141 lines
3.8 KiB
C++
141 lines
3.8 KiB
C++
/**********************************************************************
|
|
*
|
|
* GEOS - Geometry Engine Open Source
|
|
* http://geos.osgeo.org
|
|
*
|
|
* Copyright (C) 2020 Paul Ramsey <pramsey@cleverelephant.ca>
|
|
*
|
|
* This is free software; you can redistribute and/or modify it under
|
|
* the terms of the GNU Lesser General Public Licence as published
|
|
* by the Free Software Foundation.
|
|
* See the COPYING file for more information.
|
|
*
|
|
**********************************************************************/
|
|
|
|
|
|
#pragma once
|
|
|
|
#include <geos/export.h>
|
|
#include <string>
|
|
#include <cstdint>
|
|
|
|
// Forward declarations
|
|
namespace geos {
|
|
namespace geom {
|
|
class Coordinate;
|
|
}
|
|
}
|
|
|
|
namespace geos {
|
|
namespace shape { // geos.shape
|
|
namespace fractal { // geos.shape.fractal
|
|
|
|
|
|
/**
|
|
* 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 HilbertCode
|
|
*/
|
|
class GEOS_DLL MortonCode {
|
|
|
|
public:
|
|
|
|
/**
|
|
* The maximum curve level that can be represented.
|
|
*/
|
|
static constexpr int MAX_LEVEL = 16;
|
|
|
|
/**
|
|
* Computes the index of the point (x,y)
|
|
* in the Morton curve ordering.
|
|
*
|
|
* @param x the x ordinate of the point
|
|
* @param y the y ordinate of the point
|
|
* @return the index of the point along the Morton curve
|
|
*/
|
|
static uint32_t encode(int x, int y);
|
|
|
|
/**
|
|
* Computes the point on the Morton curve
|
|
* for a given index.
|
|
*
|
|
* @param index the index of the point on the curve
|
|
* @return the point on the curve
|
|
*/
|
|
static geom::Coordinate decode(uint32_t index);
|
|
|
|
/**
|
|
* The number of points in the curve for the given level.
|
|
* The number of points is 2<sup>2 * level</sup>.
|
|
*
|
|
* @param level the level of the curve
|
|
* @return the number of points
|
|
*/
|
|
static uint32_t levelSize(uint32_t level);
|
|
|
|
/**
|
|
* The maximum ordinate value for points
|
|
* in the curve for the given level.
|
|
* The maximum ordinate is 2<sup>level</sup> - 1.
|
|
*
|
|
* @param level the level of the curve
|
|
* @return the maximum ordinate value
|
|
*/
|
|
static uint32_t maxOrdinate(uint32_t level);
|
|
|
|
/**
|
|
* The level of the finite Morton curve which contains at least
|
|
* the given number of points.
|
|
*
|
|
* @param numPoints the number of points required
|
|
* @return the level of the curve
|
|
*/
|
|
static uint32_t level(uint32_t numPoints);
|
|
|
|
|
|
private:
|
|
|
|
static void checkLevel(uint32_t level) ;
|
|
|
|
static uint32_t interleave(uint32_t x);
|
|
|
|
static uint32_t deinterleave(uint32_t x);
|
|
|
|
};
|
|
|
|
|
|
} // namespace geos.shape.fractal
|
|
} // namespace geos.shape
|
|
} // namespace geos
|
|
|
|
|
|
|