Perfect Circle

Perfect Circle started as a conversation in the kitchen. Josie asked, "could you make a game where you have to draw a circle from memory and it scores you on how close it actually is?" That's the entire pitch. There is no second mechanic. The game shows you a guide circle for two seconds, the guide disappears, and you have ten seconds to draw the circle freehand. The game then overlays your stroke on the true circle and grades you from F up to S based on the average distance from each of your points to the nearest point on the actual circle.

The hard part of building this game was not the rendering or the input — both were trivial canvas work. The hard part was the scoring function, because the obvious approach (measure the deviation of every mouse-event point) produces wildly wrong results. On a high-refresh-rate monitor, a slow drawer who moves the mouse carefully ends up with thousands of densely-clustered points; a fast drawer who swooshes across the screen has fewer, sparser points. Naively averaging deviation rewards the fast drawer for moving fast, not for drawing accurately. We had to resample the stroke at fixed distance intervals before scoring it, which gives a fair comparison regardless of stroke speed.

The second problem was figuring out where the player's circle actually was. If you draw a small loop and then a stray line away from it, the algorithm needs to recognise the loop as your intended circle and ignore the stray. We switched from bounding-box detection to median-distance-from-centroid, which is robust to outliers. Now if you draw a great circle with one wobble, the wobble costs you almost nothing.

How to do well. Don't try to be fast. The game rewards smooth, consistent motion. Start at the top of where you remember the guide circle being. Move steadily clockwise (or counter-clockwise, the algorithm is direction-agnostic) and try to maintain a constant rotational speed. Most people give up on the last quarter of the circle because they realise it isn't closing where they thought it would — keep going, the algorithm grades the whole stroke, not where it ends.

The grading tiers were calibrated against actual human attempts. Dad's average is C. Josie holds the household record at A-tier. The kids' friends who have played hover between D and B. S-tier is genuinely hard and we have only seen it a handful of times. If you hit it, you are objectively a better circle-drawer than 99% of people who have tried.