Surfaces wrapped around a cylinder for 3d printing

[bugatti79]

Hi All,

I am looking to determine how these Vases where modeled using maths on this webpage https://www.3dforprint.com/3dmodel/sine-wave-vase-generator/2116. It looks like the surface is parametrically defined and wrapped around a cylinder.

Interestingly he mentions

"Sine waves combine to form beautiful super positions all over these vases. You enter values for the period of each of 5 layers and interesting super positions form between the layers. Enter numbers that have meaning to you and display this vase as a conversation piece."

Hence I searched for superposition of sine waves but most referred to those of 2 waves only.

Is there some generic equation that can somehow represent the superposition of multiple waves/surfaces? Or more simply, what would the general form of the equations look like to get those surfaces generated in the pics?

Please note that I also posted the same question at this link but no reply.

https://mathematica.stackexchange.c...used-to-replicate-these-surface-plots-seen-on

Thanks!

 

[jvicens]

Hello,

Thank you for your question. It is definitely an interesting topic to explore how these vases were modeled using mathematics. From the website you provided, it seems like the surface of the vases is created using a sine wave function that is parametrically defined and wrapped around a cylinder.

To answer your question about the superposition of sine waves, there is indeed a generic equation that can represent the superposition of multiple waves/surfaces. It is called the superposition principle, which states that when two or more waves meet at a point in space, the resulting wave is the sum of the individual waves.

In the case of these vases, it seems like the different layers of the sine waves are combined to create the final surface. The specific equations used to generate these surfaces may vary, but they would likely involve the use of trigonometric functions such as sine, cosine, and tangent.

As for the general form of the equations, they would likely involve variables such as amplitude, frequency, and phase shift to control the shape and position of the waves. It is also possible that additional parameters were used to create the variations seen in the different layers of the vases.

I hope this helps answer your question. If you have any further inquiries, please feel free to ask. Best of luck with your research!