How Can a 3D Pipe Be Unwrapped into a 2D Topology?

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Discussion Overview

The discussion revolves around the challenge of unwrapping a 3D geometry of a pipe into a 2D representation. Participants explore methods for achieving this transformation, considering both regular and irregular geometries, and discuss the implications of different coordinate systems and mapping techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about methods to represent a 3D pipe defined by triangular surfaces in a 2D plane, suggesting a potential mapping approach.
  • Another participant proposes a method involving the identification of a central axis and the use of polar coordinates to convert points from 3D to 2D, specifically using the radius and angle of points relative to the coordinate system.
  • A different participant questions the applicability of the proposed method to irregular geometries, such as the carotid artery, and suggests that polar coordinates might be useful in this context.
  • Another response discusses the possibility of unwrapping irregular geometries by taking z-slices along the profile, emphasizing the need to store 3D coordinate transformations for each slice to maintain accuracy.
  • This participant also raises the idea that unwrapping may not reduce information for irregular shapes, suggesting that remaining in 3D could be simpler, especially for geometries like square ducts that have bends.

Areas of Agreement / Disagreement

Participants express varying opinions on the feasibility and methods of unwrapping both regular and irregular geometries. There is no consensus on the best approach, and the discussion remains open to multiple interpretations and techniques.

Contextual Notes

Some limitations include the assumptions made about the geometries involved and the potential complexity of storing information for irregular shapes. The discussion does not resolve the mathematical steps necessary for the transformation.

kyze
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Hi,

I am not very strong in maths, so sorry if these sounds simple. If I have a 3D geometry of a pipe which has its surface defined by triangles (such as that in Computational Fluid Dynamics or Finite Element Analysis) and I have the coordinate points for all the triangles, how can I represent the 3D object into a 2D plane.
This would be like slicing the pipe through its centre and then unwrapping it into a flat piece. Would I use some kind of mapping? Is this achievable?

Thanks!
 
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Hey kyze,

It is possible. The general way to go about it is to find a central axis of the pipe, assign an X,Y,Z coordinate system with Z along the length of the pipe. Then the conversion to flat is based on the radius of the point (vector from 0,0 to point) and the angle (in the form of total circumference).

So for a point (X,Y,Z), the flat layout would be [(theta*2*PI*radius), Z] where theta is the angle of the vector relative to your coordinate system.
 
Thanks athuss. Great idea. I guess it could also work for a square duct with a bend also? But this all leads to a final geometry which is absolutely irregular, say the carotid blood artery that need to be unwrapped. So do you think applying polar coordinates would work?
 
I guess you could unwrap an irregular geometry. And I'd say the steps that I would take is to take z-slices along the profile, where the z plane is normal to the axis. And the axis is defined by the 'center point' (found by taking the average of the points in X-Y).

But to make at any of the found 2D points valid you'd have to store a 3D coordinate transform (from say, world to your assigned) for each z-slice. Not sure what the final intent is, but unwrapping a pipe to 2D works to decrease the total information by setting the seam as an axis. In irregular geometry you can't make that assumption and need to store just as much information so staying in 3D might just be the simplest way to go? A square duct is halfway in between, but you would still need to have a packet of information to describe the bend - sort of like 2.5D?
 

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