fermat curves
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2021 ◽  
Vol 225 (1) ◽  
pp. 106465
Author(s):  
Yerko Torres-Nova
Keyword(s):  


2020 ◽  
Vol 217 ◽  
pp. 78-101
Author(s):  
Rubén A. Hidalgo
Keyword(s):  


2020 ◽  
Vol 71 (4) ◽  
pp. 1377-1417
Author(s):  
Aristides Kontogeorgis ◽  
Panagiotis Paramantzoglou

Abstract The fundamental group of Fermat and generalized Fermat curves is computed. These curves are Galois ramified covers of the projective line with abelian Galois groups H. We provide a unified study of the action of both cover Galois group H and the absolute Galois group $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ on the pro-$\ell$ homology of the curves in study. Also the relation to the pro-$\ell$ Burau representation is investigated.



Author(s):  
Payman Eskandari ◽  
Vijaya Kumar Murty
Keyword(s):  


Author(s):  
Hongrui Chen ◽  
Xingchen Liu

Abstract The slicing software process the 3D geometry into 2D slices and toolpaths for additive manufacturing processes. Most slicing software allows users to select from an array of infill patterns and to specify the overall infill volume fraction globally. However, the ability to locally control the volume fraction, and mechanical properties, is often limited. In this paper, we propose a novel toolpath enhancing algorithm to enable the local control on the volume fraction of various stock and custom infill patterns. In particular, the algorithm widens the infill pattern by directly modifying their toolpath with connected Fermat curves. By preserving the topology of the original toolpath, the connected Fermat curve not only produces predictable boosts in part performance but also minimized the printing time by eliminating extruder traversals without material deposition. The field that controls local volume fraction can be designed either manually or through optimization. The effectiveness of the proposed approach in toolpath generation is demonstrated through volume fraction fields designed by both approaches.





2020 ◽  
Vol 224 (1) ◽  
pp. 239-249 ◽  
Author(s):  
Herivelto Borges ◽  
Mariana Coutinho


2019 ◽  
Vol 14 (1) ◽  
pp. 45-67 ◽  
Author(s):  
Thierry Dana-Picard ◽  
Aharon Naiman ◽  
Witold Mozgawa ◽  
Waldemar Cieślak
Keyword(s):  


2019 ◽  
Vol 223 (7) ◽  
pp. 3057-3070
Author(s):  
Rubén A. Hidalgo ◽  
Maximiliano Leyton-Álvarez
Keyword(s):  


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