TENNIS BALLS, TRIANGULATED

Hawk-eye's success combines ever-improving modern technology and good, old-fashioned trigonometry.

Hawk-eyed line umpire

Up to 10 cameras are set up in different positions, high and low, around the court, then painstakingly calibrated to the court’s dimensions. In real time, vision processing is used to identify the centre of the ball in every frame from every camera. The system triangulates information from at least three cameras to provide a 3D position of the ball. The process is repeated for each frame so that 3D positions of the ball can be combined to produce a single trajectory of the flight of the ball, which algorithms use to calculate the ball’s exact contact area on the court. When a player challenges a line call, the trajectory and ball bounce displayed is created in virtual reality software.

Frame by frame, a very fast squishy ball In the high-speed sequence below, frames (1) and (2) show a tennis ball approaching its bounce, which at (3) shows it just touches the line upon landing. At (4), the ball’s about midway across its elliptical-shaped contact area but completely past the line. (The time elapsed between frames (1) and (4) in this sequence is is the same as a single frame of broadcast footage.) At (5), the ball is still touching the ground but now at least 10cm (the width of a line) beyond its point of first contact. Line call: in. 1

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