<p>In math, geometry and physics it is common practice to use the coordinates <span class="math-container">$(u,v)$</span> to represent an arbitrary parameterization, including those of a <a href="https://en.wikipedia.org/wiki/Surface_(mathematics)" rel="noreferrer">surface</a> in a 3d Euclidean space. Since the coordinates of the parameterisation might be arbitrary (it could be an angle, or a function of the Euclidean coordinates <span class="math-container">$(x,y,z)$</span>, or something else), it is helpful to distinguish them from the coordinates used to represent the wider Euclidean space in which the surface exists.</p>
<p>The <span class="math-container">$(u,v)$</span>-notation caught on in computer graphics for the same reason: it clarifies that the coordinates used to index into your texture do not necessarily align with the world space (or view space) coordinates <span class="math-container">$(x,y,z)$</span>, but is an index into a parameterisation of a surface in that space.</p>

CC BY-SA 4.0
2020-06-28T09:48:25.183Z
2020-06-28T13:19:58.030Z
2020-06-28T13:19:58.030Z
Jessica Hansen
<p>This is not a definitive answer, but it is generally accepted that <a href="https://en.wikipedia.org/wiki/Edwin_Catmull" rel="nofollow noreferrer">Ed Catmull</a> introduced Texture Mapping in his 1974 thesis, &quot;<a href="https://ia801307.us.archive.org/2/items/DTIC_ADA004968/DTIC_ADA004968.pdf" rel="nofollow noreferrer"><em>A SUBDIVISION ALGORITHM FOR COMPUTER DISPLAY OF CURVED SURFACES</em></a>&quot;</p>
<p>In that, he uses (U,V) to access the image data (see the page labeled 36 in the above)</p>
<blockquote>
<p>MAPPING<br>
Photographs, drawings, or any picture can be mapped onto bivariate patches. This
is one of the most interesting consequences of the patch splitting algorithm. It
gives a method for putting texture, drawings, or photographs onto surfaces....<br><br>
...If a photograph is scanned in at a resolution of x times y then every
element can be referenced by u·x and v·y where 0&lt;=u,v&lt;=1. In general, one could think of the intensity as a function l(u,v) where I references a picture.</p>
</blockquote>
<p>I believe this thesis also introduced the concept of the Z-Buffer (Page 32)</p>

CC BY-SA 4.0
2020-06-16T14:33:51.780Z
2020-07-01T09:29:54.890Z
2020-07-01T09:29:54.890Z
Simon F
<p>Is there some historical reason texture coordinates are often called UVs?</p>
<p>I get that vertex positions are x, y, z but even OpenGL has <code>TEXTURE_WRAP_S</code> and <code>TEXTURE_WRAP_T</code> and GLSL has aliases so if texture coord is in a <code>vec</code> you can access it with</p>
<pre><code>someVec.st
</code></pre>
<p>but not</p>
<pre><code>someVec.uv  (these would be the 3rd and 4th elements of the vector)
</code></pre>
<p>And yet pretty much every modeling package calls them UVs – <a href="https://https://knowledge.autodesk.com/support/maya/learn-explore/caas/CloudHelp/cloudhelp/2018/ENU/Maya-Modeling/files/GUID-73BF7546-3BF2-44F3-9192-15A024CEC173-htm.html#:%7E:text=The%20UV%20Editor%20lets%20you,in%20the%20Modeling%20menu%20set" rel="nofollow noreferrer">Maya</a>, <a href="https://docs.blender.org/manual/en/latest/editors/uv/index.html" rel="nofollow noreferrer">Blender</a>, <a href="https://docs.unity3d.com/Packages/com.unity.probuilder@4.0/manual/uv-editor.html" rel="nofollow noreferrer">Unity</a>, <a href="https://docs.unrealengine.com/en-US/Engine/Content/Types/StaticMeshes/HowTo/UVChannels/index.html" rel="nofollow noreferrer">Unreal</a>, <a href="https://knowledge.autodesk.com/support/3ds-max/learn-explore/caas/CloudHelp/cloudhelp/2017/ENU/3DSMax/files/GUID-A7CC32F5-40BE-4DE5-A364-05E7986D4BA5-htm.html" rel="nofollow noreferrer">3ds Max</a></p>
<p>Where does the term UVs come from?<br />
Is this a known part of computer graphics history or is the reason they are called UVs lost in pixels of cg time?</p>

CC BY-SA 4.0
2020-06-16T18:10:56.833Z
In mathematics and physics it's common practice to denote the standard spatial coordinates in 3D with $x,y,z$. Similarly, if you study surfaces (especially in differential geometry) people usually use $u,v$, or $s,t$, or $\alpha, \beta$ for the surface parametrisation. In CG $u,v$ seems to have stuck around, but those are simply variables used to describe the coordinates in texture space in this instance. If you want there to be no ambiguity you should call them texture coordinates.
lightxbulb
CC BY-SA 4.0
2020-06-17T01:25:32.717Z
Further reading: [UV mapping](https://en.wikipedia.org/wiki/UV_mapping). This concept is used in radar, too, to [map angular coordinates to a rectangular plane](https://www.mathworks.com/help/phased/ref/azel2uv.html#bs9sl0i-1).
zaen
<texture><geometry><uv-mapping>
Why are texture coordinates often called UVs?
samanthaj
# Why are texture coordinates often called UVs?

(Asked by: username_0 on 2020-06-16)

Is there some historical reason texture coordinates are often called UVs?

I get that vertex positions are x, y, z but even OpenGL has `TEXTURE_WRAP_S` and `TEXTURE_WRAP_T` and GLSL has aliases so if texture coord is in a `vec` you can access it with

```
someVec.st

```

but not

```
someVec.uv  (these would be the 3rd and 4th elements of the vector)

```

And yet pretty much every modeling package calls them UVs – [Maya](https://https://knowledge.autodesk.com/support/maya/learn-explore/caas/CloudHelp/cloudhelp/2018/ENU/Maya-Modeling/files/GUID-73BF7546-3BF2-44F3-9192-15A024CEC173-htm.html#:%7E:text=The%20UV%20Editor%20lets%20you,in%20the%20Modeling%20menu%20set), [Blender](https://docs.blender.org/manual/en/latest/editors/uv/index.html), [Unity](https://docs.unity3d.com/Packages/com.unity.probuilder@4.0/manual/uv-editor.html), [Unreal](https://docs.unrealengine.com/en-US/Engine/Content/Types/StaticMeshes/HowTo/UVChannels/index.html), [3ds Max](https://knowledge.autodesk.com/support/3ds-max/learn-explore/caas/CloudHelp/cloudhelp/2017/ENU/3DSMax/files/GUID-A7CC32F5-40BE-4DE5-A364-05E7986D4BA5-htm.html)

Where does the term UVs come from?  
Is this a known part of computer graphics history or is the reason they are called UVs lost in pixels of cg time?

**Tags:** texture, geometry, uv-mapping

> **Comments:**
> **username_1**: In mathematics and physics it's common practice to denote the standard spatial coordinates in 3D with $x,y,z$. Similarly, if you study surfaces (especially in differential geometry) people usually use $u,v$, or $s,t$, or $\alpha, \beta$ for the surface parametrisation. In CG $u,v$ seems to have stuck around, but those are simply variables used to describe the coordinates in texture space in this instance. If you want there to be no ambiguity you should call them texture coordinates.  
> **username_2**: Further reading: [UV mapping](https://en.wikipedia.org/wiki/UV_mapping). This concept is used in radar, too, to [map angular coordinates to a rectangular plane](https://www.mathworks.com/help/phased/ref/azel2uv.html#bs9sl0i-1).  

---

## 2 answers

### Answer by username_3 on 2020-06-28. Score: 7

In math, geometry and physics it is common practice to use the coordinates $(u,v)$ to represent an arbitrary parameterization, including those of a [surface](https://en.wikipedia.org/wiki/Surface_(mathematics)) in a 3d Euclidean space. Since the coordinates of the parameterisation might be arbitrary (it could be an angle, or a function of the Euclidean coordinates $(x,y,z)$, or something else), it is helpful to distinguish them from the coordinates used to represent the wider Euclidean space in which the surface exists.

The $(u,v)$-notation caught on in computer graphics for the same reason: it clarifies that the coordinates used to index into your texture do not necessarily align with the world space (or view space) coordinates $(x,y,z)$, but is an index into a parameterisation of a surface in that space.


---

### Answer by username_4 on 2020-06-16. Score: 6

This is not a definitive answer, but it is generally accepted that [Ed Catmull](https://en.wikipedia.org/wiki/Edwin_Catmull) introduced Texture Mapping in his 1974 thesis, "[*A SUBDIVISION ALGORITHM FOR COMPUTER DISPLAY OF CURVED SURFACES*](https://ia801307.us.archive.org/2/items/DTIC_ADA004968/DTIC_ADA004968.pdf)"

In that, he uses (U,V) to access the image data (see the page labeled 36 in the above)

> MAPPING  
> Photographs, drawings, or any picture can be mapped onto bivariate patches. This
> is one of the most interesting consequences of the patch splitting algorithm. It
> gives a method for putting texture, drawings, or photographs onto surfaces....  
>   
> ...If a photograph is scanned in at a resolution of x times y then every
> element can be referenced by u·x and v·y where 0<=u,v<=1. In general, one could think of the intensity as a function l(u,v) where I references a picture.

I believe this thesis also introduced the concept of the Z-Buffer (Page 32)


---

