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++ // Copyright (C) 2016 The Qt Company Ltd.
++ // SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
++ // Qt-Security score:significant reason:default
++ #include "qwebmercator_p.h"
++
++ #include "qgeocoordinate.h"
++
++ #include <qnumeric.h>
++ #include <qmath.h>
++
++ #include "qdoublevector2d_p.h"
++
++ QT_BEGIN_NAMESPACE
++ // We reverse the y-direction to make North be its decreasing direction, which
++ // is "up" in computer graphics. We offset it by 0.5 to put the range -85 deg to
++ // +85 deg latitude into the unit interval. The x-coordinate maps the range from
++ // -180 deg to +180 deg longitude into its unit interval, with The Prime
++ // Meridian mapped to x = 0.5. The x-coordinate is formally periodic, with
++ // period 1, so adding or subtracting any whole number gets a representation of
++ // the same longitude.
++
++ // As latitudes approach ±90, the Mercator y-Coordinate aproaches ∓infinity. We
++ // limit that to avoid numerical problems. Here the limit, -4 <= y <= 5, is
++ // chosen such that only points beyond ±89.9999999999 deg latituide are cut off,
++ // which matches the accuracy of qFuzzyCompare()
++ const static double yCutOff = 4.0;
++
++ QDoubleVector2D QWebMercator::coordToMercator(const QGeoCoordinate &coord)
++ {
++ const double x = coord.longitude() / 360.0 + 0.5;
++ const double lat = coord.latitude();
++ const double y = (1.0 - std::log(std::tan(qDegreesToRadians((90.0 + lat) / 2.0))) / M_PI) / 2.0;
++ return QDoubleVector2D(x, qBound(-yCutOff, y, 1.0 + yCutOff));
++ }
++
++ double QWebMercator::realmod(const double a, const double b)
++ {
++ quint64 div = static_cast<quint64>(a / b);
++ return a - static_cast<double>(div) * b;
++ }
++
++ QGeoCoordinate QWebMercator::mercatorToCoord(const QDoubleVector2D &mercator)
++ {
++ double fx = mercator.x();
++ const double fy = mercator.y();
++
++ double lat;
++ if (fy <= -yCutOff)
++ lat = 90.0;
++ else if (fy >= 1.0 + yCutOff)
++ lat = -90.0;
++ else
++ lat = qRadiansToDegrees(2.0 * std::atan(std::exp(M_PI * (1.0 - 2.0 * fy)))) - 90.0;
++
++ if (fx < 0) // Map to the +ve unit interval:
++ fx = 1.0 - realmod(-fx, 1.0);
++ const double lng = realmod(fx, 1.0) * 360.0 - 180.0;
++
++ return QGeoCoordinate(lat, lng, 0.0);
++ }
++
++ QGeoCoordinate QWebMercator::coordinateInterpolation(const QGeoCoordinate &from,
++ const QGeoCoordinate &to, qreal progress)
++ {
++ QDoubleVector2D s = QWebMercator::coordToMercator(from);
++ QDoubleVector2D e = QWebMercator::coordToMercator(to);
++
++ double x;
++
++ if (0.5 < qAbs(e.x() - s.x())) {
++ // handle dateline crossing
++ double ex = e.x();
++ double sx = s.x();
++ if (ex < sx)
++ sx -= 1.0;
++ else if (sx < ex)
++ ex -= 1.0;
++
++ x = (1.0 - progress) * sx + progress * ex;
++
++ if (!qFuzzyIsNull(x) && (x < 0.0))
++ x += 1.0;
++
++ } else {
++ x = (1.0 - progress) * s.x() + progress * e.x();
++ }
++
++ double y = (1.0 - progress) * s.y() + progress * e.y();
++
++ QGeoCoordinate result = QWebMercator::mercatorToCoord(QDoubleVector2D(x, y));
++ result.setAltitude((1.0 - progress) * from.altitude() + progress * to.altitude());
++
++ return result;
++ }
++
++ QT_END_NAMESPACE