approach_rate()

double MayaFlux::Kinesis::approach_rate ( std::span< const double >  a, std::span< const double >  b, double  dt  )

inlinenoexcept

Rate at which two streams approach or separate.

Parameters

a	First span, chronological order
b	Second span, chronological order, same length as a
dt	Seconds per sample

Returns

Least-squares slope of |a - b| over the window, per second; negative means the streams are converging, positive diverging

Distinct from correlation, which asks whether two streams move in the same direction as each other, not whether they are getting nearer. Two streams can correlate strongly while one holds steady and the other drifts away from it, or diverge while both move in the same direction at different rates. This is the direct measure of mutual approach the dancers-and-a-third-point case needs: not whether the third point's motion resembles either hand's, but whether it is closing on the gap between them.

Operates on scalar streams. A caller with vector positions supplies the scalar separation (glm::length of the difference, or a projected distance) rather than raw components, since "approaching" is a statement about a single distance, not about three independent axes each separately trending.

Definition at line 192 of file Relation.hpp.

{
    const size_t n = a.size();
    if (n != b.size() || n < 2 || dt <= 0.0)
        return 0.0;
 
    std::vector<double> separation(n);
    for (size_t i = 0; i < n; ++i)
        separation[i] = std::abs(a[i] - b[i]);
 
    return Stochastic::Estimate::trend_slope(separation) / dt;
}

References a, b, and MayaFlux::Kinesis::Stochastic::Estimate::trend_slope().

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