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what is most interesting to me about bezier curves is how they introduce a 'time' parameter.

referring to how they switch from two coordiates (function arguments) into just the one 'time' argument.

this is most clear in Bartosz Cieachanowski explanation.

then the whole topic gets really going when they add multiple lines all parametrized with the one 'time' argument.

This sort of calculation, where you map t → (x,y) is normally covered in Calc 3, along with how to rewrite r(t) to r(s) where s is a distance parameter rather than a time parameter which can be useful if you’re plotting the Bézier as individual points rather than as line segments.

It's just a parameter and thinking of it as time is not helpful. When you get to Bezier surfaces they have 2 such parameters often called U and V. Thinking of it as time breaks down then.

Two-dimensional time seems perfectly cromulent to me

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