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Singular Foliations for Knit Graph Design

Published: 13 July 2024 Publication History

Abstract

We build upon the stripes-based knit planning framework of [Mitra et al. 2023], and view the resultant stripe pattern through the lens of singular foliations. This perspective views the stripes, and thus the candidate course rows or wale columns, as integral curves of a vector field specified by the spinning form of [Knöppel et al. 2015]. We show how to tightly control the topological structure of this vector field with linear level set constraints, preventing helicing of any integral curve. Practically speaking, this obviates the stripe placement constraints of [Mitra et al. 2023] and allows for shifting and variation of the stripe frequency without introducing additional helices. En route, we make the first explicit algebraic characterization of spinning form level set structure within singular triangles, and replace the standard interpolant with an “effective” one that improves the robustness of knit graph generation. We also extend the model of [Mitra et al. 2023] to surfaces with genus, via a Morse-based cylindrical decomposition, and implement automatic singularity pairing on the resulting components.

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  • (2024)KODA: Knit-program Optimization by Dependency AnalysisProceedings of the 37th Annual ACM Symposium on User Interface Software and Technology10.1145/3654777.3676405(1-15)Online publication date: 13-Oct-2024

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cover image ACM Conferences
SIGGRAPH '24: ACM SIGGRAPH 2024 Conference Papers
July 2024
1106 pages
ISBN:9798400705250
DOI:10.1145/3641519
This work is licensed under a Creative Commons Attribution International 4.0 License.

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Published: 13 July 2024

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  1. computational knitting
  2. foliations

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  • (2024)KODA: Knit-program Optimization by Dependency AnalysisProceedings of the 37th Annual ACM Symposium on User Interface Software and Technology10.1145/3654777.3676405(1-15)Online publication date: 13-Oct-2024

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