Answers.Body: <p>Whenever a system is being modelled in three dimensions, you can be sure that tensors either can or are being used. Most of the systems I can think of are either simulated volumetric data, or a combination of real measurements and interpolated values.</p>
  <h2>CAD and BIM</h2>
  <p>Computer-Aided Design, or CAD, if quite commonly used in engineering. It's quite natural that, if they are modelling a mechanical system, that they need information regarding the materials they are considering to use to make the device; A little bit of googling showed that <a href="https://knowledge.autodesk.com/support/inventor/learn-explore/caas/sfdcarticles/sfdcarticles/What-are-differences-between-Inertia-Tensor-and-Area-Moments-of-Inertia-with-respect-to-principal-Axes-in-Inventor-Region-Properties.html" rel="nofollow noreferrer">Autodesks Inventor computes inertia tensors</a> and their <a href="https://knowledge.autodesk.com/search-result/caas/CloudHelp/cloudhelp/2017/ENU/SimMech-UsersGuide/files/GUID-E2ADA0DB-37FE-487E-ABFC-02A7286DC6F6-htm.html" rel="nofollow noreferrer">mechanical simulation software computes stress tensors</a>.</p>
  <p>BIM is essentially CAD for the construction industry, but again, a lot of the same kind of information regarding the materials used is needed; Else, the building may collapse.</p>
  <h2>Geology</h2>
  <p>Modelling the stability of soil to construct a skyscraper may require 3D data. There is an <a href="https://gis.stackexchange.com/questions/15876/3d-subsurface-modelling">old question at gis.stackexchange</a> discussing software used to model geological systems. Of those, <a href="https://www.aquaveo.com/software/gms-groundwater-modeling-system-introduction" rel="nofollow noreferrer">this one</a> and <a href="http://www.petrosys.com.au/products-services/surface-modeling-volumetrics/" rel="nofollow noreferrer">this other one</a> still seems to be up.</p>
  <h2>Meteorology</h2>
  <p>Most meteorological data, to the best of my knowledge, is two-dimensional. However, weather radar can be used to extract 3D data with information about precipitation and motion.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-11-21T15:34:36.693Z
Answers.LastActivityDate: 2021-11-21T15:51:32.677Z
Answers.LastEditDate: 2021-11-21T15:51:32.677Z
Answers.UserDisplayName: Avatrin
Body: <p>Recently I heard about the term volumetric data. The definition for volumetric data is as follows</p>
  <p>#1: <a href="https://www.sciencedirect.com/topics/computer-science/volumetric-data" rel="nofollow noreferrer">Definition</a></p>
  <blockquote>
  <p>Volumetric data is typically a set S of samples <span class="math-container">$(x, y, z, v)$</span>,
  representing the value v of some property of the data, at a 3D
  location <span class="math-container">$(x, y, z)$</span>. If the value is simply a 0 or a 1, with a value
  of 0 indicating background and a value of 1 indicating the object,
  then the data is referred to as binary data. The data may instead be
  multivalued, with the value representing some measurable property of
  the data, including, for example, color, density, heat, or pressure.</p>
  </blockquote>
  <p>#2: <a href="https://www.sciencedirect.com/topics/computer-science/volumetric-dataset" rel="nofollow noreferrer">Some more details</a></p>
  <blockquote>
  <p>A volumetric dataset consists of information at sample locations in
  some space. The information may be a scalar (such as density in a
  computed tomography (CT) scan), a vector (such as velocity in a flow
  field), or a higher-order tensor (such as energy, density, and
  momentum in computational fluid dynamics (CFD)). The space is usually
  3D, consisting of either three spatial dimensions or another
  combination of spatial and frequency dimensions.</p>
  </blockquote>
  <p>In simple words, I can say that volumetric data is nothing but a three-dimensional collection of tensors.</p>
  <p>The articles linked above contain some examples of volumetric data in the medical (and probably physics) domain.</p>
  <p>Are there any other simple real-world examples for volumetric data other than the medical and physics domain and physics?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-11-21T11:00:27.200Z
Comments.Text: "Physics" is quite broad... That eliminates several engineering applications I can think of. However, you mention medicine, where it's mostly used by biophysicists, so by physics, do you mean pure/theoretical physics?
Comments.UserDisplayName: Avatrin
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-11-21T14:09:19.433Z
Comments.Text: @Avatrin Yeah, I do mean pure/theoretical physics.
Comments.UserDisplayName: hanugm
Tags: <datasets><applications>
Title: Is there any simple example for volumetric data except from physics and medicine?
UserDisplayName: hanugm
ThreadText: # Is there any simple example for volumetric data except from physics and medicine?
  
  (Asked by: username_0 on 2021-11-19)
  
  Recently I heard about the term volumetric data. The definition for volumetric data is as follows
  
  #1: [Definition](https://www.sciencedirect.com/topics/computer-science/volumetric-data)
  
  > Volumetric data is typically a set S of samples $(x, y, z, v)$,
  > representing the value v of some property of the data, at a 3D
  > location $(x, y, z)$. If the value is simply a 0 or a 1, with a value
  > of 0 indicating background and a value of 1 indicating the object,
  > then the data is referred to as binary data. The data may instead be
  > multivalued, with the value representing some measurable property of
  > the data, including, for example, color, density, heat, or pressure.
  
  #2: [Some more details](https://www.sciencedirect.com/topics/computer-science/volumetric-dataset)
  
  > A volumetric dataset consists of information at sample locations in
  > some space. The information may be a scalar (such as density in a
  > computed tomography (CT) scan), a vector (such as velocity in a flow
  > field), or a higher-order tensor (such as energy, density, and
  > momentum in computational fluid dynamics (CFD)). The space is usually
  > 3D, consisting of either three spatial dimensions or another
  > combination of spatial and frequency dimensions.
  
  In simple words, I can say that volumetric data is nothing but a three-dimensional collection of tensors.
  
  The articles linked above contain some examples of volumetric data in the medical (and probably physics) domain.
  
  Are there any other simple real-world examples for volumetric data other than the medical and physics domain and physics?
  
  **Tags:** datasets, applications
  
  > **Comments:**
  > **username_1**: "Physics" is quite broad... That eliminates several engineering applications I can think of. However, you mention medicine, where it's mostly used by biophysicists, so by physics, do you mean pure/theoretical physics?  
  > **username_0**: @username_1 Yeah, I do mean pure/theoretical physics.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2021-11-21. Score: 1
  
  Whenever a system is being modelled in three dimensions, you can be sure that tensors either can or are being used. Most of the systems I can think of are either simulated volumetric data, or a combination of real measurements and interpolated values.
  
  ## CAD and BIM
  
  Computer-Aided Design, or CAD, if quite commonly used in engineering. It's quite natural that, if they are modelling a mechanical system, that they need information regarding the materials they are considering to use to make the device; A little bit of googling showed that [Autodesks Inventor computes inertia tensors](https://knowledge.autodesk.com/support/inventor/learn-explore/caas/sfdcarticles/sfdcarticles/What-are-differences-between-Inertia-Tensor-and-Area-Moments-of-Inertia-with-respect-to-principal-Axes-in-Inventor-Region-Properties.html) and their [mechanical simulation software computes stress tensors](https://knowledge.autodesk.com/search-result/caas/CloudHelp/cloudhelp/2017/ENU/SimMech-UsersGuide/files/GUID-E2ADA0DB-37FE-487E-ABFC-02A7286DC6F6-htm.html).
  
  BIM is essentially CAD for the construction industry, but again, a lot of the same kind of information regarding the materials used is needed; Else, the building may collapse.
  
  ## Geology
  
  Modelling the stability of soil to construct a skyscraper may require 3D data. There is an [old question at gis.stackexchange](https://gis.stackexchange.com/questions/15876/3d-subsurface-modelling) discussing software used to model geological systems. Of those, [this one](https://www.aquaveo.com/software/gms-groundwater-modeling-system-introduction) and [this other one](http://www.petrosys.com.au/products-services/surface-modeling-volumetrics/) still seems to be up.
  
  ## Meteorology
  
  Most meteorological data, to the best of my knowledge, is two-dimensional. However, weather radar can be used to extract 3D data with information about precipitation and motion.
  
  
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