https://github.com/jokergoo/sfcurve

2x2, 3x3 and nxn Space-Filling Curves
https://github.com/jokergoo/sfcurve

Last synced: 3 months ago
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2x2, 3x3 and nxn Space-Filling Curves

• Host: GitHub
• URL: https://github.com/jokergoo/sfcurve
• Owner: jokergoo
• License: other
• Created: 2024-07-04T14:52:33.000Z (6 months ago)
• Default Branch: master
• Last Pushed: 2024-09-17T10:24:33.000Z (4 months ago)
• Last Synced: 2024-09-19T16:40:14.026Z (3 months ago)
• Language: R
• Homepage: https://jokergoo.github.io/sfcurve/
• Size: 50.8 MB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: docs/readme.html
  • Changelog: NEWS
  • License: LICENSE

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README

        

sfcurve: 2x2, 3x3 and nxn Space-Filling Curves • sfcurve

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    sfcurve


    1.0.0

    

    

      

    

    


      




  Articles

  


    1. 2x2 space-Filling Curve

    2. 3x3 Peano Curve

    3. 3x3 Meander Curve

    4. Unit flipping

    5. Standard curves

    6. Shapes

    7. General 3x3 Curves

    8. 4x4 Meander Curve

    9. General nxn Curves

    10. H-Curve

    11. 3D Hilbert curve

    12. Locality of various curves

  





  Functions/Classes





  Reference



      

        


      




  

    

     

  



      



    

  





  


      
sfcurve: 2x2, 3x3 and nxn Space-Filling Curves

      Source: readme.md

    






This package provides a way to encode all possible forms of 2x2 and 3x3 space-filling curves. For example, the following eight forms correspond to the 2x2 curve on level 3 and with R(0) (bottom-in right-out base pattern with rotation of 0 degree) as the seed.



It also supports nxn curves expanded from any valid level-1 unit.



Install




devtools::install_github("jokergoo/sfcurve")





Usage



Hilbert curve (2x2):

> sfc_2x2("I", "111")

An sfc_2x2 object.

  Increase mode: 2 x 2

  Level: 3

  Expansion rule: 2x2


A sequence of 64 base patterns.

  R(0)L(270)L(0)R(90)     I(0)R(0)R(270)L(180)

  L(270)R(0)R(270)I(180)  R(180)L(90)L(180)I(270)

  .... other 4 lines ....

  I(90)L(90)L(180)R(270)  I(180)R(180)R(90)L(0)

  L(90)R(180)R(90)I(0)    R(0)L(270)L(0)R(90)

Seed: A sequence of 1 base pattern.

  I(0)

Peano curve (3x3):

> sfc_3x3_peano("I", "111")

An sfc_3x3_peano object.

  Increase mode: 3 x 3

  Level: 3

  Expansion rule: 3x3 Peano


A sequence of 729 base patterns.

  I(0)J(0)R(0)R(270)  I(180)L(180)L(270)J(0)

  I(0)J(0)I(0)L(0)    L(90)J(180)R(180)R(90)

  .... other 88 lines ....

  I(0)J(0)R(0)R(270)  I(180)L(180)L(270)J(0)

  I(0)

Seed: A sequence of 1 base pattern.

  I(0)

Meander curve (3x3):

> sfc_3x3_meander("I", "111")

An sfc_3x3_meander object.

  Increase mode: 3 x 3

  Level: 3

  Expansion rule: 3x3 Meander


A sequence of 729 base patterns.

  R(0)I(270)L(270)I(0)  L(0)L(90)R(180)R(90)

  I(0)R(0)I(270)L(270)  I(0)L(0)L(90)R(180)

  .... other 88 lines ....

  R(0)I(270)L(270)I(0)  L(0)L(90)R(180)R(90)

  I(0)

Seed: A sequence of 1 base pattern.

  I(0)

It also allows using a sequence as the seed:

p = sfc_seed("LLLILILIILIILIIILIIILIIII")

p2 = sfc_2x2(p, "1111")

plot(p2)



For more comprehensive introduction of the theory and the package, please refer to the vignettes.





License



MIT @ Zuguang Gu





  
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Developed by Zuguang Gu.





  
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