Ujin Kwon · 권우진

Numerical solvers, telemetry systems, control, and real-time engineering

C/C++ core · Stable C ABI · Python/PyPI · Unity/C#

ballistic-solver is a deployable intercept solver for moving targets under gravity and quadratic drag, with optional wind. Instead of assuming a closed-form ballistic arc, it simulates projectile motion and solves the intercept numerically.

Problem

I wanted a solver that still works when the projectile path is strongly curved by drag and the target is moving. That rules out simple vacuum-style closed forms as the main solution path.

Why Numerical Instead Of Closed-Form

  • Projectile dynamics include quadratic drag, optional wind, and fixed-step RK4 integration.
  • The hit condition is solved against a moving target, with an extended API for constant-acceleration targets.
  • The solver returns explicit status codes, diagnostic messages, and the best result found even when convergence is imperfect.

Architecture

Inputsrelative target motion, speed, drag, solver params
→
SimulationRK4 projectile integration with drag and wind
→
Residualclosest-approach miss expressed in launch-angle space
→
SolveLevenberg-Marquardt + line search + Broyden-style Jacobian refinement
→
DeployC ABI, Python package, Unity/C# interop

What I Built

  • Header-only C++ core focused on solver logic rather than app-specific wrappers.
  • Stable C ABI with plain-C data layout and fixed-size arrays for FFI-safe integration.
  • Python package with presets, utility helpers, and prebuilt binaries through PyPI.
  • Unity/C# path using P/Invoke so the same native solver can be used in game/runtime contexts.
  • Failure handling through explicit status codes such as invalid input, Jacobian failure, line-search rejection, and max-iteration exhaustion.

What This Project Proves

  • Mathematical modeling: I can translate a nonlinear physical intercept problem into a solver with explicit assumptions.
  • Numerical-method judgment: I can combine integration, residual design, damping, line search, and Jacobian updates into one practical method.
  • Deployable engineering: I can expose the same core through C ABI, Python, and Unity/C# instead of leaving it as lab-only code.
  • Debuggability: explicit statuses and best-effort outputs matter to me as much as nominal success cases.

Verified Results

From the repository README benchmark on a local Windows release build over 500 generated linear-target cases:

Preset Median Solve Time p95 Solve Time p95 Miss
fast 0.107 ms 0.233 ms 3.399e-02 m
balanced 0.219 ms 0.492 ms 7.287e-03 m
precise 0.265 ms 0.583 ms 7.655e-06 m

Limits And Failure Cases

  • The runtime using the solver must match the same physics and integration assumptions; different timesteps or integrators can invalidate the hit.
  • Strongly nonlinear cases are handled numerically, so convergence quality depends on solver settings and problem conditioning.
  • This project prioritizes deployable robustness and explicit diagnostics rather than pretending every case has a perfect analytic solution.