#hilbert-curve #hilbert #algorithm #curve

zhang_hilbert

Produces an arbitrary-sized pseudo-Hilbert scan based on “A Pseudo-Hilbert Scan for Arbitrarily-Sized Arrays” by Zhang, et al

2 releases

0.1.1 Feb 26, 2019
0.1.0 Feb 26, 2019

#1342 in Algorithms

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MIT/Apache

43KB
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zhang_hilbert

docs.rs

This crate provides iterator types that produce an arbitrary-sized pseudo-Hilbert scan based on “A Pseudo-Hilbert Scan for Arbitrarily-Sized Arrays” by Zhang, et al.

use zhang_hilbert::ArbHilbertScan32;
for [x, y] in ArbHilbertScan32::new([11, 42]) {
    assert!(x >= 0 && y >= 0 && x < 11 && y < 42);
    println!("{:?}", [x, y]);
}

Differences from the original algorithm

The last E_B(E, O) block

This implementation uses a different curve-type selection rule for the last E_B(E, O) block in a E_R(E, O) rectangle. This makes the leaving point fixed at a known point in more cases, making the output suitable for tiling.

cargo run --example hilbertgen -- -a zhang 6 7
  ,---, ,---,        ,---, ,---,
  '-, '-' ,-'        '-, '-' ,-'
  ,-' ,-, '-,        ,-' ,-, '-,
  '-, | '---'        '-, | '---'
  ,-' '-, ,--        ,-' '-----,
  '-, ,-' '-,        '-, ,-----'
  --' '-----'        --' '------
   Original      This implementation

cargo run --example hilbertgen -- -a zhang 4 3
    ,------           ,-----,
    '-----,           '-, ,-'
    ------'           --' '--
   Original      This implementation

Aspect-ratio bounded tiling

The algorithm accepts any rectangle size, but the output quality deteriorates as the proportions of the rectangle gets distant from square. ArbHilbertScanCore improves it by dividing the rectangle into multiple rectangles whose proportions are closer to square than the original rectangle is (thus their aspect ratios are bounded).

$ cargo run --example hilbertgen -- 40 7
,---, ,---, ,---, ,---, ,---, ,-, ,---, ,---, ,---, ,---, ,-, ,---, ,---, ,---,
'-, '-' ,-' '-, '-' ,-' '-, '-' '-' ,-' '-, '-' ,-' '-, '-' '-' ,-' '-, '-' ,-'
,-' ,-, '-, ,-' ,-, '-, ,-' ,-, ,-, '-, ,-' ,-, '-, ,-' ,-, ,-, '-, ,-' ,-, '-,
'-, | '---' '-, | '---' '---' | | '---' '-, | '---' '---' | | '---' '-, | '---'
,-' '-----, ,-' '-----, ,-----' '-----, ,-' '-----, ,-----' '-----, ,-' '-----,
'-, ,-----' '-, ,-----' '-----, ,-----' '-, ,-----' '-----, ,-----' '-, ,-----'
--' '---------' '-------------' '---------' '-------------' '---------' '------

$ cargo run --example hilbertgen -- -a zhang 40 7
,-----------------------, ,-, ,-, ,-, ,-, ,-, ,-, ,-, ,-, ,-, ,---------------,
'---------------------, '-' '-' '-' '-' '-' '-' '-' '-' '-' '-' ,-------------'
,---------------------' ,-, ,-, ,-, ,-, ,-, ,-, ,-, ,-, ,-, ,-, '-------------,
'-----------------------' '-' '-' '-' '-' '-' | | '-' '-' '-' '---------------'
,---------------------------------------------' '-----------------------------,
'---------------------------------------------, ,-----------------------------'
----------------------------------------------' '------------------------------

The division function

The division function was modified for efficient implementation. As a result, it produces an different output for the input 3⋅2ⁿ.

License: MIT/Apache-2.0

Dependencies

~480KB