Saccade Velocity

Derive planar eye-path speeds from timestamped horizontal/vertical angles; finite-difference peaks are cadence-limited and not instantaneous physiological peaks.

Description

Sampled eye positions provide average velocity over each interval.

Sampled eye positions provide average velocity over each interval. The largest interval speed approximates a peak but depends on sampling resolution.

The tool returns intervalSpeedsDegreesPerSecond (interval speeds degrees per second); peakSpeedDegreesPerSecond (peak speed degrees per second); totalPathDegrees (total path degrees). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Saccade Velocity

Use Saccade Velocity when you already have timesMs, horizontalDegrees, verticalDegrees and want intervalSpeedsDegreesPerSecond, peakSpeedDegreesPerSecond, totalPathDegrees. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Saccade Velocity and understand its results

Enter timesMs, horizontalDegrees, verticalDegrees using the field table below. Match the units, ordering and data boundaries described in the calculation.
Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
Read intervalSpeedsDegreesPerSecond, peakSpeedDegreesPerSecond, totalPathDegrees. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.

Input field	Meaning	Value type and bounds	Requirement
timesMs	Times ms	list of number	Required
horizontalDegrees	Horizontal degrees	list of number	Required
verticalDegrees	Vertical degrees	list of number	Required

Require aligned positions and strictly increasing times. Sum Euclidean interval distances for total path and select the largest interval speed.

speed[deg/s] = 1000 × hypot(Δhorizontal,Δvertical)/ΔtimeMs

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "timesMs": [
      0,
      10,
      20
    ],
    "horizontalDegrees": [
      0,
      1,
      3
    ],
    "verticalDegrees": [
      0,
      0,
      0
    ]
  },
  "output": {
    "intervalSpeedsDegreesPerSecond": [
      100,
      200
    ],
    "peakSpeedDegreesPerSecond": 200,
    "totalPathDegrees": 3
  }
}

Limitations and assumptions

No differentiation smoothing, blink removal or saccade segmentation is applied; total path differs from endpoint displacement.

Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.

Alternative or Complementary methods

Saccade Latency: Interpolate the first supplied eye-speed threshold crossing after a cue; blink rejection and direction classification are not inferred. Smooth Pursuit Gain: Fit eye velocity against target velocity after caller-supplied saccade/blink exclusions; signed slope and intercept are preserved.

Methodological background: Digital Library of Mathematical Functions: Quadrature.^[1]

References

Digital Library of Mathematical Functions: Quadrature — National Institute of Standards and Technology

Similar or alternative tools

Saccade Latency
Interpolate the first supplied eye-speed threshold crossing after a cue; blink rejection and direction classification are not inferred.
Smooth Pursuit Gain
Fit eye velocity against target velocity after caller-supplied saccade/blink exclusions; signed slope and intercept are preserved.