hilbert curve algorithm - Search
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  1. Wikipedia
    https://en.wikipedia.org/wiki/Hilbert_curve

    Hilbert curve - Wikipedia

    • The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890. Because it is space-filling, its Hausdorff dimension is 2 (precisely, its image is the unit square, whose di… See more

    Applications and mapping algorithms

    Both the true Hilbert curve and its discrete approximations are useful because they give a mapping between 1D … See more

    Representation as Lindenmayer system

    The Hilbert Curve can be expressed by a rewrite system (L-system).
    Alphabet : A, B Constants : F + − Axiom : A Production rules: A → +BF−AFA−FB+ B → −AF+BFB+FA−
    Here, "F" m… See more

    Other implementations

    Graphics Gems II discusses Hilbert curve coherency, and provides implementation.
    The Hilbert Curve is commonly used among rendering images or videos. Common programs such as Blender and Cinema 4D use … See more

    Algorithmic - Hilbert Curve: Concepts & Implementation
    We will begin by looking at the inputs of the Hilbert function. In addition to the counter (n) that tracks the level from which the function begins to recursively call itself, there are six other inputs to …
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    Table of Contents
    Applications and mapping algorithms
    Representation as Lindenmayer system
    Other implementations
    See also
     

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  2. In principle, the method to construct a Hilbert curve is as follows: Choose a base shape h 0 (i), 0 ≤ i < 8 that fills a 2x2x2 space (this is the first iteration) Find a table of rotations R so that a 2x2x2 block h 1 (j) of h 0 (i) resembles h 0 (i) at a coarser level Use R to rotate shapes h 0 so they form one continuous curve

    3D Hilbert Curves - GitHub Pages

    eisenwave.github.io/voxel-compression-docs/rle/hil…
    procedure hilbert(x, y, xi, xj, yi, yj, n)/* x and y are the coordinates of the bottom left corner */ /* xi & xj are the i & j components of the unit x vector of the frame */ /* similarly yi and yj */if(n <= 0) then LineTo(x + (xi + yi)/2, y + (xj + yj)/2);else{ hilbert(x, y, yi/2, yj/2, xi/2, xj/2, n-1);

    Algorithmic - Hilbert Curve: Concepts & I…

    www.fundza.com/algorithmic/space_filling/hilbert/b…
     
  3. People also ask
    What is the Hilbert curve?
    Thus begins my latest column in American Scientist, now available in HTML or PDF. The leading actor in this story is the Hilbert curve, which illustrates Cantor’s shocking discovery by leaping out of the one-dimensional universe and filling up a two-dimensional area.

    Mapping the Hilbert curve - bit-player

    bit-player.org
    How are Hilbert curve nodal points derived?
    A simple algorithm for the generation of the nodal points of the Hilbert curve has also been derived by Sagan , though when these points are linked they produce only approximating polygons that are not a “true” representation of the Hilbert curve.

    Algorithm 781: Generating Hilbert’s Space-Filling Curve by Recursion

    dl.acm.org
    Is there a nonrecursive algorithm for Hilbert's space-filling curve?
    A rather opaque description of a nonrecursive algorithm by Butz ("Alternative Algorithm for Hilbert's Space-Filling Curve", IEEE Trans. Comp., April, 1971, pp 424-426) led to an implementation by Spencer Thomas that appeared in Graphics Gems and has been widely circulated on the net.

    GitHub - adishavit/hilbert: Doug Moore's Fast Hilbert Curve Generation

    github.com
    How does a Hilbert curve preserve locality?
    The Hilbert curve maintains locality preservation by constructing itself in a recursive manner, ensuring that points that are adjacent in the one-dimensional line remain close together in the two-dimensional grid. As the curve fills the space, it connects nearby points through its fractal pattern, effectively grouping spatially related data.

    Hilbert Curve - (Computational Geometry) - Vocab, Definition ... - Fiveable

    library.fiveable.me
    How can Hilbert curves improve performance in spatial data structures?
    Hilbert curves can significantly improve performance in spatial data structures by minimizing the distance between related points, which helps optimize search and retrieval operations.

    Hilbert Curve - (Computational Geometry) - Vocab, Definition ... - Fiveable

    library.fiveable.me
    When did David Hilbert discover the curve?
    David Hilbert discovered this trick in 1891, building on earlier work by Giuseppe Peano. The curve is not smooth, but it’s continuous—you can draw it without ever lifting the pencil from the paper—and when elaborated to all its infinite glory it touches every point in a square.

    Mapping the Hilbert curve - bit-player

    bit-player.org
    Feedback
     
  4. CG References & Tutorials
    http://www.fundza.com/algorithmic/.../h…

    Algorithmic - Hilbert Curve: Concepts & Implementation

    We will begin by looking at the inputs of the Hilbert function. In addition to the counter (n) that tracks the level from which the function begins to recursively call itself, there are six other inputs to Andrew's procedure.

     
  5. GeeksForGeeks
    https://www.geeksforgeeks.org/python …

    Python - Hilbert Curve using turtle - GeeksforGeeks

    Apr 4, 2023 · A Hilbert curve is a curve that is formed by connecting a sequence of U-shaped curves arranged and oriented in different directions. These U-shaped curves are placed at a certain step size distance apart.

  6. Wolfram MathWorld
    https://mathworld.wolfram.com/Hilbert…

    Hilbert Curve -- from Wolfram MathWorld

    4 days ago · Learn about the Hilbert curve, a plane-filling function that can be generated by a Lindenmayer system. Find out how to encode the curve with initial string "L" and string rewriting rules, and how to use the Wolfram Language to …

  7. Stack Overflow
    https://stackoverflow.com/questions/499166

    algorithm - Mapping N-dimensional value to a point on Hilbert …

  9. Codeforces
    https://codeforces.com/blog/entry/61203

    An alternative sorting order for Mo's algorithm

    But Sierpiński curve is not very convenient in implementation for integer point coordinates, so we will use another recursive curve: Hilbert curve. Let's build a Hilbert curve on a 2k × 2k matrix and visit all the cells on the matrix according …

  10. ACM Digital Library
    https://dl.acm.org/doi/pdf/10.1145/290200.290219
    [PDF]

    Algorithm 781: Generating Hilbert’s Space-Filling Curve by …

  11. scientificlib.com
    https://www.scientificlib.com/en/Mathematics/LX/HilbertCurve.html

    Hilbert curve - Scientific Lib

  12. CompuPhase
    https://www.compuphase.com/hilbert.htm

    The Hilbert curve - CompuPhase

  13. Stack Overflow
    https://stackoverflow.com/questions/14519267

    Algorithm for generating a 3D Hilbert space-filling curve in Python ...

  14. bit-player
    http://bit-player.org/2013/mapping-the-…

    Mapping the Hilbert curve - bit-player

    Apr 26, 2013 · The leading actor in this story is the Hilbert curve, which illustrates Cantor’s shocking discovery by leaping out of the one-dimensional universe and filling up a two-dimensional area. David Hilbert discovered this trick in 1891, …

  15. Github
    https://github.com/adishavit/hilbert

    GitHub - adishavit/hilbert: Doug Moore's Fast Hilbert Curve …

  16. visualize-it.github.io
    https://visualize-it.github.io/hilbert_curve/simulation.html

    Hilbert Curves | Visualize It - GitHub Pages

  17. Wikiwand
    https://www.wikiwand.com/en/articles/Hilbert_curve

    Hilbert curve - Wikiwand

  18. Github
    https://github.com/jakubcerveny/gilbert

    GitHub - jakubcerveny/gilbert: Space-filling curve for rectangular ...

  19. Github
    https://github.com/spectral3d/hilbert_hpp

    spectral3d/hilbert_hpp: C++ hilbert curve implementation. - GitHub

  20. Institution of Engineering and Technology
    https://ietresearch.onlinelibrary.wiley.com/doi/10...

    Efficient 3D Hilbert Curve Encoding and Decoding …

    Mar 1, 2022 · To solve this problem, in this paper we design efficient 3D state views for fast encoding and decoding. Based on the state views designed, a new encoding algorithm (JFK-3HE) and a new decoding algorithm (JFK-3HD) are …

  21. designcoding.net
    https://www.designcoding.net/hilbert-curve

    Hilbert Curve - designcoding

  22. Fiveable
    https://library.fiveable.me/.../hilbert-curve

    Hilbert Curve - (Computational Geometry) - Vocab, Definition

  23. A Bioinformagician
    https://jokergoo.github.io/HilbertCurve/articles/hc_general.html

    Making 2D Hilbert Curve • HilbertCurve - GitHub Pages