Quantum Atom Renderer

Status: not actively maintained. Left up as a reference.

Real-time visualization of hydrogen electron probability clouds using CDF inverse-transform sampling of exact wavefunctions, rendered as glowing point clouds in OpenGL.

What it does

Generates 100,000+ 3D points distributed according to |ψ(r,θ,φ)|² for hydrogen-like orbitals using CDF inverse-transform sampling, then renders them as additive-blended GL_POINTS with a glow fragment shader.

Supports arbitrary quantum numbers (n, l, m) up to n=5, with presets for common orbitals (1s, 2p, 3d, 4f, etc.).

Controls

• Left-drag: Orbit camera
• Scroll: Zoom
• ImGui panel: Change orbital, point count, colors, glow

Build

# Dependencies (Ubuntu/Debian)
sudo apt install libglfw3-dev libglm-dev cmake

# Build
cmake -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build -j$(nproc)

# Run
./build/atomsim

Tech Stack

• C++17, OpenGL 3.3 Core Profile
• GLFW — windowing
• GLAD2 — OpenGL loader
• GLM — math (no custom vector types)
• Dear ImGui — parameter UI
• CMake — build system

Physics

Exact hydrogen wavefunctions:

ψ_nlm(r,θ,φ) = R_nl(r) · Y_lm(θ,φ)

where R_nl uses generalized Laguerre polynomials and Y_lm uses associated Legendre polynomials. Points are sampled by inverse-transform sampling of per-axis CDFs: a radial CDF from r²·|R_nl(r)|² and a polar CDF from sin(θ)·|P_l^m(cosθ)|² (so the r² sin(θ) volume element is baked into the PDFs), with the azimuth φ drawn uniformly.

Architecture

File	Purpose
src/main.cpp	Window, render loop, ImGui controls
src/orbital.cpp	Wavefunction math + CDF sampling
src/shader.cpp	Shader compilation/linking
src/camera.cpp	Arcball camera
src/glad.c	GLAD2 OpenGL loader