Derived continuous functions

Available helpers include speed_function(), acceleration_magnitude_function(), distance_to_landmark_function(), cumulative_path_length(), heading_function(), signed_curvature_function(), turning_rate_function(), and trajectory_tortuosity().

Derivatives amplify noise

Velocity and acceleration are numerical derivatives. The package does not automatically smooth before differentiating.

Landmark distance

Distance to a source card, disclosure, or decision target can create a single interpretable continuous function.

Path length

Cumulative path length captures exploratory extent over trial time but does not preserve direction or location.

Continuous planar geometry

Version 0.31 extends the derived-function layer from kinematics to planar differential geometry.

• heading_function() returns wrapped direction in radians;
• signed_curvature_function() returns local signed path curvature;
• turning_rate_function() returns signed angular change per unit time;
• trajectory_tortuosity() returns observed path length divided by endpoint displacement.

These quantities remain conditional on the declared coordinate metric. Separately normalized horizontal/vertical axes can distort Euclidean geometry, and screen \(y\)-axis direction affects the visual interpretation of signed curvature.

Low speed is explicit

Curvature and turning direction become unstable as speed approaches zero. The package does not add a small denominator epsilon or choose a near-zero threshold silently.

Use min_speed and undefined_policy explicitly. Missing geometry remains NaN rather than being converted to zero.

Heading is circular

Wrapped angles near \(-\pi\) and \(+\pi\) are physically close but numerically distant. Standard Euclidean FPCA is therefore not automatically appropriate for wrapped heading.

More detail

See the continuous trajectory geometry method guide, worked example, and mathematical reference.