a function to turn any arbitrary function into equidistant points from [a, b] with n points.

import { collapse } from "curve_collapse";

const points = collapse((x) => x, 0, 1, 10);

assertArrayAlmostEquals(points, [
  [0, 0],
  [0.25, 0.25],
  [0.5, 0.5],
  [0.75, 0.75],
  [1, 1],
]);

This is particurally useful for displays, e.g. uniformly displaying drones on a curve during a light show (or even animating them!).

My particular use case here is to use it for displaying particles uniformly around any curve.

By using the Pygatherom Therom as an integral to find the distance travelled on a curve:

$$ \int_{0}^{b}\sqrt{1 + f'(x)^2}\ dx $$

(Desmos example)

We can first get the whole distance travelled throughout the function, split it into n parts, then solve for bound b with numerical integration.

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