAP and TMA non-directional spectra, Donelan-Banner directional spreading, spectral amplitude synthesis, time evolution of the height spectrum, packing displacement and derivative spectra for inverse FFTs, Hermitian pairing to cut transform count.

It is for intermediate-to-advanced graphics programmers implementing ocean water who can read dense math and map it to compute shaders. Prior exposure to complex numbers and FFTs helps. Full shader listings are omitted in favor of pseudocode and repository references.

The article is a free HTML page with chapters, formulae, appendices, and links to the author renderer plus cited papers. It is part one focused on simulation rather than full lighting.

It is useful when Tessendorf notes feel dated and you need a bridge from oceanographic spectra to the displacement and derivative maps a real-time renderer shades.