---
_id: '9652'
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.
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.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Michael
  full_name: Dymond, Michael
  last_name: Dymond
- first_name: Vojtech
  full_name: Kaluza, Vojtech
  id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E
  last_name: Kaluza
  orcid: 0000-0002-2512-8698
citation:
  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>
  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>
  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.
  ista: Dymond M, Kaluza V. 2023. Highly irregular separated nets. Israel Journal
    of Mathematics. 253, 501–554.
  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>.
  short: M. Dymond, V. Kaluza, Israel Journal of Mathematics 253 (2023) 501–554.
date_created: 2021-07-14T07:01:28Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2023-08-14T11:26:34Z
day: '01'
ddc:
- '515'
- '516'
department:
- _id: UlWa
doi: 10.1007/s11856-022-2448-6
external_id:
  arxiv:
  - '1903.05923'
  isi:
  - '000904950300003'
file:
- access_level: open_access
  checksum: 6fa0a3207dd1d6467c309fd1bcc867d1
  content_type: application/pdf
  creator: vkaluza
  date_created: 2021-07-14T07:41:50Z
  date_updated: 2021-07-14T07:41:50Z
  file_id: '9653'
  file_name: separated_nets.pdf
  file_size: 900422
  relation: main_file
file_date_updated: 2021-07-14T07:41:50Z
has_accepted_license: '1'
intvolume: '       253'
isi: 1
keyword:
- Lipschitz
- bilipschitz
- bounded displacement
- modulus of continuity
- separated net
- non-realisable density
- Burago--Kleiner construction
language:
- iso: eng
month: '03'
oa: 1
oa_version: Submitted Version
page: 501-554
publication: Israel Journal of Mathematics
publication_identifier:
  eissn:
  - 1565-8511
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Highly irregular separated nets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 253
year: '2023'
...
---
_id: '12972'
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.
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.
article_processing_charge: No
article_type: original
author:
- first_name: Zhenyuan
  full_name: Liu, Zhenyuan
  id: 70f0d7cf-ae65-11ec-a14f-89dfc5505b19
  last_name: Liu
  orcid: 0000-0001-9200-5690
- first_name: Michael
  full_name: Piovarci, Michael
  id: 62E473F4-5C99-11EA-A40E-AF823DDC885E
  last_name: Piovarci
- first_name: Christian
  full_name: Hafner, Christian
  id: 400429CC-F248-11E8-B48F-1D18A9856A87
  last_name: Hafner
- first_name: Raphael
  full_name: Charrondiere, Raphael
  id: a3a24133-2cc7-11ec-be88-8ddaf6f464b1
  last_name: Charrondiere
- first_name: Bernd
  full_name: Bickel, Bernd
  id: 49876194-F248-11E8-B48F-1D18A9856A87
  last_name: Bickel
  orcid: 0000-0001-6511-9385
citation:
  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>
  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>'
  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.
  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.
  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>.
  short: Z. Liu, M. Piovarci, C. Hafner, R. Charrondiere, B. Bickel, Computer Graphics
    Forum 42 (2023) 397–409.
conference:
  end_date: 2023-05-12
  location: Saarbrucken, Germany
  name: 'EG: Eurographics'
  start_date: 2023-05-08
date_created: 2023-05-16T08:47:25Z
date_published: 2023-05-08T00:00:00Z
date_updated: 2023-08-01T14:47:05Z
day: '08'
ddc:
- '004'
department:
- _id: BeBi
doi: '10.1111/cgf.14770 '
ec_funded: 1
external_id:
  isi:
  - '001000062600033'
file:
- access_level: open_access
  checksum: 4c188c2be4745467a8790bbf5d6491aa
  content_type: application/pdf
  creator: mpiovarc
  date_created: 2023-05-16T08:28:37Z
  date_updated: 2023-05-16T08:28:37Z
  file_id: '12974'
  file_name: Zhenyuan2023.pdf
  file_size: 24003702
  relation: main_file
  success: 1
file_date_updated: 2023-05-16T08:28:37Z
has_accepted_license: '1'
intvolume: '        42'
isi: 1
issue: '2'
keyword:
- embroidery
- design
- directionality
- density
- image
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 397-409
project:
- _id: eb901961-77a9-11ec-83b8-f5c883a62027
  grant_number: M03319
  name: Perception-Aware Appearance Fabrication
- _id: 24F9549A-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '715767'
  name: 'MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and
    Modeling'
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 1467-8659
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: Directionality-aware design of embroidery patterns
tmp:
  image: /images/cc_by_nc_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 42
year: '2023'
...