<p>I have come across Signed Distance Field usage in Computer Graphics in construction of vector shapes, glyphs and 3D surfaces. However I can not find much of the background mathematical theory as to why it works, under what assumptions it can reconstruct the vectors at any resolution. Can someone point me to the right resources to understand the topic better?</p>

CC BY-SA 4.0
2022-02-11T13:42:24.480Z
He cites several papers: https://aras-p.info/blog/2017/02/15/Font-Rendering-is-Getting-Interesting/
lightxbulb
CC BY-SA 4.0
2022-02-11T14:44:39.060Z
While Aras thesis is good, it is not a nice introduction to the topic, especially mathematical foundation. If you know a particular resource that delves into the topic of *why signed distance fields work* from a mathematical perspective, that would be great.
Deepak Sharma
CC BY-SA 4.0
2022-02-11T23:23:09.580Z
I was referring to the paper he cites: https://steamcdn-a.akamaihd.net/apps/valve/2007/SIGGRAPH2007_AlphaTestedMagnification.pdf
Afaik this is where the idea was introduced. To put it simply the depth bits are used to further alleviate aliasing by storing a smooth transition instead of a hard aliased one. The smoothing acts as an atialiasing filter. Maybe there are other details but I am not an expert on sdf glyph rendering.
lightxbulb
<opengl><vectors><signed-distance-field><font-rendering><bsdf>
Mathematical foundations of Signed Distance Fields in computer graphics
Deepak Sharma
# Mathematical foundations of Signed Distance Fields in computer graphics

(Asked by: username_0 on 2022-02-11)

I have come across Signed Distance Field usage in Computer Graphics in construction of vector shapes, glyphs and 3D surfaces. However I can not find much of the background mathematical theory as to why it works, under what assumptions it can reconstruct the vectors at any resolution. Can someone point me to the right resources to understand the topic better?

**Tags:** opengl, vectors, signed-distance-field, font-rendering, bsdf

> **Comments:**
> **username_1**: He cites several papers: https://aras-p.info/blog/2017/02/15/Font-Rendering-is-Getting-Interesting/  
> **username_0**: While Aras thesis is good, it is not a nice introduction to the topic, especially mathematical foundation. If you know a particular resource that delves into the topic of *why signed distance fields work* from a mathematical perspective, that would be great.  
> **username_1**: I was referring to the paper he cites: https://steamcdn-a.akamaihd.net/apps/valve/2007/SIGGRAPH2007_AlphaTestedMagnification.pdf Afaik this is where the idea was introduced. To put it simply the depth bits are used to further alleviate aliasing by storing a smooth transition instead of a hard aliased one. The smoothing acts as an atialiasing filter. Maybe there are other details but I am not an expert on sdf glyph rendering.  

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