Coding classes in the Highlands

A cubic Bezier curve is defined by four points: it starts at the first, ends at the last, and is pulled towards the two in between, called handles. It is how fonts describe letters, how SVG images store shapes, and how drawing apps turn a drag of the mouse into a smooth line. The learner writes the de Casteljau algorithm, which finds any point on the curve by repeatedly taking points part of the way along straight lines, then tries to draw a semicircular arch of radius 1, like the arch rings in the listing. The test is simple: every point on a true circle is exactly 1 from the centre, so the program measures how far each point on the curve strays.

A single Bezier curve makes a poor semicircle: it bulges nearly 2 per cent off, which on an arch 15 metres across would be some 138 millimetres. Split the arch into two quarter circles and use the handle length 4/3 times the tangent of a quarter of the angle, which gives the famous 0.5523 for a quarter circle, and the worst error falls to 0.027 per cent. Four pieces bring it below a thousandth of a per cent. Each extra piece cuts the error dramatically, which is why software splits curves rather than using one long one.

The last row is the warning. A tempting guess, handles a third of the chord long, looks smooth on screen but is more than 150 times worse than the right choice for two pieces. Both curves look like arches. Only measurement tells them apart, and the learner who wrote the error check sees it at once. We make no claim about how the real viaduct was drawn or set out in 1901; it was built long before Bezier curves were developed for car design around 1960.

So for a young person in the Highlands, learning to code in 2026 means knowing how to check that a curve is what it claims to be. The longer argument is in why teenagers should still learn to code in 2026.