Tennis

About this game

What it is

Singles tennis, in 3D, played to the ITF Rules of Tennis. This is an independent reimplementation of the sport by an outside author. It is not affiliated with, endorsed by, or connected to the International Tennis Federation or any tennis organisation. Tennis is a sport in the public domain; the ITF is its governing body and the author of the rules this game follows. The rules are quoted here for accuracy and credited below.

How to play

• Move and aim with the arrow keys or WASD. Whichever way you are pressing when you swing is the way you aim the ball.
• Space does everything with the ball: it tosses the serve, strikes it, and swings in a rally. On the serve, the toss and the strike are two separate presses — the timing of the second one is your serve.
• Shift drives the ball deeper and harder.
• 1 slice, 2 flat, 3 topspin. Spin is the thing that makes tennis tennis, and it is real physics here, not a label: topspin curves the ball down so it drops in and then kicks up off the court, and slice floats and then skids low.
• On a phone or tablet, on-screen controls appear: the stick on the left moves and aims, Swing tosses, serves and swings, hold Deep to drive deeper, and Spin cycles flat, topspin and slice. Landscape gives the widest view of the court.
• If you toss and decide not to hit, just let the ball drop. Under Rule 19, Case 1 that is not a fault, and it is not one here either.

The court, at ITF dimensions

Everything is at the sizes Rule 1 gives: the court is 23.77 m long and 8.23 m wide for singles (10.97 m for doubles, whose alley is drawn but not played). The net is 0.914 m at the centre and 1.07 m at the singles sticks, which stand 0.914 m outside the singles court. The servicelines are 6.40 m from the net and run between the singles sidelines.

Rule 1 says “All court measurements shall be made to the outside of the lines” and Rule 12 says “If a ball touches a line, it is regarded as touching the court bounded by that line.” So the in/out boundary here is the outer edge of each line and touching it is in. A ball landing on the centre serviceline is in both service courts, because that line bounds both.

The ball, and where its bounce comes from

The ball is the ITF's own reference ball: 57.6 g and 6.60 cm across. Its bounciness was not chosen. Appendix I requires a Type 2 ball to rebound between 135 cm and 147 cm, and the ITF test method ITF TB 04/01 drops it from 254 cm — measuring both the drop and the rebound to the bottom of the ball. That test was simulated, with air drag, at the ITF's own laboratory conditions (20 °C, 60 % humidity, 102 kPa), and the coefficient of restitution solved for: 0.7745. Ignoring drag would have given 0.745, which rebounds only 130.8 cm and would fail ITF approval.

The flight

Drag and the Magnus force use published measurements, not tuning: a drag coefficient of 0.55 for a new ball, rising with spin, and a lift coefficient that never exceeds 0.5. Held out from that fitting, the literature also says a ball served at any speed lands at about 75 % of its serve speed; this engine gives 72.5 % across 30–60 m/s, and the gap is traced to the source quoting two different drag coefficients on the same page. See CREDITS.txt for the full account.

The scoring

Rule 5.a: Love, 15, 30, 40, game, with the server's score called first; at three points all the score is Deuce, and after Deuce you need two consecutive points. Rule 6.b: six games with a margin of two wins a set, and at six games all a tie-break is played. Rule 5.b: the tie-break is first to seven with a margin of two, the opener serves one point and then each player serves two, and Rule 10 changes ends every six points and after every odd game of a set. Rule 17 starts every game and every tie-break from the right half and alternates.

Rule 6 requires an event to announce how its final set is played, so the Match menu offers the choices and labels each one: the ITF tie-break set, the Rule 6.a advantage set, the 10-point tie-break at 6–6 used at the Grand Slams since 2022, and the Appendix V match tie-break. “No-Ad” scoring is also Appendix V.

What is faithful and what is not

• Faithful: every court and net dimension, the ball's mass and size, the derived coefficient of restitution, the line rules, the service geometry, the two-serve rule and the service let, the full scoring machine including the tie-break rotation and change of ends, and drag and Magnus from published measurement.
• Reconstructed — nothing in the rules fixes these, and they are invented: how fast a player runs and how far they reach, how hard and how accurately they swing, the opponent's skill levels, the friction of each surface, the shape of the net between the two heights Rule 1 fixes, and the ball's moment of inertia.
• Not modelled: doubles, wind, sun, altitude, ball wear, spin decay in flight, a speed-dependent coefficient of restitution, and the growth of the ball's contact patch with impact speed. Changing ends is tracked and displayed exactly as Rule 10 requires, but because the court is symmetric and there is no wind or sun here, it does not change how the ball behaves.

Credit

Rules and all quoted figures: ITF Rules of Tennis 2023 and ITF Approved Tennis Balls, Classified Surfaces & Recognised Courts, both published by the International Tennis Federation. Aerodynamics: Rod Cross, Ball Trajectories (University of Sydney), quoting the measurements of Štěpánek. Full citations, and a list of every reconstructed number, are in CREDITS.txt.