This post discusses the computation of saccade lengths and amplitudes.
Saccade amplitude
\[Saccade ~ Duration ~ = ~ Saccade ~ end ~ time ~ - ~ Saccade ~ start ~ time\] During the saccade duration, identify the \(minimum\) and \(maximum\) \(gaze ~ positions\).
\[Saccade ~ Amplitude ~ = ~ \frac {abs (max(gaze) ~ – ~ min (gaze))} {abs (centre ~ target ~ A ~ position ~ – ~ peripheral ~ target ~ B ~ position)}\]
Saccade trajectory
\[Saccade ~ Trajectory ~ Distance ~ = ~ abs(Saccade ~ end ~ time ~ – ~ Saccade ~ start ~ time) + 1) \times Saccade ~ average ~ velocity\]
Euclidean distance
Saccade start and gaze end positions can be used to calculate the Euclidean distance in degrees.
\[dx = \frac {(genx ~ – ~ gstx)} {(eupdx + supdx)/2.0)}\]
\[dx = \frac {(geny ~ – ~ gsty)} {(eupdy + supdy)/2.0)}\]
\[Saccade ~ Euclidean ~ Distance ~ = ~ \sqrt{(dx \times dx + dy \times dy)}\]
Here:
\(supd\) and \(eupd\) are start and end angular resolutions.
Note that the saccade trajectory distance is longer than saccade Euclidean distance.
Similarly, we can calculate the Euclidean distances for gaze fixation.