129 lines
3.5 KiB
C++
129 lines
3.5 KiB
C++
/**********************************************************************
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*
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* GEOS - Geometry Engine Open Source
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* http://geos.osgeo.org
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*
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* Copyright (C) 2020 Paul Ramsey <pramsey@cleverelephant.ca>
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*
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* This is free software; you can redistribute and/or modify it under
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* the terms of the GNU Lesser General Public Licence as published
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* by the Free Software Foundation.
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* See the COPYING file for more information.
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*
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**********************************************************************/
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#pragma once
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#include <geos/export.h>
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#include <string>
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#include <cstdint>
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// Forward declarations
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namespace geos {
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namespace geom {
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class Coordinate;
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}
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}
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namespace geos {
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namespace shape { // geos.shape
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namespace fractal { // geos.shape.fractal
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/**
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* Encodes points as the index along finite planar Hilbert curves.
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*
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* The planar Hilbert Curve is a continuous space-filling curve.
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* In the limit the Hilbert curve has infinitely many vertices and fills
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* the space of the unit square.
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* A sequence of finite approximations to the infinite Hilbert curve
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* is defined by the level number.
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* The finite Hilbert curve at level n H(n) contains 2^n+1 points.
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* Each finite Hilbert curve defines an ordering of the
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* points in the 2-dimensional range square containing the curve.
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* Curves fills the range square of side 2^level.
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* Curve points have ordinates in the range [0, 2^level - 1].
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* The index of a point along a Hilbert curve is called the Hilbert code.
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* The code for a given point is specific to the level chosen.
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*
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* This implementation represents codes using 32-bit integers.
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* This allows levels 0 to 16 to be handled.
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* The class supports encoding points in the range of a given level curve
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* and decoding the point for a given code value.
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*
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* The Hilbert order has the property that it tends to preserve locality.
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* This means that codes which are near in value will have spatially proximate
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* points. The converse is not always true - the delta between
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* codes for nearby points is not always small. But the average delta
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* is small enough that the Hilbert order is an effective way of linearizing space
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* to support range queries.
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*
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* @author Martin Davis
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*
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* @see MortonCode
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*/
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class GEOS_DLL HilbertCode {
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public:
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/**
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* The maximum curve level that can be represented.
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*/
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static constexpr int MAX_LEVEL = 16;
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static geom::Coordinate decode(uint32_t level, uint32_t i);
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static uint32_t encode(uint32_t level, uint32_t x, uint32_t y);
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/**
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* The number of points in the curve for the given level.
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* The number of points is 2^(2 * level).
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*
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* @param level the level of the curve
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* @return the number of points
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*/
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static uint32_t levelSize(uint32_t level);
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/**
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* The maximum ordinate value for points
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* in the curve for the given level.
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* The maximum ordinate is 2^level - 1.
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*
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* @param level the level of the curve
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* @return the maximum ordinate value
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*/
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static uint32_t maxOrdinate(uint32_t level);
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/**
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* The level of the finite Hilbert curve which contains at least
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* the given number of points.
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*
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* @param numPoints the number of points required
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* @return the level of the curve
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*/
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static uint32_t level(uint32_t numPoints);
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private:
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static uint32_t deinterleave(uint32_t x);
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static uint32_t interleave(uint32_t x);
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static uint32_t prefixScan(uint32_t x);
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static uint32_t descan(uint32_t x);
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static void checkLevel(uint32_t level);
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};
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} // namespace geos.shape.fractal
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} // namespace geos.shape
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} // namespace geos
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