GLSL setup for a Fast Fourier Transform of two complex matrices

$ npm install glsl-fft

var fft = require('glsl-fft');

// Set up a forward transform:
var forwardTransform = fft({
  width: 4,
  height: 2,
  input: 'a',
  ping: 'b',
  pong: 'c',
  output: 'd',
  forward: true,
});

// Output is a list of passes:
// => [
//  {input: 'a', output: 'c', horizontal: true, forward: true, resolution: [ 0.25, 0.5 ], normalization: 1, subtransformSize: 2},
//  {input: 'c', output: 'b', horizontal: true, forward: true, resolution: [ 0.25, 0.5 ], normalization: 1, subtransformSize: 4},
//  {input: 'b', output: 'd', horizontal: false, forward: true, resolution: [ 0.25, 0.5 ], normalization: 1, subtransformSize: 2}
// ]

Usage of the GLSL fragment shader using the above parameters as uniforms:

precision highp float;

#pragma glslify: fft = require(glsl-fft)

uniform sampler2D src;
uniform vec2 resolution;
uniform float subtransformSize, normalization;
uniform bool horizontal, forward;

void main () {
  gl_FragColor = fft(src, resolution, subtransformSize, horizontal, forward, normalization);
}

See example/index.js for a fully worked angular Gaussian blur example using regl.

This shader computes the 2D Fast Fourier Transform of two complex input matrices contained in a single four-channel floating point (or half float) WebGL texture. The red and green channels contain the real and imaginary components of the first matrix, while the blue and alpha channels contain the real and imaginary components of the second matrix. The results match and are tested against ndarray-fft.

This module does not interface with WebGL or have WebGL-specific peer dependencies. It only performs the setup work and exposes a fragment shader that performs the Fourier transform.

This module is designed for use with glslify, though it's not required. It also works relatively effortlessly with regl, though that's also not required. At minimum, you'll need no less than two float or half-float WebGL framebuffers, including input, output, and two buffers to ping-pong back and forth between during the passes. The ping-pong framebuffers may include the input and output framebuffers as long as the parity of the number of steps permits the final output without requiring an extra copy operation.

The size of the textures must be a power of two, but not necessarily square.

As far as fast Fourier transforms go, it's not really optimized at all, though it's faster than transferring data to and from the GPU each time you need to compute a Fourier transform. The biggest strike against it is the number of passes. That could be optimized, but I don't currently have the time. Would gladly accept a PR though.

Perform the setup work required to use the FFT kernel in the fragment shader, index.glsl. Input arguments are:

• input (Any): An identifier or object for the input framebuffer.
• output (Any): An identifier or object for the final output framebuffer.
• ping (Any): An identifier or object for the first ping-pong framebuffer.
• pong (Any): An identifier or object for the second ping-pong framebuffer.
• forward (Boolean): true if the transform is in the forward direction.
• size (Number): size of the input, equal to the width and height. Must be a power of two.
• width (Number): width of the input. Must be a power of two. Ignored if size is specified.
• height (Number): height of the input. Must be a power of two. Ignored if size is specifid.
• splitNormalization: (Boolean): If true, normalize by 1 / √(width * height) on both the forward and inverse transforms. If false, normalize by 1 / (width * height) on only the inverse transform. Default is true. Provided to avoid catastrophic overflow during the forward transform when using half-float textures. One-way transforms will match ndarray-fft only if false.

Returns a list of passes. Each object in the list is a set of parameters that must either be used to bind the correct framebuffers or passed as uniforms to the fragment shader.

Returns the gl_FragColor in order to perform a single pass of the FFT comptuation. Uniforms map directly to the output of the JavaScript setup function, with the exception of src which is a sampler2D for the input framebuffer or texture.

Parameters are:

• resolution: a vec2 containing 1 / width and 1 / height.
• dxy (optional): Either a float representing the sample spacing in either direction, or a vec2 representing the sample spacing in the horizontal and vertical directions, respectively.

Returns vec2(kx, ky), where kx and ky are the angular wavenumbers of the corresponding texel of the Fourier Transformed data.

• ndarray-fft
• glsl-rfft

© Ricky Reusser 2017. MIT License. Based on the filtering example of David Li. See LICENSE for more details.