osrm-backend/DataStructures/Coordinate.cpp

/*

Copyright (c) 2013, Project OSRM, Dennis Luxen, others
All rights reserved.

Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list
of conditions and the following disclaimer.
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list of conditions and the following disclaimer in the documentation and/or
other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

*/

#include <osrm/Coordinate.h>
#include "../Util/MercatorUtil.h"
#include "../Util/SimpleLogger.h"
#include "../Util/StringUtil.h"

#include <boost/assert.hpp>

#ifndef NDEBUG
#include <bitset>
#endif
#include <iostream>
#include <limits>

FixedPointCoordinate::FixedPointCoordinate()
    : lat(std::numeric_limits<int>::min()), lon(std::numeric_limits<int>::min())
{
}

FixedPointCoordinate::FixedPointCoordinate(int lat, int lon) : lat(lat), lon(lon)
{
#ifndef NDEBUG
    if (0 != (std::abs(lat) >> 30))
    {
        std::bitset<32> y(lat);
        SimpleLogger().Write(logDEBUG) << "broken lat: " << lat << ", bits: " << y;
    }
    if (0 != (std::abs(lon) >> 30))
    {
        std::bitset<32> x(lon);
        SimpleLogger().Write(logDEBUG) << "broken lon: " << lon << ", bits: " << x;
    }
#endif
}

void FixedPointCoordinate::Reset()
{
    lat = std::numeric_limits<int>::min();
    lon = std::numeric_limits<int>::min();
}
bool FixedPointCoordinate::isSet() const
{
    return (std::numeric_limits<int>::min() != lat) && (std::numeric_limits<int>::min() != lon);
}
bool FixedPointCoordinate::isValid() const
{
    if (lat > 90 * COORDINATE_PRECISION || lat < -90 * COORDINATE_PRECISION ||
        lon > 180 * COORDINATE_PRECISION || lon < -180 * COORDINATE_PRECISION)
    {
        return false;
    }
    return true;
}
bool FixedPointCoordinate::operator==(const FixedPointCoordinate &other) const
{
    return lat == other.lat && lon == other.lon;
}

double FixedPointCoordinate::ApproximateDistance(const int lat1,
                                                 const int lon1,
                                                 const int lat2,
                                                 const int lon2)
{
    BOOST_ASSERT(lat1 != std::numeric_limits<int>::min());
    BOOST_ASSERT(lon1 != std::numeric_limits<int>::min());
    BOOST_ASSERT(lat2 != std::numeric_limits<int>::min());
    BOOST_ASSERT(lon2 != std::numeric_limits<int>::min());
    double RAD = 0.017453292519943295769236907684886;
    double lt1 = lat1 / COORDINATE_PRECISION;
    double ln1 = lon1 / COORDINATE_PRECISION;
    double lt2 = lat2 / COORDINATE_PRECISION;
    double ln2 = lon2 / COORDINATE_PRECISION;
    double dlat1 = lt1 * (RAD);

    double dlong1 = ln1 * (RAD);
    double dlat2 = lt2 * (RAD);
    double dlong2 = ln2 * (RAD);

    double dLong = dlong1 - dlong2;
    double dLat = dlat1 - dlat2;

    double aHarv = pow(sin(dLat / 2.0), 2.0) + cos(dlat1) * cos(dlat2) * pow(sin(dLong / 2.), 2);
    double cHarv = 2. * atan2(sqrt(aHarv), sqrt(1.0 - aHarv));
    // earth radius varies between 6,356.750-6,378.135 km (3,949.901-3,963.189mi)
    // The IUGG value for the equatorial radius is 6378.137 km (3963.19 miles)
    const double earth = 6372797.560856;
    return earth * cHarv;
}

double FixedPointCoordinate::ApproximateDistance(const FixedPointCoordinate &c1,
                                                 const FixedPointCoordinate &c2)
{
    return ApproximateDistance(c1.lat, c1.lon, c2.lat, c2.lon);
}

double FixedPointCoordinate::ApproximateEuclideanDistance(const FixedPointCoordinate &c1,
                                                 const FixedPointCoordinate &c2)
{
    return ApproximateEuclideanDistance(c1.lat, c1.lon, c2.lat, c2.lon);
}

double FixedPointCoordinate::ApproximateEuclideanDistance(const int lat1,
                                                          const int lon1,
                                                          const int lat2,
                                                          const int lon2)
{
    BOOST_ASSERT(lat1 != std::numeric_limits<int>::min());
    BOOST_ASSERT(lon1 != std::numeric_limits<int>::min());
    BOOST_ASSERT(lat2 != std::numeric_limits<int>::min());
    BOOST_ASSERT(lon2 != std::numeric_limits<int>::min());

    const double RAD = 0.017453292519943295769236907684886;
    const double float_lat1 = (lat1 / COORDINATE_PRECISION) * RAD;
    const double float_lon1 = (lon1 / COORDINATE_PRECISION) * RAD;
    const double float_lat2 = (lat2 / COORDINATE_PRECISION) * RAD;
    const double float_lon2 = (lon2 / COORDINATE_PRECISION) * RAD;

    const double x = (float_lon2 - float_lon1) * cos((float_lat1 + float_lat2) / 2.);
    const double y = (float_lat2 - float_lat1);
    const double earth_radius = 6372797.560856;
    return sqrt(x * x + y * y) * earth_radius;
}

// Yuck! Code duplication. This function is also in EgdeBasedNode.h
double FixedPointCoordinate::ComputePerpendicularDistance(const FixedPointCoordinate &point,
                                                          const FixedPointCoordinate &segA,
                                                          const FixedPointCoordinate &segB)
{
    const double x = lat2y(point.lat / COORDINATE_PRECISION);
    const double y = point.lon / COORDINATE_PRECISION;
    const double a = lat2y(segA.lat / COORDINATE_PRECISION);
    const double b = segA.lon / COORDINATE_PRECISION;
    const double c = lat2y(segB.lat / COORDINATE_PRECISION);
    const double d = segB.lon / COORDINATE_PRECISION;
    double p, q, nY;
    if (std::abs(a - c) > std::numeric_limits<double>::epsilon())
    {
        const double m = (d - b) / (c - a); // slope
        // Projection of (x,y) on line joining (a,b) and (c,d)
        p = ((x + (m * y)) + (m * m * a - m * b)) / (1. + m * m);
        q = b + m * (p - a);
    }
    else
    {
        p = c;
        q = y;
    }
    nY = (d * p - c * q) / (a * d - b * c);

    // discretize the result to coordinate precision. it's a hack!
    if (std::abs(nY) < (1. / COORDINATE_PRECISION))
    {
        nY = 0.;
    }

    double r = (p - nY * a) / c;
    if (std::isnan(r))
    {
        r = ((segB.lat == point.lat) && (segB.lon == point.lon)) ? 1. : 0.;
    }
    else if (std::abs(r) <= std::numeric_limits<double>::epsilon())
    {
        r = 0.;
    }
    else if (std::abs(r - 1.) <= std::numeric_limits<double>::epsilon())
    {
        r = 1.;
    }
    FixedPointCoordinate nearest_location;
    BOOST_ASSERT(!std::isnan(r));
    if (r <= 0.)
    { // point is "left" of edge
        nearest_location.lat = segA.lat;
        nearest_location.lon = segA.lon;
    }
    else if (r >= 1.)
    { // point is "right" of edge
        nearest_location.lat = segB.lat;
        nearest_location.lon = segB.lon;
    }
    else
    { // point lies in between
        nearest_location.lat = y2lat(p) * COORDINATE_PRECISION;
        nearest_location.lon = q * COORDINATE_PRECISION;
    }
    BOOST_ASSERT(nearest_location.isValid());
    const double approximated_distance =
        FixedPointCoordinate::ApproximateDistance(point, nearest_location);
    BOOST_ASSERT(0. <= approximated_distance);
    return approximated_distance;
}

double FixedPointCoordinate::ComputePerpendicularDistance(const FixedPointCoordinate &coord_a,
                                                   const FixedPointCoordinate &coord_b,
                                                   const FixedPointCoordinate &query_location,
                                                   FixedPointCoordinate &nearest_location,
                                                   double &r)
{
    BOOST_ASSERT(query_location.isValid());

    const double x = lat2y(query_location.lat / COORDINATE_PRECISION);
    const double y = query_location.lon / COORDINATE_PRECISION;
    const double a = lat2y(coord_a.lat / COORDINATE_PRECISION);
    const double b = coord_a.lon / COORDINATE_PRECISION;
    const double c = lat2y(coord_b.lat / COORDINATE_PRECISION);
    const double d = coord_b.lon / COORDINATE_PRECISION;
    double p, q /*,mX*/, nY;
    if (std::abs(a - c) > std::numeric_limits<double>::epsilon())
    {
        const double m = (d - b) / (c - a); // slope
        // Projection of (x,y) on line joining (a,b) and (c,d)
        p = ((x + (m * y)) + (m * m * a - m * b)) / (1. + m * m);
        q = b + m * (p - a);
    }
    else
    {
        p = c;
        q = y;
    }
    nY = (d * p - c * q) / (a * d - b * c);

    // discretize the result to coordinate precision. it's a hack!
    if (std::abs(nY) < (1. / COORDINATE_PRECISION))
    {
        nY = 0.;
    }

    r = (p - nY * a) / c; // These values are actually n/m+n and m/m+n , we need
    // not calculate the explicit values of m an n as we
    // are just interested in the ratio
    if (std::isnan(r))
    {
        r = ((coord_b.lat == query_location.lat) && (coord_b.lon == query_location.lon)) ? 1. : 0.;
    }
    else if (std::abs(r) <= std::numeric_limits<double>::epsilon())
    {
        r = 0.;
    }
    else if (std::abs(r - 1.) <= std::numeric_limits<double>::epsilon())
    {
        r = 1.;
    }
    BOOST_ASSERT(!std::isnan(r));
    if (r <= 0.)
    {
        nearest_location.lat = coord_a.lat;
        nearest_location.lon = coord_a.lon;
    }
    else if (r >= 1.)
    {
        nearest_location.lat = coord_b.lat;
        nearest_location.lon = coord_b.lon;
    }
    else
    {
        // point lies in between
        nearest_location.lat = y2lat(p) * COORDINATE_PRECISION;
        nearest_location.lon = q * COORDINATE_PRECISION;
    }
    BOOST_ASSERT(nearest_location.isValid());

    // TODO: Replace with euclidean approximation when k-NN search is done
    // const double approximated_distance = FixedPointCoordinate::ApproximateEuclideanDistance(
    const double approximated_distance =
        FixedPointCoordinate::ApproximateDistance(query_location, nearest_location);
    BOOST_ASSERT(0. <= approximated_distance);
    return approximated_distance;
}

void FixedPointCoordinate::convertInternalLatLonToString(const int value, std::string &output)
{
    char buffer[12];
    buffer[11] = 0; // zero termination
    output = printInt<11, 6>(buffer, value);
}

void FixedPointCoordinate::convertInternalCoordinateToString(const FixedPointCoordinate &coord,
                                                             std::string &output)
{
    std::string tmp;
    tmp.reserve(23);
    convertInternalLatLonToString(coord.lon, tmp);
    output = tmp;
    output += ",";
    convertInternalLatLonToString(coord.lat, tmp);
    output += tmp;
}

void
FixedPointCoordinate::convertInternalReversedCoordinateToString(const FixedPointCoordinate &coord,
                                                                std::string &output)
{
    std::string tmp;
    tmp.reserve(23);
    convertInternalLatLonToString(coord.lat, tmp);
    output = tmp;
    output += ",";
    convertInternalLatLonToString(coord.lon, tmp);
    output += tmp;
}

void FixedPointCoordinate::Output(std::ostream &out) const
{
    out << "(" << lat / COORDINATE_PRECISION << "," << lon / COORDINATE_PRECISION << ")";
}

double FixedPointCoordinate::GetBearing(const FixedPointCoordinate &A, const FixedPointCoordinate &B)
{
    double delta_long = DegreeToRadian(B.lon / COORDINATE_PRECISION - A.lon / COORDINATE_PRECISION);

    const double lat1 = DegreeToRadian(A.lat / COORDINATE_PRECISION);
    const double lat2 = DegreeToRadian(B.lat / COORDINATE_PRECISION);

    const double y = sin(delta_long) * cos(lat2);
    const double x = cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(delta_long);
    double result = RadianToDegree(atan2(y, x));
    while (result < 0.)
    {
        result += 360.;
    }

    while (result >= 360.)
    {
        result -= 360.;
    }
    return result;
}

double FixedPointCoordinate::GetBearing(const FixedPointCoordinate &other) const
{
    double delta_long = DegreeToRadian(lon / COORDINATE_PRECISION - other.lon / COORDINATE_PRECISION);

    const double lat1 = DegreeToRadian(other.lat / COORDINATE_PRECISION);
    const double lat2 = DegreeToRadian(lat / COORDINATE_PRECISION);

    const double y = sin(delta_long) * cos(lat2);
    const double x = cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(delta_long);
    double result = RadianToDegree(atan2(y, x));
    while (result < 0.)
    {
        result += 360.;
    }

    while (result >= 360.)
    {
        result -= 360.;
    }
    return result;
}

double FixedPointCoordinate::DegreeToRadian(const double degree)
{
    return degree * (M_PI / 180.);
}

double FixedPointCoordinate::RadianToDegree(const double radian)
{
    return radian * (180. / M_PI);
}

// double PointSegmentDistanceSquared( double px, double py,
//                                     double p1x, double p1y,
//                                     double p2x, double p2y,
//                                     double& t,
//                                     double& qx, double& qy)
// {
//     static const double kMinSegmentLenSquared = 0.00000001;  // adjust to suit.  If you use float, you'll probably want something like 0.000001f
//     static const double kEpsilon = 1.0E-14;  // adjust to suit.  If you use floats, you'll probably want something like 1E-7f
//     double dx = p2x - p1x;
//     double dy = p2y - p1y;
//     double dp1x = px - p1x;
//     double dp1y = py - p1y;
//     const double segLenSquared = (dx * dx) + (dy * dy);
//     if (segLenSquared >= -kMinSegmentLenSquared && segLenSquared <= kMinSegmentLenSquared)
//     {
//         // segment is a point.
//         qx = p1x;
//         qy = p1y;
//         t = 0.0;
//         return ((dp1x * dp1x) + (dp1y * dp1y));
//     }
//     else
//     {
//         // Project a line from p to the segment [p1,p2].  By considering the line
//         // extending the segment, parameterized as p1 + (t * (p2 - p1)),
//         // we find projection of point p onto the line.
//         // It falls where t = [(p - p1) . (p2 - p1)] / |p2 - p1|^2
//         t = ((dp1x * dx) + (dp1y * dy)) / segLenSquared;
//         if (t < kEpsilon)
//         {
//             // intersects at or to the "left" of first segment vertex (p1x, p1y).  If t is approximately 0.0, then
//             // intersection is at p1.  If t is less than that, then there is no intersection (i.e. p is not within
//             // the 'bounds' of the segment)
//             if (t > -kEpsilon)
//             {
//                 // intersects at 1st segment vertex
//                 t = 0.0;
//             }
//             // set our 'intersection' point to p1.
//             qx = p1x;
//             qy = p1y;
//             // Note: If you wanted the ACTUAL intersection point of where the projected lines would intersect if
//             // we were doing PointLineDistanceSquared, then qx would be (p1x + (t * dx)) and qy would be (p1y + (t * dy)).
//         }
//         else if (t > (1.0 - kEpsilon))
//         {
//             // intersects at or to the "right" of second segment vertex (p2x, p2y).  If t is approximately 1.0, then
//             // intersection is at p2.  If t is greater than that, then there is no intersection (i.e. p is not within
//             // the 'bounds' of the segment)
//             if (t < (1.0 + kEpsilon))
//             {
//                 // intersects at 2nd segment vertex
//                 t = 1.0;
//             }
//             // set our 'intersection' point to p2.
//             qx = p2x;
//             qy = p2y;
//             // Note: If you wanted the ACTUAL intersection point of where the projected lines would intersect if
//             // we were doing PointLineDistanceSquared, then qx would be (p1x + (t * dx)) and qy would be (p1y + (t * dy)).
//         }
//         else
//         {
//             // The projection of the point to the point on the segment that is perpendicular succeeded and the point
//             // is 'within' the bounds of the segment.  Set the intersection point as that projected point.
//             qx = p1x + (t * dx);
//             qy = p1y + (t * dy);
//         }
//         // return the squared distance from p to the intersection point.  Note that we return the squared distance
//         // as an optimization because many times you just need to compare relative distances and the squared values
//         // works fine for that.  If you want the ACTUAL distance, just take the square root of this value.
//         double dpqx = px - qx;
//         double dpqy = py - qy;
//         return ((dpqx * dpqx) + (dpqy * dpqy));
//     }
// }

// public float DistanceOfPointToLine2(PointF p1, PointF p2, PointF p)
// {
//   //          (y1-y2)x + (x2-x1)y + (x1y2-x2y1)
//   //d(P,L) = --------------------------------
//   //         sqrt( (x2-x1)pow2 + (y2-y1)pow2 )

//   double ch = (p1.Y - p2.Y) * p.X + (p2.X - p1.X) * p.Y + (p1.X * p2.Y - p2.X * p1.Y);
//   double del = Math.Sqrt(Math.Pow(p2.X - p1.X, 2) + Math.Pow(p2.Y - p1.Y, 2));
//   double d = ch / del;
//   return (float)d;
// }