A biomechanically-grounded mouse movement algorithm that outperforms WindMouse across every metric that matters for human-like trajectory generation.
Built for my PhD research on novel mouse movement humanization techniques.
SigmaDrift generates point-to-point mouse trajectories using six interacting components from computational motor control research:
- Sigma-lognormal velocity primitives — asymmetric bell-shaped speed profiles from Plamondon's Kinematic Theory
- Two-phase surge architecture — ballistic stroke (~93% of distance) followed by 0-2 corrective sub-movements
- Ornstein-Uhlenbeck lateral drift — mean-reverting stochastic hand drift
- Signal-dependent noise — motor noise scales with command magnitude (Harris-Wolpert), making Fitts' Law emerge naturally
- Speed-modulated physiological tremor — 8-12 Hz tremor suppressed during fast ballistic movement
- Gamma-distributed inter-sample timing — non-constant polling intervals matching real hardware behavior
Same distance (~630px), same target width (20px):
| Metric | SigmaDrift | WindMouse | Real Human |
|---|---|---|---|
| Movement Time | 827 ms | 499 ms | ~750-850 ms |
| Fitts' Compliance | Yes (~8%) | No | Yes |
| Sub-Movements | 2 | 15 | 1-3 |
| Path Efficiency | 0.985 | 0.973 | 0.95-0.99 |
| Velocity Profile | Bell-shaped | Jagged | Bell-shaped |
Header-only C++20, zero dependencies.
#include "motor_synergy.h"
auto path = motor_synergy::generate(start_x, start_y, target_x, target_y);
for (auto& pt : path) {
// pt.x, pt.y = position
// pt.t = timestamp in ms
}Custom configuration:
motor_synergy::config cfg;
cfg.target_width = 16.0;
cfg.overshoot_prob = 0.20;
auto path = motor_synergy::generate(x0, y0, x1, y1, cfg);
auto m = motor_synergy::compute_metrics(path, x1, y1, cfg.target_width, dist);The included Win32 visualization harness (main.cpp) provides side-by-side comparison:
- Space — generate SigmaDrift trajectory (animated)
- W — generate WindMouse trajectory
- R — record your own mouse movement
- S — export trajectories to CSV
- +/- — adjust target width
Bottom panel shows velocity profile graphs for all trajectories overlaid.
Visual Studio 2022 with C++20. Open SigmaDrift.slnx, build x64 Release.
- Plamondon — Kinematic Theory of Rapid Human Movements
- Flash & Hogan (1985) — Minimum-jerk model
- Harris & Wolpert (1998) — Signal-dependent noise
- Muller et al. (2017) — Control-theoretic models of pointing
- Acien et al. (2022) — BeCAPTCHA-Mouse
- Liu et al. (2024) — DMTG diffusion-based generation
