Interactive, high-performance visualiser for hydrogen-like electron orbitals. Implements normalized hydrogenic radial functions and real spherical harmonics, with browser-first rendering paths for CPU, WebGL, and WebGPU.

• Physically motivated math: normalized hydrogenic radial R_nl(r) with associated Laguerre recurrence, and real normalized Y_lm(θ,φ) via associated Legendre (supports l ≤ 3 [...]
• Four render paths:
  • Instanced: InstancedMesh spheres or billboard impostors.
  • Points: single BufferGeometry with importance sampling (fast CPU).
  • GPU (WebGL): render‑to‑texture sampling + shader point cloud.
  • WebGPU: compute shader sampling + render shader (Chrome/Edge).
• Importance sampling: inverse CDF tables for |R|² r² and |Y|² sinθ; no rejection loops in Points mode.
• Smooth X/Y/Z snaps with easing; orientation axes overlay (bottom-left).
• Clear separation between the HTML shell (index.html) and the runtime controller (src/main.js) to avoid duplicate initialization paths.

• Modern browser with WebGL2. GPU (WebGL) mode needs float color buffer support: EXT_color_buffer_float or WEBGL_color_buffer_float.
• WebGPU mode: Chrome/Edge with WebGPU enabled (Chrome 113+). Falls back automatically if unavailable.

1. Serve the folder locally (recommended to avoid file URL issues):
   • Python 3: python3 -m http.server 8000
   • Node: npx http-server -c-1
2. Open http://localhost:8000/index.html.

Opening index.html directly from disk also works for most features, but some GPU paths may be limited by browser security.

• Right panel: orbital presets (1s, 2s/3s/4s; 2p/3p/4p; 3d/4d variants).
• Bottom panel controls:
  • Density: number of points (performance/quality).
  • Adaptive: incremental updates vs full refresh.
  • Mode: Instanced → Points → GPU (WebGL) → WebGPU.
  • Cull: toggle depth testing/writing for point clouds.
  • Pause, Clear, Save PNG.
• Orientation overlay (bottom‑left): mini axes + buttons X/Y/Z/Reset with smooth transitions.
• Mouse: drag to orbit, wheel to zoom.

• Points (CPU):
  • One BufferGeometry; positions and per‑point ψ updated each refresh.
  • Size/alpha modulated by |ψ|; zoom‑aware alpha for clarity.
• GPU (WebGL):
  • Renders samples into an RGBA32F target; point shader reads (x,y,z,ψ).
  • Requires WebGL2 + float render targets.
• WebGPU:
  • Compute pass samples via inverse CDFs; point sprites are rendered directly from the generated particle buffer.

• Radial functions use normalized hydrogenic forms in atomic units, computed via a stable Laguerre recurrence.
• Real spherical harmonics are normalized; sampling tables use |Y|² sinθ and |R|² r² to draw from |ψ|² directly.

• Point size: edit uPointSize in src/main.js and src/gpu/webglSampler.js, plus the WebGPU point size constant in src/gpu/webgpuPipeline.js.
• Performance: lower Density, use Points or GPU mode; WebGPU is fastest if available.

• “GPU mode fell back to Points”: your GPU/driver likely lacks float color buffer support; use Points/WebGPU.
• WebGPU unavailable: ensure your browser version supports WebGPU and it’s enabled; the app will fall back to other modes.

• Run unit tests: npm test
• CI runs the same tests on push/PR via GitHub Actions (see .github/workflows/ci.yml).

See LICENSE.