[{"external_id":{"isi":["000904950300003"],"arxiv":["1903.05923"]},"status":"public","citation":{"short":"M. Dymond, V. Kaluza, Israel Journal of Mathematics 253 (2023) 501–554.","chicago":"Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” <i>Israel Journal of Mathematics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s11856-022-2448-6\">https://doi.org/10.1007/s11856-022-2448-6</a>.","ieee":"M. Dymond and V. Kaluza, “Highly irregular separated nets,” <i>Israel Journal of Mathematics</i>, vol. 253. Springer Nature, pp. 501–554, 2023.","apa":"Dymond, M., &#38; Kaluza, V. (2023). Highly irregular separated nets. <i>Israel Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11856-022-2448-6\">https://doi.org/10.1007/s11856-022-2448-6</a>","mla":"Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” <i>Israel Journal of Mathematics</i>, vol. 253, Springer Nature, 2023, pp. 501–54, doi:<a href=\"https://doi.org/10.1007/s11856-022-2448-6\">10.1007/s11856-022-2448-6</a>.","ista":"Dymond M, Kaluza V. 2023. Highly irregular separated nets. Israel Journal of Mathematics. 253, 501–554.","ama":"Dymond M, Kaluza V. Highly irregular separated nets. <i>Israel Journal of Mathematics</i>. 2023;253:501-554. doi:<a href=\"https://doi.org/10.1007/s11856-022-2448-6\">10.1007/s11856-022-2448-6</a>"},"intvolume":"       253","has_accepted_license":"1","oa":1,"publication_status":"published","ddc":["515","516"],"date_published":"2023-03-01T00:00:00Z","year":"2023","acknowledgement":"This work was done while both authors were employed at the University of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35.","_id":"9652","date_updated":"2023-08-14T11:26:34Z","abstract":[{"lang":"eng","text":"In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study weaker notions of equivalence of separated nets and demonstrate that such notions also give rise to distinct equivalence classes. Put differently, we find occurrences of particularly strong divergence of separated nets from the integer lattice. Our approach generalises that of Burago and Kleiner and McMullen which takes place largely in a continuous setting. Existence of irregular separated nets is verified via the existence of non-realisable density functions ρ:[0,1]d→(0,∞). In the present work we obtain stronger types of non-realisable densities."}],"month":"03","oa_version":"Submitted Version","type":"journal_article","page":"501-554","file_date_updated":"2021-07-14T07:41:50Z","date_created":"2021-07-14T07:01:28Z","volume":253,"language":[{"iso":"eng"}],"isi":1,"keyword":["Lipschitz","bilipschitz","bounded displacement","modulus of continuity","separated net","non-realisable density","Burago--Kleiner construction"],"publication_identifier":{"eissn":["1565-8511"]},"quality_controlled":"1","doi":"10.1007/s11856-022-2448-6","department":[{"_id":"UlWa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","article_processing_charge":"No","scopus_import":"1","article_type":"original","publication":"Israel Journal of Mathematics","file":[{"date_created":"2021-07-14T07:41:50Z","access_level":"open_access","date_updated":"2021-07-14T07:41:50Z","file_id":"9653","checksum":"6fa0a3207dd1d6467c309fd1bcc867d1","relation":"main_file","content_type":"application/pdf","file_size":900422,"creator":"vkaluza","file_name":"separated_nets.pdf"}],"day":"01","author":[{"full_name":"Dymond, Michael","first_name":"Michael","last_name":"Dymond"},{"last_name":"Kaluza","first_name":"Vojtech","id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","orcid":"0000-0002-2512-8698","full_name":"Kaluza, Vojtech"}],"arxiv":1,"title":"Highly irregular separated nets"},{"publication":"Computer Graphics Forum","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"article_type":"original","ec_funded":1,"article_processing_charge":"No","publisher":"Wiley","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"BeBi"}],"title":"Directionality-aware design of embroidery patterns","author":[{"first_name":"Zhenyuan","last_name":"Liu","full_name":"Liu, Zhenyuan","orcid":"0000-0001-9200-5690","id":"70f0d7cf-ae65-11ec-a14f-89dfc5505b19"},{"id":"62E473F4-5C99-11EA-A40E-AF823DDC885E","full_name":"Piovarci, Michael","first_name":"Michael","last_name":"Piovarci"},{"id":"400429CC-F248-11E8-B48F-1D18A9856A87","full_name":"Hafner, Christian","last_name":"Hafner","first_name":"Christian"},{"last_name":"Charrondiere","first_name":"Raphael","full_name":"Charrondiere, Raphael","id":"a3a24133-2cc7-11ec-be88-8ddaf6f464b1"},{"first_name":"Bernd","last_name":"Bickel","full_name":"Bickel, Bernd","id":"49876194-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6511-9385"}],"day":"08","file":[{"file_size":24003702,"content_type":"application/pdf","relation":"main_file","creator":"mpiovarc","file_name":"Zhenyuan2023.pdf","success":1,"date_created":"2023-05-16T08:28:37Z","access_level":"open_access","file_id":"12974","date_updated":"2023-05-16T08:28:37Z","checksum":"4c188c2be4745467a8790bbf5d6491aa"}],"keyword":["embroidery","design","directionality","density","image"],"conference":{"start_date":"2023-05-08","location":"Saarbrucken, Germany","name":"EG: Eurographics","end_date":"2023-05-12"},"isi":1,"issue":"2","language":[{"iso":"eng"}],"project":[{"grant_number":"M03319","name":"Perception-Aware Appearance Fabrication","_id":"eb901961-77a9-11ec-83b8-f5c883a62027"},{"_id":"24F9549A-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling","grant_number":"715767"}],"doi":"10.1111/cgf.14770 ","quality_controlled":"1","publication_identifier":{"issn":["1467-8659"]},"_id":"12972","acknowledgement":"This work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 715767 – MATERIALIZABLE), and FWF Lise Meitner (Grant M 3319). We thank the anonymous reviewers for their insightful feedback; Solal Pirelli, Shardul Chiplunkar, and Paola Mejia for proofreading; everyone in the visual computing group at ISTA for inspiring lunch and coffee breaks; Thibault Tricard for help producing the results of Phasor Noise.","year":"2023","volume":42,"date_created":"2023-05-16T08:47:25Z","file_date_updated":"2023-05-16T08:28:37Z","page":"397-409","type":"journal_article","oa_version":"Published Version","month":"05","abstract":[{"lang":"eng","text":"Embroidery is a long-standing and high-quality approach to making logos and images on textiles. Nowadays, it can also be performed via automated machines that weave threads with high spatial accuracy. A characteristic feature of the appearance of the threads is a high degree of anisotropy. The anisotropic behavior is caused by depositing thin but long strings of thread. As a result, the stitched patterns convey both color and direction. Artists leverage this anisotropic behavior to enhance pure color images with textures, illusions of motion, or depth cues. However, designing colorful embroidery patterns with prescribed directionality is a challenging task, one usually requiring an expert designer. In this work, we propose an interactive algorithm that generates machine-fabricable embroidery patterns from multi-chromatic images equipped with user-specified directionality fields.We cast the problem of finding a stitching pattern into vector theory. To find a suitable stitching pattern, we extract sources and sinks from the divergence field of the vector field extracted from the input and use them to trace streamlines. We further optimize the streamlines to guarantee a smooth and connected stitching pattern. The generated patterns approximate the color distribution constrained by the directionality field. To allow for further artistic control, the trade-off between color match and directionality match can be interactively explored via an intuitive slider. We showcase our approach by fabricating several embroidery paths."}],"date_updated":"2023-08-01T14:47:05Z","intvolume":"        42","citation":{"short":"Z. Liu, M. Piovarci, C. Hafner, R. Charrondiere, B. Bickel, Computer Graphics Forum 42 (2023) 397–409.","chicago":"Liu, Zhenyuan, Michael Piovarci, Christian Hafner, Raphael Charrondiere, and Bernd Bickel. “Directionality-Aware Design of Embroidery Patterns.” <i>Computer Graphics Forum</i>. Wiley, 2023. <a href=\"https://doi.org/10.1111/cgf.14770 \">https://doi.org/10.1111/cgf.14770 </a>.","ieee":"Z. Liu, M. Piovarci, C. Hafner, R. Charrondiere, and B. Bickel, “Directionality-aware design of embroidery patterns,” <i>Computer Graphics Forum</i>, vol. 42, no. 2. Wiley, pp. 397–409, 2023.","apa":"Liu, Z., Piovarci, M., Hafner, C., Charrondiere, R., &#38; Bickel, B. (2023). Directionality-aware design of embroidery patterns. <i>Computer Graphics Forum</i>. Saarbrucken, Germany: Wiley. <a href=\"https://doi.org/10.1111/cgf.14770 \">https://doi.org/10.1111/cgf.14770 </a>","mla":"Liu, Zhenyuan, et al. “Directionality-Aware Design of Embroidery Patterns.” <i>Computer Graphics Forum</i>, vol. 42, no. 2, Wiley, 2023, pp. 397–409, doi:<a href=\"https://doi.org/10.1111/cgf.14770 \">10.1111/cgf.14770 </a>.","ista":"Liu Z, Piovarci M, Hafner C, Charrondiere R, Bickel B. 2023. Directionality-aware design of embroidery patterns. Computer Graphics Forum. 42(2), 397–409.","ama":"Liu Z, Piovarci M, Hafner C, Charrondiere R, Bickel B. Directionality-aware design of embroidery patterns. <i>Computer Graphics Forum</i>. 2023;42(2):397-409. doi:<a href=\"https://doi.org/10.1111/cgf.14770 \">10.1111/cgf.14770 </a>"},"status":"public","external_id":{"isi":["001000062600033"]},"date_published":"2023-05-08T00:00:00Z","ddc":["004"],"publication_status":"published","oa":1,"has_accepted_license":"1"}]