An electronic system comprising: a display interface configured to display a calibration point; a sensor, coupled to the display interface, and configured to: capture a first gesture directed at the calibration point from a first position; capture a second gesture directed at the calibration point from a second position, wherein the second position is different from the first position; and a control unit, coupled to the display interface, and configured to: generate a transformation matrix based on the calibration point in a display coordinate system and an intersection based on the first gesture and the second gesture; capture a third gesture directed at the display interface; and determine a first appendage position of the third gesture in the sensor coordinate system; determine a second appendage position of the third gesture in the sensor coordinate system; calculate a transformed first point in the display coordinate system by applying the transformation matrix to the first appendage position; calculate a transformed second point in the display coordinate system by applying the transformation matrix to the second appendage position; generate a ray casting vector based on the transformed first point and the transformed second point; generate the position indicator based on an intersection of the ray casting vector with a display plane in the display coordinate system; and control the display interface to display the position indicator on the display interface; wherein the first gesture, the second gesture, and the third gesture are each a motion of an appendage of a user; and wherein the intersection based on the first gesture and the second gesture is determined based on a first calibration vector for representing the first gesture and a second calibration vector for representing the second gesture. a display interface configured to display a calibration point; a sensor, coupled to the display interface, and configured to: capture a first gesture directed at the calibration point from a first position; capture a second gesture directed at the calibration point from a second position, wherein the second position is different from the first position; and capture a first gesture directed at the calibration point from a first position; capture a second gesture directed at the calibration point from a second position, wherein the second position is different from the first position; and a control unit, coupled to the display interface, and configured to: generate a transformation matrix based on the calibration point in a display coordinate system and an intersection based on the first gesture and the second gesture; capture a third gesture directed at the display interface; and determine a first appendage position of the third gesture in the sensor coordinate system; determine a second appendage position of the third gesture in the sensor coordinate system; calculate a transformed first point in the display coordinate system by applying the transformation matrix to the first appendage position; calculate a transformed second point in the display coordinate system by applying the transformation matrix to the second appendage position; generate a ray casting vector based on the transformed first point and the transformed second point; generate the position indicator based on an intersection of the ray casting vector with a display plane in the display coordinate system; and control the display interface to display the position indicator on the display interface; wherein the first gesture, the second gesture, and the third gesture are each a motion of an appendage of a user; and wherein the intersection based on the first gesture and the second gesture is determined based on a first calibration vector for representing the first gesture and a second calibration vector for representing the second gesture. determine a second appendage position of the third gesture in the sensor coordinate system; calculate a transformed first point in the display coordinate system by applying the transformation matrix to the first appendage position; calculate a transformed second point in the display coordinate system by applying the transformation matrix to the second appendage position; generate a ray casting vector based on the transformed first point and the transformed second point; generate the position indicator based on an intersection of the ray casting vector with a display plane in the display coordinate system; and control the display interface to display the position indicator on the display interface; wherein the first gesture, the second gesture, and the third gesture are each a motion of an appendage of a user; and wherein the intersection based on the first gesture and the second gesture is determined based on a first calibration vector for representing the first gesture and a second calibration vector for representing the second gesture.