--- title: A cautionary tale about continuity | daily.dev description: A developer building a solid modeling kernel encountered a subtle rendering bug while designing a cabin model: a sawtooth roof pattern appeared as a flat... canonical: https://daily.dev/posts/a-cautionary-tale-about-continuity-v0uiywcz9 twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: A cautionary tale about continuity | daily.dev og:description: A developer building a solid modeling kernel encountered a subtle rendering bug while designing a cabin model: a sawtooth roof pattern appeared as a flat... og:url: https://daily.dev/posts/a-cautionary-tale-about-continuity-v0uiywcz9 og:image: https://api.daily.dev/og/posts/v0UIywCz9.png og:image:alt: A cautionary tale about continuity 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. # A cautionary tale about continuity **[Matt Keeter](https://daily.dev/sources/mattkeeter)** · 3 min read · 0 upvotes · 0 comments ## Summary A developer building a solid modeling kernel encountered a subtle rendering bug while designing a cabin model: a sawtooth roof pattern appeared as a flat surface. The root cause was a jump discontinuity in the modulo operator used to create domain repetition. Because automatic differentiation returns undefined gradients at the discontinuity, surface normals were computed incorrectly, making shingles invisible. The fix involves constructing each tooth of the sawtooth wave using constructive solid geometry so that the field is continuous at the domain boundaries before applying domain repetition with modulo. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: --- Tags: [#graphics-programming](https://daily.dev/tags/graphics-programming) [View this post on daily.dev](https://daily.dev/posts/a-cautionary-tale-about-continuity-v0uiywcz9) ```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":"A cautionary tale about continuity","url":"https://daily.dev/posts/a-cautionary-tale-about-continuity-v0uiywcz9","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/a-cautionary-tale-about-continuity-v0uiywcz9"},"datePublished":"2026-03-31T12:29:58.055Z","dateModified":"2026-03-31T12:57:20.120Z","description":"A developer building a solid modeling kernel encountered a subtle rendering bug while designing a cabin model: a sawtooth roof pattern appeared as a flat...","image":"https://media.daily.dev/image/upload/s--2-1xRawN--/f_auto/v1722860399/public/Placeholder%2011","thumbnailUrl":"https://media.daily.dev/image/upload/s--2-1xRawN--/f_auto/v1722860399/public/Placeholder%2011","isAccessibleForFree":true,"articleSection":"Matt Keeter","inLanguage":"en","publisher":{"@type":"Organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180}},"author":{"@type":"Organization","name":"Matt Keeter","logo":"https://media.daily.dev/image/upload/logos/placeholder.jpg","url":"https://daily.dev/sources/mattkeeter"},"commentCount":0,"discussionUrl":"https://daily.dev/posts/a-cautionary-tale-about-continuity-v0uiywcz9","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":0},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"graphics-programming","timeRequired":"PT3M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"Matt Keeter","item":"https://daily.dev/sources/mattkeeter"},{"@type":"ListItem","position":3,"name":"A cautionary tale about continuity"}]} ```