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Comment by liontwist | Hacker News Reader

Category theory is a great tool for thinking about programming language design (especially types in functional programming). In some sense that translates to better programming, but there’s a lot more math topics that are likely to be directly applicable day to day.

Do you know how to evaluate a polynomial efficiently? Fit a curve to points? Solve a linear system? What the Fourier transform is for? If no, hold off on the categories.

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Is Bézier curves not enough to fit curve to points? Just checking as I am very curious about this problem.

The answer is obviously no, but I’m not the right person to explain (biochemist).

For some reason you were downvoted down to oblivion, and I think that was unfair.

Bézier curves parameterise a curve with points. When people talk about "fitting a curve" I would expect they mean fitting a model rather than that the curve is fully determined by the points. Typically people fit linear or low-order polynomials, it'd be a weird day where someone wanted to use a Bézier for their model - those curves weren't designed for being statistically tractable or interesting.

See https://en.wikipedia.org/wiki/Curve_fitting

To expand upon roenxi's answer: Bezier curves are an example of creating a cubic (degree 3) parametric polynomial curve by using four points to describe where you want it to go.

Curve fitting is about starting with a cloud of points, and trying to decide how to draw a polynomial (of whatever degree you want) that does a good job of describing the trend line of those points.

Then you can use that polynomial to approximately interpolate points between the samples, or extrapolate points beyond the samples as an example.

No. Here are two common and practical kinds of curve fitting:

1. Least squared polynomial fit.

This finds a curve that approximates a set of (x, y) pairs.

2. Polynomial interpolation

This makes a polynomial which goes exactly through the given points.

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