This is a screen shot from an animation generated by a matplotlib example

enter image description here

the key part in the code is

    R = 1 - np.sqrt(X**2 + Y**2)
    Z = np.cos(2 * np.pi * X + phi) * R

corresponding equation is

$\left(- \sqrt{X^{2} + Y^{2}} + 1\right) \cos{\left (2 \pi X + \phi \right )}$

Could some give an explanation or hint about this kind of equation?

Is there a name of this type of graphics?

usually cosine/sine could generate something like a (half) circle, what does R part do?


1 Answer 1


The R part generates a cone where the point is at (0, 0, 1) and it spreads out below that. It meets the x-y plane at the unit circle:

A cone with the point at (0, 0, 1) and spreading out downward

The cos component defines an extruded cosine wave along the X-axis:

The graph of cos(2*π*x)

So the final equation takes the cosine wave and multiplies its amplitude by the cone. It will have full amplitude at the origin, and decrease to 0 at the unit circle on the x-y plane. Past that it becomes negative:

Multiplying the second equation by the first

The phi component shifts the sine wave forward or backward along the x axis.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.