URSA — Chord Length Distribution Estimator

Interactive chord length distribution estimator for a rectangular volume (Messenger & Ash, Single Event Phenomena, Eq. 1.38), built with Dear ImGui and ImPlot.

cmake cpp glfw imgui implot opengl physics-simulation radiation-effects single-event-effects

Background

Implements Approximation No. 2 (Eq. 1.38) for the cumulative chord length distribution C(s), from:

G. C. Messenger and M. S. Ash, Single Event Phenomena, Chapter 1, Section 1.4 "Chord Distribution Functions".

For a box with dimensions a, b, c (where c is the smallest dimension) and space diagonal s_max = sqrt(a^2 + b^2 + c^2):

k = 2.37c / (1.80c + s_max)

C(s) = (1 - k) * (s_max^3.8 - s^3.8) / (s_max^3.8 - c^3.8) * (c/s)^2   for s >= c
C(s) = 1 - k * (s/c)                                                   for s <  c

C(s) is the probability that a randomly oriented, isotropic particle track chord through the volume has length >= s.

Building

Requires CMake 3.16+, a C++17 compiler, and OpenGL/X11 development headers (on Debian/Ubuntu: libgl-dev libx11-dev libxrandr-dev libxinerama-dev libxcursor-dev libxi-dev libxkbcommon-dev). GLFW, Dear ImGui, and ImPlot are fetched automatically via CMake FetchContent — no manual dependency setup needed.

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build -j$(nproc)

Running

./build/chord_length_estimator

This opens a window with sliders for the box dimensions a, b, c and a chord length probe s, live readouts of the volume, s_max, and C(s), and a log-scale plot of C(s) across the full chord length range.