# Surfaces wrapped around a cylinder for 3d printing

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• bugatti79
In summary, the vases on the website mentioned were modeled using a parametrically defined sine wave wrapped around a cylinder. The superposition of multiple waves was used to create the final surface, with the specific equations involving the use of trigonometric functions and various parameters such as amplitude, frequency, and phase shift.
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?

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

Thanks!

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.

## 1. What is a surface wrapped around a cylinder for 3d printing?

A surface wrapped around a cylinder for 3d printing is a 3-dimensional object created using a 3d printer that has a cylindrical shape and a surface that wraps around it.

## 2. How is a surface wrapped around a cylinder created for 3d printing?

A surface wrapped around a cylinder for 3d printing is created using a 3d modeling software or by scanning an existing object. The software then creates a digital file that can be used by a 3d printer to print the object layer by layer.

## 3. What are the benefits of using surfaces wrapped around a cylinder for 3d printing?

Surfaces wrapped around a cylinder for 3d printing can be used to create complex and intricate designs that cannot be achieved with traditional manufacturing methods. They also have a smooth and seamless finish, making them ideal for creating functional and aesthetically pleasing objects.

## 4. What materials can be used for 3d printing surfaces wrapped around a cylinder?

Many materials can be used for 3d printing surfaces wrapped around a cylinder, including plastics, metals, and even ceramics. The choice of material will depend on the specific requirements of the object being printed.

## 5. What are the limitations of 3d printing surfaces wrapped around a cylinder?

One limitation of 3d printing surfaces wrapped around a cylinder is the size of the object that can be printed. Most 3d printers have a limited build volume, which restricts the size of the object that can be printed. Additionally, certain designs may be difficult to print due to their complexity or lack of support structures.

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