An expanding visual notebook: whenever I finish an algorithm, I add a way to inspect it. A reusable C++ visualization library makes transforms, fitting, graphs and intermediate states easy to visualize and compare; examples include 3D Fourier decomposition with animated signals and 2D Gaussian splat fitting. Some algorithms are visually simple, and the shared framework favors showing their internal state over a polished individual presentation.
Explore connections Brochure · 6 chapters ↓
Fourier studies and Gaussian fitting expose the intermediate representation that connects an input to a reconstruction.
Start from a signal or a target image.
Inspect Fourier coefficients or a set of Gaussian primitives.
Filter bands or optimize the fitting parameters.
Compare the visible result with its original target.
Related techniques belong to one family. Follow a family into the interface, recorded results and mathematical detail.
01 / 03Follow a source into frequency space, then reconstruct selected contributions.
02 / 03Gaussian fitting and other algorithm studies reuse the same visualization tools.
03 / 03See which studies are available in the browser and why the volume viewers still need a port.
Whenever I finish an algorithm, I want to see it work. This growing notebook reuses a visualization library for controls, coordinated views and intermediate states. Its strongest study links 3D Fourier regions to reconstructed volumes; the broader collection values informative inspection, while dedicated projects give selected ideas a more polished interface.
Scan the descriptions and figures, or open a layer for the implementation and mathematical detail.
Follow a source into frequency space, then reconstruct selected contributions.
The desktop 3D FFT study connects a source volume, its spatial-frequency spectrum and a partial reconstruction in one coordinated view. Selecting a frequency region shows its reconstructed contribution; selecting several regions shows their sum. A familiar transform becomes a concrete question about which scales and directions create a visible structure.
The filter bank separates octants, spherical or logarithmic shells, azimuth wedges, polar cones, spherical sectors and axis slabs. Each tile pairs its region of frequency space with the volume reconstructed from that region. Camera motion is shared across the major views, and animated sources can be decomposed again as they evolve. This is a distinctive use of the workbench rather than a claim to a new FFT algorithm.
The 3D viewer is currently available in the desktop application. The browser's 2D FFT and radial/angular filter bank provide a smaller, live version of the same source → spectrum → selection → reconstruction idea.
A mask multiplies the complex Fourier coefficients, including their phase, before an inverse transform. The magnitude image is only a view of the spectrum. It cannot reconstruct the volume on its own.
The implemented filter bank assigns each frequency bin to one band. By linearity, the sum of the band reconstructions recovers the source up to numerical error. The display uses the real part of each inverse transform; opposite frequency regions are related by conjugate symmetry for a real source. A band's visible contribution can include positive and negative structure, so it is not an independent positive percentage of the final image. Volume transfer functions and compositing further change its apparent brightness.
The native implementation computes the forward FFT once, masks the shared coefficients for each region, and runs an inverse FFT per band. Native workers parallelize those inverse transforms. Rebuilding an animated source repeats that work and uploads the band volumes to the renderer; more bands and larger grids increase both computation and display work.
The reusable volume viewer currently uses desktop GLSL 330. Porting that rendering path and the threaded rebuild is separate from compiling the CPU FFT kernel to WebAssembly.
A two-dimensional discrete Fourier transform expresses an image in spatial-frequency components. Low frequencies describe broad variation; high frequencies contribute fine detail and rapid changes. Frequency is measured across the image, not across time.
The lab displays the input, spectrum and reconstructed image together. Editing a frequency mask and reconstructing makes the relationship visible. A low-pass mask tends to soften edges; a high-pass mask emphasizes variation.
Radial and angular masks partition the spatial-frequency plane. The resulting images expose scale and orientation as separate properties of the same signal.
A browser launch opens this 2D study directly. The 3D filter-bank volume viewer is a different display path and remains outside the browser build.
Gaussian fitting and other algorithm studies reuse the same visualization tools.
Each primitive has a center, width, angle and amplitude. The reconstruction is assembled from oriented Gaussian functions. Analytic gradients and Adam update those parameters against the target image.
The browser uses the same fitting kernel in serial form. The default 96 primitives and 64 × 64 fitting grid keep the live optimization approachable; increasing either adds CPU work. The ellipse overlay shows where the representation spends its capacity.
The goal is simple: make the computation visible. I add an algorithm to this collection when I finish it, reusing coordinated views, controls and playback instead of building a new application each time. This is my baseline for inspecting an implementation.
I first imagined a small language for authoring these showcases. That became more machinery than the task needed, so the practical result is a library that makes visualization convenient. Informativeness takes priority here: some studies are visually simple, and a general interface is not always the clearest way to explain a particular algorithm.
For ideas I find especially interesting, I also build dedicated visualizers with more careful interaction and composition. Those take more manual work; the shared workbench lets the wider collection keep growing.
| Route | Purpose | Presentation scope |
|---|---|---|
| 3D FFT decomposition | Connect frequency regions with spatial contributions | Desktop study |
| 2D FFT and filter banks | Make source, spectrum and reconstruction directly comparable | Live browser companion |
| Gaussian image fitting | Inspect an image representation while its parameters are optimized | Live optimization study |
| Further algorithm studies | Explore other intermediate representations | Shared framework, varying depth of presentation |
See which studies are available in the browser and why the volume viewers still need a port.
The browser application compiles the C++ engines and Dear ImGui interface through Emscripten. The 2D FFT, filter-bank and Gaussian-fitting studies provide a live route into Theory Workbench. The native volume viewers remain outside this build; the reason is their rendering and execution setup, not an inability to compute an FFT in WebAssembly.
Larger grids, more fitting primitives and repeated transforms can increase the cost of synchronous CPU work. That performance boundary is different from an excluded viewer. The shared Fortune entrance separately documents its own geometric and numerical limits.
| Feature | Browser status | Reason or boundary |
|---|---|---|
| 2D FFT and 2D filter bank | Available | CPU transform with browser-compatible presentation |
| 2D Gaussian fitting | Available, serial | Analytic-gradient Adam remains active; larger grids/counts add synchronous CPU work |
| 3D FFT volume, KLT eigenvolumes, voxel/JFA3D viewer | Excluded | Their shared desktop GLSL 330 volume renderer has not been ported to GLSL ES/WebGL2 |
| 4D FFT and 3D FFT filter bank | Excluded | Same unported volume renderer; larger transforms/filter-bank rebuilds also use native asynchronous workers |
| Standalone linear-programming interface | Excluded pending validation | No established CPU-solver incompatibility; this UI has not been validated for the browser |