Exploring Lissajous Curve in 3D: From 2D Shape to Real World Representation

  • Thread starter tejolson
  • Start date
  • Tags
    3d Curve
In summary, the Lissajous Curve is a 2d shape that can be represented in 3d. It has a different shape depending on how it is viewed, and it is already known.
  • #1
tejolson
8
0
I'm trying to figure out how to do a Lissajous Curve in 3d. It has a 2d shape in the real world, so if it's in the real world, then there must be a 3d shape to it.

Here is the crazy version, it has 8 variants of the last pic layered and it's at 45 45 0
attachment.php?attachmentid=58007&stc=1&d=1366341051.jpg


This is the one above and it is at 0 0 0
attachment.php?attachmentid=58008&stc=1&d=1366341051.jpg


Here is my version of that Lissajous by itself.
attachment.php?attachmentid=58009&stc=1&d=1366341051.jpg


There are a million different ways to make pretty shapes out of that curve, but I'm pretty sure there is only one way it can be represented in 3d if it is to represent a real world example.
 

Attachments

  • s 4, c 5.jpg
    s 4, c 5.jpg
    21.5 KB · Views: 1,306
  • s 4, c 5, top.jpg
    s 4, c 5, top.jpg
    18 KB · Views: 648
  • s 4, c 5, simple.jpg
    s 4, c 5, simple.jpg
    18.1 KB · Views: 943
Physics news on Phys.org
  • #2
tejolson said:
It has a 2d shape in the real world, so if it's in the real world, then there must be a 3d shape to it.

Why? Do you not believe in flat things? Yes, in the real world even a piece of thin paper has some thickness, so technically you are right, but I think you are carrying the concept to a point where it does not helpfully go.

... but I'm pretty sure there is only one way it can be represented in 3d if it is to represent a real world example.

Why? Why should it have ANY 3D representation?
 
  • #3
You're talking about a math function, I'm talking about something real. It is made with light. Some guy used two mirrors to make it. It's in 2d because it was viewed in 2d as it reflected off the wall. As I understand it there is a way to slow down light in a vacuum. Maybe I can see a 3d representation that way. But I'm thinking it won't work because a photon is to small to see?

It's a wave function that uses binomial distribution. From what I understand quantum physics uses probability, and binomial distribution is part of probability. So I'm thinking there is a connection and I want to understand it.


attachment.php?attachmentid=58024&stc=1&d=1366379070.jpg
 

Attachments

  • helment.jpg
    helment.jpg
    26.4 KB · Views: 702
Last edited:
  • #4
Yup, I'm right. Apparently there was an experiment done a long long time ago. A professor told me the 3d version of the x,z or y,z plane is itself a Lissajous figure. So that makes those figures above correct. Unfortunately this means this stuff is already known. And since it's already known then it's been done and it does not need to be redone. If anyone knows who did this experiment in 3D, I would very much like to know. The professor that talked to me was unsure about the details.
 
  • #5


I would like to clarify that a Lissajous Curve is a mathematical concept that represents the motion of a point moving in two perpendicular directions at the same time. It is commonly used in physics, engineering, and astronomy to study oscillations and vibrations.

When it comes to representing a Lissajous Curve in 3D, there are several ways to do so. One approach is to use the parametric equations that describe the curve in 2D and add a third dimension to it. This can be done by adding a third variable, such as time, to the equations.

Another approach is to use computer software to plot the curve in 3D space. This allows for more flexibility and creativity in the design of the curve. In fact, the examples provided in the content are most likely created using such software.

It is important to note that while a Lissajous Curve can be represented in 3D space, it is still a mathematical concept and does not have a physical shape in the real world. However, it can be used to model real-world phenomena, such as the motion of a pendulum or a vibrating string.

In conclusion, exploring Lissajous Curve in 3D can be a fascinating and creative endeavor, but it is important to understand that it is a mathematical concept and not a physical object in the real world.
 

What is a Lissajous Curve in 3D?

A Lissajous Curve in 3D is a three-dimensional representation of a mathematical curve formed by the intersection of two sinusoidal waves with different frequencies and phases. It is named after French mathematician Jules Antoine Lissajous.

How is a Lissajous Curve in 3D created?

A Lissajous Curve in 3D is created by plotting the x, y, and z coordinates of a point on a graph, where the x and y coordinates are determined by the amplitudes and frequencies of two sinusoidal waves, and the z coordinate is determined by a third sinusoidal wave with a different frequency and phase.

What are the applications of Lissajous Curve in 3D?

Lissajous Curve in 3D has many applications in science and engineering, such as in the study of oscillatory motion, electronic circuits, and acoustics. It is also commonly used in signal processing and data visualization.

What is the significance of the shape of a Lissajous Curve in 3D?

The shape of a Lissajous Curve in 3D is determined by the ratio of the frequencies and phases of the intersecting waves. This makes it a useful tool for analyzing and understanding the relationship between different harmonic motions.

Can a Lissajous Curve in 3D be projected onto a 2D plane?

Yes, a Lissajous Curve in 3D can be projected onto a 2D plane by fixing the value of the third wave and plotting the resulting 2D curve. This is commonly done in music visualizers and oscilloscopes to represent sound waves.

Similar threads

  • Sci-Fi Writing and World Building
Replies
1
Views
389
Replies
5
Views
334
  • Differential Geometry
Replies
5
Views
4K
  • Linear and Abstract Algebra
Replies
2
Views
869
  • Special and General Relativity
Replies
5
Views
1K
Replies
2
Views
1K
  • Science Fiction and Fantasy Media
Replies
0
Views
853
Replies
33
Views
22K
Replies
1
Views
743
Replies
2
Views
767
Back
Top