Class MortonCode

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 Mₙ contains 2ⁿ⁺¹ points. It fills the range square of side 2ˡᵉᵛᵉˡ. Curve points have ordinates in the range [0, 2ˡᵉᵛᵉˡ - 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.

Inheritance
object
MortonCode
Inherited Members
Namespace: NetTopologySuite.Shape.Fractal
Assembly: NetTopologySuite.dll
Syntax
public static class MortonCode

Fields

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MaxLevel

The maximum curve level that can be represented.

Declaration
public static readonly int MaxLevel
Field Value
Type Description
int

Methods

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Decode(int)

Computes the point on the Morton curve for a given index.

Declaration
public static Coordinate Decode(int index)
Parameters
Type Name Description
int index

The index of the point on the curve.
Returns
Type Description
Coordinate

The point on the curve.
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Encode(int, int)

Computes the index of the point (x,y) in the Morton curve ordering.

Declaration
public static int Encode(int x, int y)
Parameters
Type Name Description
int x

The x ordinate of the point.
int y

The y ordinate of the point.
Returns
Type Description
int

The index of the point along the Morton curve.
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Level(int)

The level of the finite Morton curve which contains at least the given number of points.

Declaration
public static int Level(int numPoints)
Parameters
Type Name Description
int numPoints

The number of points required.
Returns
Type Description
int

The level of the curve.
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MaxOrdinate(int)

The maximum ordinate value for points in the curve for the given level. The maximum ordinate is 2ˡᵉᵛᵉˡ - 1.

Declaration
public static int MaxOrdinate(int level)
Parameters
Type Name Description
int level

The level of the curve.
Returns
Type Description
int

The maximum ordinate value.
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Size(int)

The number of points in the curve for the given level. The number of points is 2²ˡᵉᵛᵉˡ.

Declaration
public static int Size(int level)
Parameters
Type Name Description
int level

The level of the curve
Returns
Type Description
int

The number of points.

See Also