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7 months ago in Applied Mathematics , Computational Physics By Ramesh

How can I obtain a sine function along a path defined by a known curve?

In my computational modeling work, I need to simulate a wave-like disturbance that propagates along a pre-defined nonlinear path, like a parabola or a spline. Simply using a standard sine over x-axis coordinates distorts the wave. How do I formally define the sine function such that its oscillation follows the curve's geometry?

ArcLength Parametrization SineFunction

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By Suresh Answered 5 months ago

This is a classic problem in geometric modeling. I've implemented this for simulating stress waves. The solution is parametrization. First, define your curve parametrically, e.g., r(s) = [x(s), y(s)], where 's' is ideally the arc length for uniform wave speed. Your sine function then becomes amplitude * sin(2πs / wavelength + phase). You plot the final coordinates as [x(s), y(s)] with the sine value acting as a displacement normal to the curve or modulating a property. This keeps the wave's frequency consistent along the path.

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