The orientation of human eyes is uniquely defined with respect to their gaze direction, known as Donders' law. Further, the manner in which the eyes follow Donders' law varies as a function of the situation. When the head is stationary, the Donders' surfaces are flat planes but they tilt when eye fixation distance changes. These planes also shift and rotate when head orientation changes with respect to the direction of gravito-inertial acceleration. When the head is free to rotate, the Donders' surfaces are twisted. In this paper, we present a systematic method to analyze the kinematics of the eye under different gaze situations utilizing the measurement of alignment between various coordinate frames. Kinematic equations are presented for various eye movements ranging from simple head-fixed monocular shifts of eye gaze to complex eye-head shifts of gaze. At each stage, we show that simulated eye orientations that derived from our equations are able to capture the variations of Donders' surfaces and they are comparable with experimental results in the literature. The final equations we propose provide the unified kinematics of head-upright far gaze, head-upright binocular fixation, head static tilted monocular gaze and head-free monocular gaze.