curvature()

float MayaFlux::Kinesis::curvature ( const glm::vec2 &  vel, const glm::vec2 &  accel, float  min_speed = 1e-3F  )

inlinenoexcept

Signed curvature from velocity and acceleration.

Parameters

vel	Velocity vector
accel	Acceleration vector
min_speed	Speed below which curvature is reported as 0 rather than computed. Default 1e-3, not 1e-6: curvature divides by speed^3, so at real input scales (e.g. normalized 0..1 tablet coordinates per second, where a slow-moving stroke is speed 0.05-0.5) a guard near machine epsilon never fires, and the cubic denominator still amplifies ordinary acceleration noise into numbers in the thousands. The threshold has to be picked relative to the caller's actual speed scale, not left at a constant close to zero; 1e-3 is a reasonable default for normalized 0..1 spatial data but a caller working in different units (pixels, millimeters) should pass one appropriate to that scale rather than rely on this default.

Returns

(vx*ay - vy*ax) / |v|^3, or 0 when speed is below min_speed

dtheta/ds rather than dtheta/dt: speed-independent, so a sharp corner drawn slowly and the same corner drawn fast report the same curvature, unlike angular_velocity which conflates turn sharpness with pace. Positive is a leftward (CCW) bend, negative rightward. Even with a correctly scaled min_speed, curvature remains numerically sensitive near that threshold since it is still a cubic denominator; treat curvature values from low-speed samples as low-confidence regardless of whether they cleared the guard.

Definition at line 418 of file Differential.hpp.

{
    const float speed_sq = glm::dot(vel, vel);
    const float spd = std::sqrt(speed_sq);
    if (spd < min_speed)
        return 0.0F;
    return cross_2d(vel, accel) / (speed_sq * spd);
}

References cross_2d().

Referenced by channel_curvature(), compute_path_curvature(), and curvature_from_history().

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