Z-Order Curve
Definition
A Z-order curve converts multidimensional coordinates into a linear sequence by interleaving bits.
A space-filling mapping that converts multidimensional coordinates into a one-dimensional order by bit interleaving.
Simply explained
Points on a plane receive a common order. Their coordinates are interwoven so that spatial proximity is partially preserved.
Why it matters in practice
The term helps to select, develop, evaluate AI systems in a well-founded manner and realistically assess their technical risks.
Example from business
A geodata service maps tile coordinates to Morton codes for spatial range queries.
Limits and pitfalls
- Proximity is only partially preserved; edge areas and dimensions influence clustering and query performance.
Origin & history
Guy M. Morton described the ordering for geographic file systems in 1966.
Use in mid-sized companies
- Possible example: A geodata service maps tile coordinates to Morton codes for spatial range queries.
Frequently asked questions
What does Z-order curve mean?
A space-filling mapping that converts multidimensional coordinates into a one-dimensional order through bit interleaving. What should you watch out for? Proximity is only partially preserved; boundary areas and dimensions influence clustering and query performance.
Sources
- A Computer Oriented Geodetic Data Base · Morton, A Computer Oriented Geodetic Data Base
Source checked on 10.10.2026. Editorial application examples are hypothetical; no evidence of real customer results.
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