Encodes points as the index along the planar Morton (Z-order) curve.
The planar Morton (Z-order) curve is a continuous space-filling curve. The Morton curve defines an ordering of the points in the positive quadrant of the plane. The index of a point along the Morton curve is called the Morton code.
A sequence of subsets of the Morton curve can be defined by a level number. Each level subset occupies a square range. The curve at level n M(n) contains 2^(n + 1) points. It fills the range square of side 2^level. Curve points have ordinates in the range [0, 2^level - 1]. The code for a given point is identical at all levels. The level simply determines the number of points in the curve subset and the size of the range square.
This implementation represents codes using 32-bit integers. This allows levels 0 to 16 to be handled. The class supports encoding points and decoding the point for a given code value.
The Morton order has the property that it tends to preserve locality. This means that codes which are near in value will have spatially proximate points. The converse is not always true - the delta between codes for nearby points is not always small. But the average delta is small enough that the Morton order is an effective way of linearizing space to support range queries.
- Author
- Martin Davis
- See also
- HilbertCode
