<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>

CC BY-SA 4.0
2021-11-21T15:34:36.693Z
2021-11-21T15:51:32.677Z
2021-11-21T15:51:32.677Z
Avatrin
<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>

CC BY-SA 4.0
2021-11-21T11:00:27.200Z
"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?
Avatrin
CC BY-SA 4.0
2021-11-21T14:09:19.433Z
@Avatrin Yeah, I do mean pure/theoretical physics.
hanugm
<datasets><applications>
Is there any simple example for volumetric data except from physics and medicine?
hanugm
# 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.  

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## 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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