Hilbert Curve

A C++ package for the Hilbert Curve in n dimensions. To use the code, just include the header file in folder 'include'.

To initialize the class:

HilbertCurve::HilbertCurve hilbertCurve(n, p);

where

• n is the number of dimensions
• p is the number of iterations

To get the Hilbert value of point (5, 5, 5)

std::vector<unsigned long> point{5, 5, 5};
unsigned long hilbertValue = hilbertCurve.hilbertNumberFromPoint(point);

To get the point with Hilbert value 100

std::vector<unsigned long> point = hilbertCurve.pointFromHilbertNumber(100)

You can also create a custom class and functor to sort with respect to Hilbert values (see the example)

// create some entities
Entity e1(1, 30, 2, 1000);
Entity e2(2, 32, 6, 1500.5);
Entity e3(3, 40, 15, 780.8);
Entity e4(4, 31, 4, 860.6);
Entity e5(5, 45, 20, 2043.4);

std::vector<Entity *> entities{&e1, &e2, &e3, &e4, &e5};

// sort the entities w.r.t. Hilber value
std::vector<unsigned long> hilbertValues;
hilbertCurve.sortData<Entity, struct myFunctor>(entities, myFunctor, hilbertValues);

You can find more documentation in the project's page.

Example

There is an example in the folder src. We create a custom class Entity, a functor which takes an instance of that class and maps it to a point in the hypercube lattice in 3D, and then we sort a vector of Entity objects, with respect to their Hilbert value.

To run the example:

cmake .
make
./hilbertCurve

Issues

• Let n be the number of dimensions and p the number of iterations. Due to the way we compute the binary representation of numbers, it must hold that np < size_of(long) * 8. In most computers that would be np < 64.