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Sinusoid or not sinusoid

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Emerald V

Sinusoid or not sinusoid

It is a sinusoid:

sin-XY.png

Is it a sinusoid or this curve has any other name?

sin-Polar.png

I will not sleep until I get an answer!

3 REPLIES 3
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Re: Sinusoid or not sinusoid

Its a Cardioide! Try sin(x)-1 instead of sin(x) and use a regular polar plot (with zero in the centre).

Werner_E_0-1602458231371.gif

 

You may see it every morning on the surface of your cup of coffee because the caustic of a circle is a Cardoide.

https://en.wikipedia.org/wiki/File:Caustique.jpg

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Re: Sinusoid or not sinusoid

My method to animate the cardiod

Cardioid.png

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Re: Sinusoid or not sinusoid

What your pic shows is an Epicycloid (or Hypercycloid).

Most of them don't have special names.
Only if r1=r2 its called a Cardioid and if r1=2*r2 its called a Nephroid.

 

If a circle rolls INSIDE another, the path is called a Hypocycloid.

 

And if you watch for the path of a point not on the perimeter of the circle, its called a trochoide.

 

 

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