A system and method for generating data suitable for determining a parameter of a human eye. The method includes receiving a first image of the eye for a first time from a camera of known camera intrinsics defining an image plane, and determining a first ellipse in the first image. The method includes determining a first eye intersecting line expected to intersect a center of the eyeball at the first time as a line which is, in the direction of the orientation vector, parallel-shifted to the first center line by an expected distance between the center of the eyeball and a center of the pupil.