Signed Distance Fields For all your rendering needs By Tristan Hume

Image credit: Warren Moore, Inigio Quilez, Tom Beddard

Contents — 2D distance fields — 3D distance fields — Fractals

Background: Antialiasing Image credit: Wikipedia

Standard Text Rasterization — Raster all glyphs to texture with antialiasing at all required sizes — Render quads with texture coordinates pointing into the atlas Has to render glyph for every size! This makes pinch-zooming and text in 3D worlds slow or blurry.

Signed Distance Fields (SDFs) — The distance to the nearest point on the object's boundary — Negative on the inside of the object

Rendering Text with SDFs — Apply a smooth step function in a shader — Can add outline/glow to text by modifying mapping — Same texture can look good at a variety of sizes

Text in 3D worlds — Size of text on screen can change rapidly, poor fit for glyph atlases — Detailed in a 2007 paper by Chris Green at Valve

Problem: Rounded Corners — If text is rendered much bigger than SDF texture, corners get rounded — Solution: fancy tricks with multiple distance fields — The msdfgen project on Github can do this for you

3D SDFs

Ray Marching Distance Fields — Allows you to quickly ray trace distance fields — Fast enough to run in real time on a GPU fragment shader — Step as far as the distance field tells you is safe — Can compute normals using numerical slope

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ClayBook: What did you just see? — World stored as a signed distance field in 586MB 3D SDF texture — Fluid simulation done on GPU produces SDF every frame — Shape morphing done simply by linearly interpolating distance fields — Tracing cones through distance field for antialiasing and soft shadows — Use distance field information to approximate ambient occlusion

Modeling — Can use functions to calculate distance field as required — Inigo Quilez has a handy page with tons of these formulas — Unlike a 3D texture, doesn't take tons of space and can be evaluated accurately at any point

Constructive Solid Geometry — Really easy to combine primitives into models — Just use math: min, max

SDF only fanciness

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3D Fractals! — People have figured out how to use derivatives of Mandelbrot-style iteration fractals as distance estimators. — Most famous are the Mandelbulb and Mandelbox

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The End