Morton Codes (Z-Order Curves)

Last Updated 14 June, 2026

by David Spuler, Ph.D.

Research on Morton Codes (Z-Order Curves)

Research papers include:

Marek Vinkler, Jiri Bittner, and Vlastimil Havran. 2017. Extended Morton codes for high performance bounding volume hierarchy construction. In Proceedings of High Performance Graphics (HPG '17). Association for Computing Machinery, New York, NY, USA, Article 9, 1–8. https://doi.org/10.1145/3105762.3105782 https://dl.acm.org/doi/abs/10.1145/3105762.3105782
G. Zhou, Q. Pan, T. Yue, Q. Wang, H. Sha, S. Huang, and X. Liu, 02 May 2018, Vector and Raster Data Storage Based on Morton Code, https://isprs-archives.copernicus.org/articles/XLII-3/2523/2018/isprs-archives-XLII-3-2523-2018.html
Chi-Yen Huang and Kuo-Liang Chung, 1997, Manipulating images by using Run-length Morton Codes International Journal of Pattern Recognition and Artificial Intelligence, Vol. 11, No. 06, pp. 889-907, https://doi.org/10.1142/S0218001497000408 https://www.worldscientific.com/doi/abs/10.1142/S0218001497000408
Wikipedia, June 2026, Z-order curve, https://en.wikipedia.org/wiki/Z-order_curve
Morton, G. M. , 1966, A computer Oriented Geodetic Data Base; and a New Technique in File Sequencing, Technical Report, Ottawa, Canada: IBM Ltd. https://domino.research.ibm.com/library/cyberdig.nsf/papers/0DABF9473B9C86D48525779800566A39/$File/Morton1966.pdf
Qiuhao Zeng, Jerry Huang, Peng Lu, Gezheng Xu, Boxing Cen, Charles Ling, Boyu Wang, 1 Apr 2025 (v3), ZETA: Leveraging Z-order Curves for Efficient Top-k Attention, https://arxiv.org/abs/2501.14577
Christian Berger, Lukas Birkemeyer, 20 Apr 2023, ZEBRA: Z-order Curve-based Event Retrieval Approach to Efficiently Explore Automotive Data, https://arxiv.org/abs/2304.10232
Guozhong Li, Muhannad Alhumaidi, Spiros Skiadopoulos, Panos Kalnis, 4 Nov 2025 (v2), LLMComp: A Language Modeling Paradigm for Error-Bounded Scientific Data Compression (Technical Report), https://arxiv.org/abs/2510.23632
Jaber J. Hasbestan, Inanc Senocak, 1 Dec 2017, Binarized octree generation for Cartesian adaptive mesh refinement around immersed geometries, https://arxiv.org/abs/1712.00408
Nhut Le, Ehsan Karimi, Maryam Rahnemoonfar, 16 May 2026, OPTNet: Ordering Point Transformer Network for Post-disaster 3D Semantic Segmentation, https://arxiv.org/abs/2605.17197
Jens Stücker, Oliver Hahn, Lukas Winkler, Adrian Gutierrez Adame, Thomas Flöss, 7 Apr 2026, JZ-Tree: GPU friendly neighbour search and friends-of-friends with dual tree walks in JAX plus CUDA, https://arxiv.org/abs/2604.05885
Shuyuan Li, Yuheng Liu, Yuxiang Wang, Zimu Zhou, Kaining Zhang & Yongxin Tong, 2026, MiniRFANN: Range Filtered Approximate Vector Similarity Search on Edge Devices. Data Sci. Eng., https://doi.org/10.1007/s41019-025-00343-5 https://link.springer.com/content/pdf/10.1007/s41019-025-00343-5_reference.pdf
Mannat Khurana, Sanyam Jain, Rishav Agarwal, 26 May 2026, Generative Animations: A Multi-Model Pipeline for Prompt-Driven Motion Synthesis, https://arxiv.org/abs/2605.27203
Guofeng Mei, Wei Lin, Luigi Riz, Yujiao Wu, Yiming Wang, Fabio Poiesi, 2026, Efficient Encoder-Free Fourier-based 3D Large Multimodal Model, Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2026, pp. 23785-23794, https://openaccess.thecvf.com/content/CVPR2026/html/Mei_Efficient_Encoder-Free_Fourier-based_3D_Large_Multimodal_Model_CVPR_2026_paper.html
Hoai-Chau Tran, Chi H. Nguyen, Duy M. H. Nguyen, Mathias Niepert, Fan Lai, Khoa D. Doan, 17 May 2026, SparseSAM: Structured Sparsification of Activations in Segment Anything Models, https://arxiv.org/abs/2605.17633