Improving Curl Noise

J. Andreas Bærentzen; Jonàs Martínez; Jeppe Revall Frisvad; Sylvain Lefebvre

doi:10.1145/3757377.3763980

Improving Curl Noise

J. Andreas Bærentzen, Jonàs Martínez, Jeppe Revall Frisvad, Sylvain Lefebvre

Université de Lorraine

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Abstract

We introduce a divergence-free 𝑛D vector noise defined as the 𝑛-dimensional cross product of the gradients of 𝑛 − 1 noise functions. We show that this vector noise function is divergence-free and hence volume preserving for any dimension 𝑛. Our method enables precise integration and extends to new settings by substituting noise functions with implicit surfaces, (hyper)surfaces, or custom functions. We demonstrate applications including image warping, surface texturing, noise bounded by implicit surfaces, anisotropic curl-noise, and high-dimensional point jittering up to 7D

Original language	English
Title of host publication	Proceedings of the The 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia (SA 2025)
Number of pages	10
Publisher	Association for Computing Machinery
ISBN (Electronic)	979-8-4007-2137-3/25/12
DOIs	https://doi.org/10.1145/3757377.3763980
Publication status	Accepted/In press - 2025
Event	The 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia - Hong Kong, Hong Kong Duration: 15 Dec 2025 → 18 Dec 2025

Conference

Conference	The 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia
Country/Territory	Hong Kong
City	Hong Kong
Period	15/12/2025 → 18/12/2025

Keywords

Procedural noise
Curl noise
Divergencefree
Vector fields

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10.1145/3757377.3763980Licence: CC BY

FulltextAccepted author manuscript, 51 MBLicence: CC BY

Cite this

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title = "Improving Curl Noise",

abstract = "We introduce a divergence-free 𝑛D vector noise defined as the 𝑛-dimensional cross product of the gradients of 𝑛 − 1 noise functions. We show that this vector noise function is divergence-free and hence volume preserving for any dimension 𝑛. Our method enables precise integration and extends to new settings by substituting noise functions with implicit surfaces, (hyper)surfaces, or custom functions. We demonstrate applications including image warping, surface texturing, noise bounded by implicit surfaces, anisotropic curl-noise, and high-dimensional point jittering up to 7D",

keywords = "Procedural noise, Curl noise, Divergencefree, Vector fields",

author = "B{\ae}rentzen, \{J. Andreas\} and Jon{\`a}s Mart{\'i}nez and Frisvad, \{Jeppe Revall\} and Sylvain Lefebvre",

year = "2025",

doi = "10.1145/3757377.3763980",

language = "English",

booktitle = "Proceedings of the The 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia (SA 2025)",

publisher = "Association for Computing Machinery",

address = "United States",

note = "The 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia, SIGGRAPH ; Conference date: 15-12-2025 Through 18-12-2025",

}

Bærentzen, JA, Martínez, J, Frisvad, JR & Lefebvre, S 2025, Improving Curl Noise. in Proceedings of the The 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia (SA 2025). Association for Computing Machinery, The 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia, Hong Kong, Hong Kong, 15/12/2025. https://doi.org/10.1145/3757377.3763980

Improving Curl Noise. / Bærentzen, J. Andreas; Martínez, Jonàs; Frisvad, Jeppe Revall et al.
Proceedings of the The 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia (SA 2025). Association for Computing Machinery, 2025.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Improving Curl Noise

AU - Bærentzen, J. Andreas

AU - Martínez, Jonàs

AU - Frisvad, Jeppe Revall

AU - Lefebvre, Sylvain

PY - 2025

Y1 - 2025

N2 - We introduce a divergence-free 𝑛D vector noise defined as the 𝑛-dimensional cross product of the gradients of 𝑛 − 1 noise functions. We show that this vector noise function is divergence-free and hence volume preserving for any dimension 𝑛. Our method enables precise integration and extends to new settings by substituting noise functions with implicit surfaces, (hyper)surfaces, or custom functions. We demonstrate applications including image warping, surface texturing, noise bounded by implicit surfaces, anisotropic curl-noise, and high-dimensional point jittering up to 7D

AB - We introduce a divergence-free 𝑛D vector noise defined as the 𝑛-dimensional cross product of the gradients of 𝑛 − 1 noise functions. We show that this vector noise function is divergence-free and hence volume preserving for any dimension 𝑛. Our method enables precise integration and extends to new settings by substituting noise functions with implicit surfaces, (hyper)surfaces, or custom functions. We demonstrate applications including image warping, surface texturing, noise bounded by implicit surfaces, anisotropic curl-noise, and high-dimensional point jittering up to 7D

KW - Procedural noise

KW - Curl noise

KW - Divergencefree

KW - Vector fields

U2 - 10.1145/3757377.3763980

DO - 10.1145/3757377.3763980

M3 - Article in proceedings

BT - Proceedings of the The 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia (SA 2025)

PB - Association for Computing Machinery

T2 - The 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia

Y2 - 15 December 2025 through 18 December 2025

ER -

Improving Curl Noise

Abstract

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Keywords

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