Abstract
An N-dimensional space-filling curve (SFC) is a continuous, surjective1 (onto) function from the unit interval [0, 1] to the N-dimensional unit hypercube [0, 1]N. In particular, a 2-dimensional space-filling curve is a continuous curve that passes through every point of the unit square [0,1]2.
A function f from a domain X to a codomain Y is said to be surjective if its values span its whole codomain; that is, for every y in Y, there is at least one x in X such that f(x) = y.
A function f from a domain X to a codomain Y is said to be bijective if for every y in Y there is exactly one x in X such that f(x) = y.
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(2007). Space-Filling Curve Tool Paths. In: Advanced Numerical Methods to Optimize Cutting Operations of Five-Axis Milling Machines. Springer Series in Advanced Manufacturing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71121-6_4
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