.png){kind=icon}
.png){kind=icon}
Return
Weaving Geodesic Foliations
.png){kind=icon}
PRE
AI
DOI：10.1145/3306346.3323043.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We study discrete geodesic foliations of surfaces-foliations whose leaves are all approximately geodesic curves-and develop several new variational algorithms for computing such foliations. Our key insight is a relaxation of vector field integrability in the discrete setting, which allows us to optimize for curl-free unit vector fields that remain well-defined near singularities and robustly recover a scalar function whose gradient is well aligned to these fields. We then connect the physics governing surfaces woven out of thin ribbons to the geometry of geodesic foliations, and present a design and fabrication pipeline for approximating surfaces of arbitrary geometry and topology by triaxially-woven structures, where the ribbon layout is determined by a geodesic foliation on a sixfold branched cover of the input surface. We validate the effectiveness of our pipeline on a variety of simulated and fabricated woven designs, including an example for readers to try at home.
Keywords:
Discrete Differential Geometry
Vector Field Design
Digital Fabrication
Texture Synthesis
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
9.5
Papers:
4.7K
Citations:
3.6W