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I'm curious about how to find an f(x) equation for the "wave" logo of the Vans Shoes. It's a simple 1-dimensional wave. I've been thinking about this for a month and couldn't get the answer. Here's an image for a reference: vans' wave

enter image description here

Could someone possibly explain how to get that f(x) equation?

Brian Tung
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andirkh
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    While I'm sure someone will come up with an acceptable formula, it's mathematically important to know that there isn't just one formula that will work; lots of functions will have graphs shaped like that wave. – Greg Martin Jan 23 '20 at 16:50
  • What types of curves have you thought of using? – Andrew Chin Jan 23 '20 at 16:53
  • My first guess would be a rounded tractrix, sometimes called a HundKurve, because it's the curve a dog would follow if he's on a leash but striving to reach a bone too far from the straight path he is meant to be on. – lulu Jan 23 '20 at 17:08

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There are too many possibilities to play with.. and is quite subjective, even as a flat 3D curve approximation.

Can rotate the given curve here a bit and adjust $x$ domain. Parametric plot given can be put into $y=f(x)$ form.

Shoe Curve

Narasimham
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