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C++ header-only library with methods to efficiently encode/decode Morton codes in/from 2D/3D coordinates
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Libmorton v0.2

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  • Libmorton is a C++11 header-only library with methods to efficiently encode/decode 64, 32 and 16-bit Morton codes and coordinates, in 2D and 3D. Morton order is also known as Z-order or the Z-order curve.
  • Libmorton is a lightweight and portable library - the only dependencies are standard C++ headers. Architecture-specific optimizations are available.
  • More info and some benchmarks in these blogposts: Morton encoding, Libmorton and BMI2 instruction set


Include libmorton/morton.h. This will always have stub functions that point to the most efficient way to encode/decode Morton codes. If you want to test out alternative (and possibly slower) methods, you can find them in libmorton/morton2D.h and libmorton/morton3D.h. All libmorton functionality is in the libmorton namespace to avoid conflicts.

// ENCODING 2D / 3D morton codes, of length 32 and 64 bits
inline uint_fast32_t morton2D_32_encode(const uint_fast16_t x, const uint_fast16_t y);
inline uint_fast64_t morton2D_64_encode(const uint_fast32_t x, const uint_fast32_t y);
inline uint_fast32_t morton3D_32_encode(const uint_fast16_t x, const uint_fast16_t y, const uint_fast16_t z);
inline uint_fast64_t morton3D_64_encode(const uint_fast32_t x, const uint_fast32_t y, const uint_fast32_t z);
// DECODING 2D / 3D morton codes, of length 32 and 64 bits
inline void morton2D_32_decode(const uint_fast32_t morton, uint_fast16_t& x, uint_fast16_t& y);
inline void morton2D_64_decode(const uint_fast64_t morton, uint_fast32_t& x, uint_fast32_t& y);
inline void morton3D_32_decode(const uint_fast32_t morton, uint_fast16_t& x, uint_fast16_t& y, uint_fast16_t& z);
inline void morton3D_64_decode(const uint_fast64_t morton, uint_fast32_t& x, uint_fast32_t& y, uint_fast32_t& z);

If you want to take advantage of the BMI2 instruction set (only available on Intel Haswell processors and newer), make sure __BMI2__ is defined before you include morton.h. This is definitely the fastest method, but limited to certain newer CPU's.


No installation is required (just download the headers and include them), but I was informed libmorton is packaged for Microsoft's VCPKG system as well, if you want a more controlled environment to install C++ packages in.


The test folder contains tools I use to test correctness and performance of the libmorton implementation. This section is under heavy re-writing, but might contain some useful code for advanced usage.


If you use libmorton in your published paper or work, please reference it, for example as follows:

author = "Jeroen Baert",
title = "Libmorton: C++ Morton Encoding/Decoding Library",
howpublished = "\url{}",
year = "2018"}

Publications / products that use libmorton

I'm always curious what libmorton ends up on. If you end up using it, send me an e-mail!

  • Sylvain Rousseau and Tamy Boubekeur, 2017. Fast lossy compression of 3D unit vector sets (PDF)
  • Jan Watter, 2018. Generation of complex numerical meshes using space-filling curves (PDF)
  • Esri
  • Cesium Ion

Thanks / See ALso

  • To @gnzlbg and his Rust implementation bitwise for finding bugs in the Magicbits code
  • @kevinhartman made a C++14 library that supports N-dimensional morton codes morton-nd. He upstreamed a lot of fixes back to libmorton - thanks!
  • Everyone making comments and suggestions on the original blogpost
  • Fabian Giesen's post on Morton Codes


  • Write better test suite (with L1/L2 trashing, better tests, ...)
  • A better naming system for the functions, because m3D_e_sLUT_shifted? That escalated quickly.
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