--- title: Analytic Fog Rendering With Volumetric Primitives description: A deep-dive into analytic fog rendering using volumetric primitives with varying density. Covers the Beer-Lambert Law, heterogeneous volumes, and the... canonical: https://daily.dev/posts/analytic-fog-rendering-with-volumetric-primitives-d5urdkooj twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Analytic Fog Rendering With Volumetric Primitives | daily.dev og:description: A deep-dive into analytic fog rendering using volumetric primitives with varying density. Covers the Beer-Lambert Law, heterogeneous volumes, and the... og:url: https://daily.dev/posts/analytic-fog-rendering-with-volumetric-primitives-d5urdkooj og:image: https://api.daily.dev/og/posts/D5URDkOOj.png og:image:alt: Analytic Fog Rendering With Volumetric Primitives og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Analytic Fog Rendering With Volumetric Primitives **[Hacker News](https://daily.dev/sources/hn)** · 10 min read · 0 upvotes · 0 comments ## Summary A deep-dive into analytic fog rendering using volumetric primitives with varying density. Covers the Beer-Lambert Law, heterogeneous volumes, and the limitations of ray-marching. Derives closed-form antiderivatives for five radial density functions (linear, quadratic, quartic, spiky, and Gaussian) to compute transmittance along a ray without numerical integration. Includes GLSL-style code snippets for each function and links to a Shadertoy implementation. Also briefly discusses lighting hacks, particle system integration, and boolean CSG operations for fog-of-war effects. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Similar posts on daily.dev - [A series of tricks and techniques I learned doing tiny GLSL demos](https://daily.dev/posts/a-series-of-tricks-and-techniques-i-learned-doing-tiny-glsl-demos-hwkufqxor) · Hacker News · 0 upvotes · 0 comments --- Tags: [#game-development](https://daily.dev/tags/game-development), [#graphics-programming](https://daily.dev/tags/graphics-programming) [View this post on daily.dev](https://daily.dev/posts/analytic-fog-rendering-with-volumetric-primitives-d5urdkooj) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"Analytic Fog Rendering With Volumetric Primitives","url":"https://daily.dev/posts/analytic-fog-rendering-with-volumetric-primitives-d5urdkooj","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/analytic-fog-rendering-with-volumetric-primitives-d5urdkooj"},"datePublished":"2026-03-07T02:04:55.351Z","dateModified":"2026-03-07T02:05:34.656Z","description":"A deep-dive into analytic fog rendering using volumetric primitives with varying density. 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