Class HilbertCode
Encodes points as the index along finite planar Hilbert curves.
The planar Hilbert Curve is a continuous space-filling curve. In the limit the Hilbert curve has infinitely many vertices and fills the space of the unit square. A sequence of finite approximations to the infinite Hilbert curve is defined by the level number. The finite Hilbert curve at level n Hₙ contains 2ⁿ⁺¹ points. Each finite Hilbert curve defines an ordering of the points in the 2-dimensional range square containing the curve. Curves fills the range square of side 2ˡᵉᵛᵉˡ. Curve points have ordinates in the range [0, 2ˡᵉᵛᵉˡ - 1]. The index of a point along a Hilbert curve is called the Hilbert code. The code for a given point is specific to the level chosen.
This implementation represents codes using 32-bit integers. This allows levels 0 to 16 to be handled. The class supports encoding points in the range of a given level curve and decoding the point for a given code value.
The Hilbert 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 Hilbert order is an effective way of linearizing space to support range queries.
Inherited Members
Namespace: NetTopologySuite.Shape.Fractal
Assembly: NetTopologySuite.dll
Syntax
public static class HilbertCodeFields
| Improve this Doc View SourceMaxLevel
The maximum curve level that can be represented.
Declaration
public static readonly int MaxLevelField Value
| Type | Description |
|---|---|
| Int32 |
Methods
| Improve this Doc View SourceDecode(Int32, Int32)
Computes the point on a Hilbert curve of given level for a given code index. The point ordinates will lie in the range [0, 2ˡᵉᵛᵉˡ - 1].
Declaration
public static Coordinate Decode(int level, int index)Parameters
| Type | Name | Description |
|---|---|---|
| Int32 | level | The Hilbert curve level. |
| Int32 | index | The index of the point on the curve. |
Returns
| Type | Description |
|---|---|
| Coordinate | The point on the Hilbert curve. |
Encode(Int32, Int32, Int32)
Encodes a point (x,y) in the range of the the Hilbert curve at a given level as the index of the point along the curve. The index will lie in the range [0, 2ˡᵉᵛᵉˡ⁺¹].
Declaration
public static int Encode(int level, int x, int y)Parameters
| Type | Name | Description |
|---|---|---|
| Int32 | level | The level of the Hilbert curve. |
| Int32 | x | The x ordinate of the point. |
| Int32 | y | The y ordinate of the point. |
Returns
| Type | Description |
|---|---|
| Int32 | The index of the point along the Hilbert curve. |
Level(Int32)
The level of the finite Hilbert curve which contains at least the given number of points.
Declaration
public static int Level(int numPoints)Parameters
| Type | Name | Description |
|---|---|---|
| Int32 | numPoints | The number of points required. |
Returns
| Type | Description |
|---|---|
| Int32 | The level of the curve. |
MaxOrdinate(Int32)
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 |
|---|---|---|
| Int32 | level | The level of the curve. |
Returns
| Type | Description |
|---|---|
| Int32 | The maximum ordinate value. |
Size(Int32)
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 |
|---|---|---|
| Int32 | level | The level of the curve |
Returns
| Type | Description |
|---|---|
| Int32 | The number of points. |