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Intersect.cpp
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/**
* \file Intersect.cpp
* \brief Implementation for GeographicLib::Intersect class
*
* Copyright (c) Charles Karney (2023) <karney@alum.mit.edu> and licensed under
* the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#include <GeographicLib/Intersect.hpp>
#include <limits>
#include <utility>
#include <algorithm>
#include <set>
using namespace std;
namespace GeographicLib {
Intersect::Intersect(const Geodesic& geod)
: _geod(geod)
, _a(_geod.EquatorialRadius())
, _f(_geod.Flattening())
, _rR(sqrt(_geod.EllipsoidArea() / (4 * Math::pi())))
, _d(_rR * Math::pi()) // Used to normalize intersection points
, _eps(3 * numeric_limits<real>::epsilon())
, _tol(_d * pow(numeric_limits<real>::epsilon(), 3/real(4)))
, _delta(_d * pow(numeric_limits<real>::epsilon(), 1/real(5)))
, _comp(_delta)
, _cnt0(0)
, _cnt1(0)
, _cnt2(0)
, _cnt3(0)
, _cnt4(0)
{
_t1 = _t4 = _a * (1 - _f) * Math::pi();
_t2 = 2 * distpolar(90);
_geod.Inverse(0, 0, 90, 0, _t5); _t5 *= 2;
if (_f > 0) {
_t3 = distoblique();
_t4 = _t1;
} else {
_t3 = _t5;
_t4 = polarb();
swap(_t1, _t2);
}
_d1 = _t2 / 2;
_d2 = 2 * _t3 / 3;
_d3 = _t4 - _delta;
if (! (_d1 < _d3 && _d2 < _d3 && _d2 < 2 * _t1) )
throw GeographicErr("Ellipsoid too eccentric for Closest");
}
Intersect::Point
Intersect::Closest(Math::real latX, Math::real lonX, Math::real aziX,
Math::real latY, Math::real lonY, Math::real aziY,
const Intersect::Point& p0, int* c) const {
return Closest(_geod.Line(latX, lonX, aziX, LineCaps),
_geod.Line(latY, lonY, aziY, LineCaps),
p0, c);
}
Intersect::Point
Intersect::Closest(const GeodesicLine& lineX, const GeodesicLine& lineY,
const Intersect::Point& p0, int* c) const {
XPoint p = ClosestInt(lineX, lineY, XPoint(p0));
if (c) *c = p.c;
return p.data();
}
Intersect::Point
Intersect::Segment(Math::real latX1, Math::real lonX1,
Math::real latX2, Math::real lonX2,
Math::real latY1, Math::real lonY1,
Math::real latY2, Math::real lonY2,
int& segmode, int* c) const {
return Segment(_geod.InverseLine(latX1, lonX1, latX2, lonX2, LineCaps),
_geod.InverseLine(latY1, lonY1, latY2, lonY2, LineCaps),
segmode, c);
}
Intersect::Point
Intersect::Segment(const GeodesicLine& lineX,
const GeodesicLine& lineY, int& segmode, int* c) const {
XPoint p = SegmentInt(lineX, lineY, segmode);
if (c) *c = p.c;
return p.data();
}
Intersect::Point
Intersect::Next(Math::real latX, Math::real lonX,
Math::real aziX, Math::real aziY, int* c) const {
return Next(_geod.Line(latX, lonX, aziX, LineCaps),
_geod.Line(latX, lonX, aziY, LineCaps), c);
}
Intersect::Point
Intersect::Next(const GeodesicLine& lineX, const GeodesicLine& lineY,
int* c) const {
XPoint p = NextInt(lineX, lineY);
if (c) *c = p.c;
return p.data();
}
std::vector<Intersect::Point>
Intersect::All(Math::real latX, Math::real lonX, Math::real aziX,
Math::real latY, Math::real lonY, Math::real aziY,
Math::real maxdist, const Point& p0) const {
return All(_geod.Line(latX, lonX, aziX, LineCaps),
_geod.Line(latY, lonY, aziY, LineCaps),
maxdist, p0);
}
std::vector<Intersect::Point>
Intersect::All(Math::real latX, Math::real lonX, Math::real aziX,
Math::real latY, Math::real lonY, Math::real aziY,
Math::real maxdist, std::vector<int>& c, const Point& p0)
const {
return All(_geod.Line(latX, lonX, aziX, LineCaps),
_geod.Line(latY, lonY, aziY, LineCaps),
maxdist, c, p0);
}
std::vector<Intersect::Point>
Intersect::All(const GeodesicLine& lineX, const GeodesicLine& lineY,
Math::real maxdist, const Point& p0) const {
vector<int> c;
return AllInternal(lineX, lineY, maxdist, p0, c, false);
}
std::vector<Intersect::Point>
Intersect::All(const GeodesicLine& lineX, const GeodesicLine& lineY,
Math::real maxdist, std::vector<int>& c, const Point& p0)
const {
return AllInternal(lineX, lineY, maxdist, p0, c, true);
}
Intersect::XPoint
Intersect::Spherical(const GeodesicLine& lineX, const GeodesicLine& lineY,
const Intersect::XPoint& p) const {
// threshold for coincident geodesics and intersections; this corresponds
// to about 4.3 nm on WGS84.
real latX, lonX, aziX, latY, lonY, aziY;
lineX.Position(p.x , latX, lonX, aziX);
lineY.Position(p.y, latY, lonY, aziY);
real z, aziXa, aziYa;
_geod.Inverse(latX, lonX, latY, lonY, z, aziXa, aziYa);
real sinz = sin(z/_rR), cosz = cos(z/_rR);
// X = interior angle at X, Y = exterior angle at Y
real dX, dY, dXY,
X = Math::AngDiff(aziX, aziXa, dX), Y = Math::AngDiff(aziY, aziYa, dY),
XY = Math::AngDiff(X, Y, dXY);
real s = copysign(real(1), XY + (dXY + dY - dX)); // inverted triangle
// For z small, sinz -> z, cosz -> 1
// ( sinY*cosX*cosz - cosY*sinX) =
// (-sinX*cosY*cosz + cosX*sinY) -> sin(Y-X)
// for z = pi, sinz -> 0, cosz -> -1
// ( sinY*cosX*cosz - cosY*sinX) -> -sin(Y+X)
// (-sinX*cosY*cosz + cosX*sinY) -> sin(Y+X)
real sinX, cosX; Math::sincosde(s*X, s*dX, sinX, cosX);
real sinY, cosY; Math::sincosde(s*Y, s*dY, sinY, cosY);
real sX, sY;
int c;
if (z <= _eps * _rR) {
sX = sY = 0; // Already at intersection
// Determine whether lineX and lineY are parallel or antiparallel
if (fabs(sinX - sinY) <= _eps && fabs(cosX - cosY) <= _eps)
c = 1;
else if (fabs(sinX + sinY) <= _eps && fabs(cosX + cosY) <= _eps)
c = -1;
else
c = 0;
} else if (fabs(sinX) <= _eps && fabs(sinY) <= _eps) {
c = cosX * cosY > 0 ? 1 : -1;
// Coincident geodesics, place intersection at midpoint
sX = cosX * z/2; sY = -cosY * z/2;
// alt1: sX = cosX * z; sY = 0;
// alt2: sY = -cosY * z; sX = 0;
} else {
// General case. [SKIP: Divide args by |sinz| to avoid possible
// underflow in {sinX,sinY}*sinz; this is probably not necessary].
// Definitely need to treat sinz < 0 (z > pi*R) correctly. Without
// this we have some convergence failures in Basic.
sX = _rR * atan2(sinY * sinz, sinY * cosX * cosz - cosY * sinX);
sY = _rR * atan2(sinX * sinz, -sinX * cosY * cosz + cosX * sinY);
c = 0;
}
return XPoint(sX, sY, c);
}
Intersect::XPoint
Intersect::Basic(const GeodesicLine& lineX, const GeodesicLine& lineY,
const Intersect::XPoint& p0) const {
++_cnt1;
XPoint q = p0;
for (int n = 0;
n < numit_ ||
GEOGRAPHICLIB_PANIC("Convergence failure in Intersect");
++n) {
++_cnt0;
XPoint dq = Spherical(lineX, lineY, q);
q += dq;
if (q.c || !(dq.Dist() > _tol)) break; // break if nan
}
return q;
}
Intersect::XPoint
Intersect::ClosestInt(const GeodesicLine& lineX, const GeodesicLine& lineY,
const Intersect::XPoint& p0) const {
const int num = 5;
const int ix[num] = { 0, 1, -1, 0, 0 };
const int iy[num] = { 0, 0, 0, 1, -1 };
bool skip[num] = { 0, 0, 0, 0, 0 };
XPoint q; // Best intersection so far
for (int n = 0; n < num; ++n) {
if (skip[n]) continue;
XPoint qx = Basic(lineX, lineY, p0 + XPoint(ix[n] * _d1, iy[n] * _d1));
qx = fixcoincident(p0, qx);
if (_comp.eq(q, qx)) continue;
if (qx.Dist(p0) < _t1) { q = qx; ++_cnt2; break; }
if (n == 0 || qx.Dist(p0) < q.Dist(p0)) { q = qx; ++_cnt2; }
for (int m = n + 1; m < num; ++m)
skip[m] = skip[m] ||
qx.Dist(p0 + XPoint(ix[m]*_d1, iy[m]*_d1)) < 2*_t1 - _d1 - _delta;
}
return q;
}
Intersect::XPoint
Intersect::NextInt(const GeodesicLine& lineX, const GeodesicLine& lineY)
const {
const int num = 8;
const int ix[num] = { -1, -1, 1, 1, -2, 0, 2, 0 };
const int iy[num] = { -1, 1, -1, 1, 0, 2, 0, -2 };
bool skip[num] = { 0, 0, 0, 0, 0, 0, 0, 0 };
XPoint z(0,0), // for excluding the origin
q(Math::infinity(), 0); // Best intersection so far
for (int n = 0; n < num; ++n) {
if (skip[n]) continue;
XPoint qx = Basic(lineX, lineY, XPoint(ix[n] * _d2, iy[n] * _d2));
qx = fixcoincident(z, qx);
bool zerop = _comp.eq(z, qx);
if (qx.c == 0 && zerop) continue;
if (qx.c && zerop) {
for (int sgn = -1; sgn <= 1; sgn+=2) {
real s = ConjugateDist(lineX, sgn * _d, false);
XPoint qa(s, qx.c*s, qx.c);
if (qa.Dist() < q.Dist()) { q = qa; ++_cnt2; }
}
} else {
if (qx.Dist() < q.Dist()) { q = qx; ++_cnt2; }
}
for (int sgn = -1; sgn <= 1; ++sgn) {
// if qx.c == 0 only process sgn == 0
// if zerop skip sgn == 0
if ((qx.c == 0 && sgn != 0) || (zerop && sgn == 0)) continue;
XPoint qy = qx.c ? qx + Point(sgn * _d2, qx.c * sgn *_d2) : qx;
for (int m = n + 1; m < num; ++m)
skip[m] = skip[m] ||
qy.Dist(XPoint(ix[m]*_d2, iy[m]*_d2)) < 2*_t1 - _d2 - _delta;
}
}
return q;
}
Intersect::XPoint
Intersect::SegmentInt(const GeodesicLine& lineX, const GeodesicLine& lineY,
int& segmode) const {
// The conjecture is that whenever two geodesic segments intersect, the
// intersection is the one that is closest to the midpoints of segments.
// If this is proven, set conjectureproved to true.
const bool conjectureproved = false;
real sx = lineX.Distance(), sy = lineY.Distance();
// p0 is center of [sx,sy] rectangle, q is intersection closest to p0
XPoint p0 = XPoint(sx/2, sy/2), q = ClosestInt(lineX, lineY, p0);
q = fixsegment(sx, sy, q);
segmode = segmentmode(sx, sy, q);
// Are corners of [sx,sy] rectangle further from p0 than q?
if (!conjectureproved && segmode != 0 && p0.Dist() >= p0.Dist(q)) {
int segmodex = 1;
XPoint qx;
// Cycle through 4 corners of [sx,sy] rectangle
for (int ix = 0; ix < 2 && segmodex != 0; ++ix) {
for (int iy = 0; iy < 2 && segmodex != 0; ++iy) {
XPoint t(ix * sx, iy * sy); // corner point
// Is corner outside next intersection exclusion circle?
if (q.Dist(t) >= 2 * _t1) {
++_cnt3;
qx = Basic(lineX, lineY, t);
// fixsegment is not needed because the coincidence line must just
// slice off a corner of the sx x sy rectangle.
qx = fixcoincident(t, qx);
// No need to check if equal to q, because result is only accepted
// if segmode != 0 && segmodex == 0.
segmodex = segmentmode(sx, sy, qx);
}
}
}
if (segmodex == 0) { ++_cnt4; segmode = 0; q = qx; }
}
return q;
}
std::vector<Intersect::XPoint>
Intersect::AllInt0(const GeodesicLine& lineX,
const GeodesicLine& lineY,
Math::real maxdist, const XPoint& p0) const {
real maxdistx = maxdist + _delta;
const int m = int(ceil(maxdistx / _d3)), // process m x m set of tiles
m2 = m*m + (m - 1) % 2, // add center tile if m is even
n = m - 1; // Range of i, j = [-n:2:n]
real d3 = maxdistx/m; // d3 <= _d3
vector<XPoint> start(m2);
vector<bool> skip(m2, false);
int h = 0, c0 = 0;
start[h++] = p0;
for (int i = -n; i <= n; i += 2)
for (int j = -n; j <= n; j += 2) {
if (!(i == 0 && j == 0))
start[h++] = p0 + XPoint( d3 * (i + j) / 2, d3 * (i - j) / 2);
}
// assert(h == m2);
set<XPoint, SetComp> r(_comp); // Intersections found
set<XPoint, SetComp> c(_comp); // Closest coincident intersections
vector<XPoint> added;
for (int k = 0; k < m2; ++k) {
if (skip[k]) continue;
XPoint q = Basic(lineX, lineY, start[k]);
if (r.find(q) != r.end() // intersection already found
// or it's on a line of coincident intersections already processed
|| (c0 != 0 && c.find(fixcoincident(p0, q)) != c.end()))
continue;
added.clear();
if (q.c != 0) {
// This value of q.c must be constitent with c0
// assert(c0 == 0 || c0 == q.c);
c0 = q.c;
// Process coincident intersections
q = fixcoincident(p0, q);
c.insert(q);
// Elimate all existing intersections on this line (which
// didn't set c0).
for (auto qp = r.begin(); qp != r.end(); ) {
if (_comp.eq(fixcoincident(p0, *qp, c0), q)) {
qp = r.erase(qp);
}
else
++qp;
}
real s0 = q.x;
XPoint qc;
real t, m12, M12, M21;
lineX.GenPosition(false, s0,
GeodesicLine::REDUCEDLENGTH |
GeodesicLine::GEODESICSCALE,
t, t, t, t, m12, M12, M21, t);
// Compute line of conjugate points
for (int sgn = -1; sgn <= 1; sgn += 2) {
real sa = 0;
do {
sa = ConjugateDist(lineX, s0 + sa + sgn*_d, false, m12, M12, M21)
- s0;
qc = q + XPoint(sa, c0*sa);
added.push_back(qc);
r.insert(qc);
} while (qc.Dist(p0) <= maxdistx);
}
}
added.push_back(q);
r.insert(q);
for (auto qp = added.cbegin(); qp != added.cend(); ++qp) {
for (int l = k + 1; l < m2; ++l)
skip[l] = skip[l] || qp->Dist(start[l]) < 2*_t1 - d3 - _delta;
}
}
// Trim intersections to maxdist
for (auto qp = r.begin(); qp != r.end(); ) {
if (!(qp->Dist(p0) <= maxdist))
qp = r.erase(qp);
else
++qp;
}
vector<XPoint> v(r.size());
int i = 0;
for (auto p = r.cbegin(); p != r.cend(); ++p)
v[i++] = *p;
sort(v.begin(), v.end(), RankPoint(p0));
return v;
}
std::vector<Intersect::Point>
Intersect::AllInternal(const GeodesicLine& lineX, const GeodesicLine& lineY,
Math::real maxdist, const Point& p0,
std::vector<int>& c, bool cp) const {
const vector<XPoint>
v = AllInt0(lineX, lineY, fmax(real(0), maxdist), XPoint(p0));
int i = int(v.size());
vector<Point> u(i);
if (cp) c.resize(i);
for (int j = 0; j < i; ++j) {
u[j] = v[j].data();
if (cp) c[j] = v[j].c;
}
return u;
}
Math::real Intersect::distpolar(Math::real lat1, Math::real* lat2)
const {
GeodesicLine line = _geod.Line(lat1, 0, 0,
GeodesicLine::REDUCEDLENGTH |
GeodesicLine::GEODESICSCALE |
GeodesicLine::DISTANCE_IN);
real s = ConjugateDist(line, (1 + _f/2) * _a * Math::pi() / 2, true);
if (lat2) {
real t;
line.GenPosition(false, s, GeodesicLine::LATITUDE,
*lat2, t, t, t, t, t, t, t);
}
return s;
}
Math::real Intersect::polarb(Math::real* lata, Math::real* latb) const {
if (_f == 0) {
if (lata) *lata = 64;
if (latb) *latb = 90-64;
return _d;
}
real
lat0 = 63, s0 = distpolar(lat0),
lat1 = 65, s1 = distpolar(lat1),
lat2 = 64, s2 = distpolar(lat2),
latx = lat2, sx = s2;
// Solve for ds(lat)/dlat = 0 with a quadratic fit
for (int i = 0; i < 10; ++i) {
real den = (lat1-lat0)*s2 + (lat0-lat2)*s1 + (lat2-lat1)*s0;
if (!(den < 0 || den > 0)) break; // Break if nan
real latn = ((lat1-lat0)*(lat1+lat0)*s2 + (lat0-lat2)*(lat0+lat2)*s1 +
(lat2-lat1)*(lat2+lat1)*s0) / (2*den);
lat0 = lat1; s0 = s1;
lat1 = lat2; s1 = s2;
lat2 = latn; s2 = distpolar(lat2);
if (_f < 0 ? (s2 < sx) : (s2 > sx)) {
sx = s2;
latx = lat2;
}
}
if (lata) *lata = latx;
if (latb) distpolar(latx, latb);
return 2 * sx;
}
// Find {semi-,}conjugate point relative to s0 which is close to s1.
Math::real Intersect::ConjugateDist(const GeodesicLine& line, Math::real s3,
bool semi, Math::real m12,
Math::real M12, Math::real M21) const {
// semi = false: solve for m23 = 0 using dm23/ds3 = M32
// semi = true : solve for M23 = 0 using dM23/ds3 = - (1 - M23*M32)/m23
// Here 2 is point with given m12, M12, M21 and default values s.t. point 2
// = point 1.
real s = s3;
for (int i = 0; i < 100; ++i) {
real t, m13, M13, M31;
line.GenPosition(false, s,
GeodesicLine::REDUCEDLENGTH |
GeodesicLine::GEODESICSCALE,
t, t, t, t, m13, M13, M31, t);
real
// See "Algorithms for geodesics", eqs. 31, 32, 33.
m23 = m13 * M12 - m12 * M13,
// when m12 -> eps, (1 - M12 * M21) -> eps^2, I suppose.
M23 = M13 * M21 + (m12 == 0 ? 0 : (1 - M12 * M21) * m13/m12),
M32 = M31 * M12 + (m13 == 0 ? 0 : (1 - M13 * M31) * m12/m13);
real ds = semi ? m23 * M23 / (1 - M23*M32) : -m23 / M32;
s = s + ds;
if (!(fabs(ds) > _tol)) break;
}
return s;
}
Math::real Intersect::conjdist(Math::real azi,
Math::real* ds,
Math::real* sp, Math::real* sm) const {
GeodesicLine line = _geod.Line(0, 0, azi, LineCaps);
real s = ConjugateDist(line, _d, false);
if (ds) {
XPoint p = Basic(line, line, XPoint(s/2, -3*s/2));
if (sp) *sp = p.x;
if (sm) *sm = p.y;
*ds = p.Dist() - 2*s;
}
return s;
}
Math::real Intersect::distoblique(Math::real* azi,
Math::real* sp,
Math::real* sm) const {
if (_f == 0) {
if (azi) *azi = 45;
if (sp) *sp = 0.5;
if (sm) *sm = -1.5;
return _d;
}
real sa, sb,
azi0 = 46, ds0, s0 = conjdist(azi0, &ds0, &sa, &sb),
azi1 = 44, ds1, s1 = conjdist(azi1, &ds1, &sa, &sb),
azix = azi1, dsx = fabs(ds1), sx = s1, sax = sa, sbx = sb;
// find ds(azi) = 0 by secant method
(void) s0;
for (int i = 0; i < 10 && ds1 != ds0; ++i) {
real azin = (azi0*ds1-azi1*ds0)/(ds1-ds0);
azi0 = azi1; s0 = s1; ds0 = ds1;
azi1 = azin; s1 = conjdist(azi1, &ds1, &sa, &sb);
if (fabs(ds1) < dsx) {
azix = azi1, sx = s1, dsx = fabs(ds1);
sax = sa; sbx = sb;
if (ds1 == 0) break;
}
}
if (azi) *azi = azix;
if (sp) *sp = sax;
if (sm) *sm = sbx;
return sx;
}
Intersect::XPoint
Intersect::fixcoincident(const Intersect::XPoint& p0,
const Intersect::XPoint& p) {
return fixcoincident(p0, p, p.c);
}
Intersect::XPoint
Intersect::fixcoincident(const Intersect::XPoint& p0,
const Intersect::XPoint& p, int c) {
if (c == 0) return p;
// eqs : [p0x-p1x = -c*(p0y-p1y), p1x = px+s, p1y = py+c*s]$
// sol : solve(eqs,[s,p1x,p1y]);
// =>
// sol:[ s = ((p0x+c*p0y) - (px+c*py))/2,
// p1x = px + ((p0x+c*p0y) - (px+c*py))/2,
// p1y = py + c * ((p0x+c*p0y) - (px+c*py))/2
// ];
real s = ((p0.x + c * p0.y) - (p.x + c * p.y))/2;
return p + XPoint(s, c*s);
}
Intersect::XPoint
Intersect::fixsegment(Math::real sx, Math::real sy,
const Intersect::XPoint& p) {
if (p.c == 0) return p;
// eq0: [p1x = px+s, p1y = py+f*s]$
// solx0:linsolve(cons(p1x=0 ,eq0),[s,p1x,p1y]);
// solx1:linsolve(cons(p1x=sx,eq0),[s,p1x,p1y]);
// soly0:linsolve(cons(p1y=0 ,eq0),[s,p1x,p1y]);
// soly1:linsolve(cons(p1y=sy,eq0),[s,p1x,p1y]);
// solx0:[s = -px ,p1x = 0 ,p1y = py-f*px ];
// solx1:[s = sx-px ,p1x = sx,p1y = py-f*(px-sx)];
// soly0:[s = -f*py ,p1x = px-f*py ,p1y = 0 ];
// soly1:[s = f*(sy-py),p1x = px-f*(py-sy),p1y = sy];
real
pya = p.y - p.c * p.x, sa = -p.x, // pxa = 0
pyb = p.y - p.c * (p.x-sx), sb = sx - p.x, // pxb = sx
pxc = p.x - p.c * p.y, sc = p.c * -p.y, // pyc = 0
pxd = p.x - p.c * (p.y-sy), sd = p.c * (sy - p.y); // pyd = sy
bool
ga = 0 <= pya && pya <= sy,
gb = 0 <= pyb && pyb <= sy,
gc = 0 <= pxc && pxc <= sx,
gd = 0 <= pxd && pxd <= sx;
real s;
// Test opposite sides of the rectangle first
if (ga && gb) s = (sa + sb) / 2;
else if (gc && gd) s = (sc + sd) / 2;
else if (ga && gc) s = (sa + sc) / 2;
else if (ga && gd) s = (sa + sd) / 2;
else if (gb && gc) s = (sb + sc) / 2;
else if (gb && gd) s = (sb + sd) / 2;
else {
// Intersection not within segments; place intersection in smallest gap.
if (p.c > 0) {
// distance from p to corner p0 is abs( (px - py) - (p0x - p0y) )
// consider corners p0 = [0, sy] and p0 = [sx, 0]
if (fabs((p.x - p.y) + sy) < fabs((p.x - p.y) - sx))
s = (sy - (p.x + p.y))/2;
else
s = (sx - (p.x + p.y))/2;
} else {
// distance from p to corner p0 is abs( (px + p.y) - (p0x + p0y) )
// consider corners p0 = [0, 0] and p0 = [sx, sy]
if (fabs(p.x + p.y) < fabs((p.x + p.y) - (sx + sy)))
s = (0 - (p.x - p.y))/2;
else
s = ((sx - sy) - (p.x - p.y))/2;
}
}
return p + XPoint(s, p.c*s);
}
}
real
GeographicLib::Math::real real
Definition GeodSolve.cpp:28
Intersect.hpp
Header for GeographicLib::Intersect class.
GEOGRAPHICLIB_PANIC
#define GEOGRAPHICLIB_PANIC(msg)
Definition Math.hpp:62
GeographicLib::GeodesicLine
A geodesic line.
Definition GeodesicLine.hpp:74
GeographicLib::GeodesicLine::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const
Definition GeodesicLine.hpp:297
GeographicLib::GeodesicLine::LATITUDE
@ LATITUDE
Definition GeodesicLine.hpp:137
GeographicLib::GeodesicLine::GEODESICSCALE
@ GEODESICSCALE
Definition GeodesicLine.hpp:176
GeographicLib::GeodesicLine::DISTANCE_IN
@ DISTANCE_IN
Definition GeodesicLine.hpp:166
GeographicLib::GeodesicLine::REDUCEDLENGTH
@ REDUCEDLENGTH
Definition GeodesicLine.hpp:171
GeographicLib::Geodesic
Geodesic calculations
Definition Geodesic.hpp:175
GeographicLib::Geodesic::InverseLine
GeodesicLine InverseLine(real lat1, real lon1, real lat2, real lon2, unsigned caps=ALL) const
Definition Geodesic.cpp:532
GeographicLib::Geodesic::Line
GeodesicLine Line(real lat1, real lon1, real azi1, unsigned caps=ALL) const
Definition Geodesic.cpp:123
GeographicLib::Geodesic::Inverse
Math::real Inverse(real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2, real &m12, real &M12, real &M21, real &S12) const
Definition Geodesic.hpp:689
GeographicLib::GeographicErr
Exception handling for GeographicLib.
Definition Constants.hpp:316
GeographicLib::Intersect::Segment
Point Segment(Math::real latX1, Math::real lonX1, Math::real latX2, Math::real lonX2, Math::real latY1, Math::real lonY1, Math::real latY2, Math::real lonY2, int &segmode, int *c=nullptr) const
Definition Intersect.cpp:72
GeographicLib::Intersect::LineCaps
static const unsigned LineCaps
Definition Intersect.hpp:84
GeographicLib::Intersect::Closest
Point Closest(Math::real latX, Math::real lonX, Math::real aziX, Math::real latY, Math::real lonY, Math::real aziY, const Point &p0=Point(0, 0), int *c=nullptr) const
Definition Intersect.cpp:55
GeographicLib::Intersect::Point
std::pair< Math::real, Math::real > Point
Definition Intersect.hpp:79
GeographicLib::Intersect::All
std::vector< Point > All(Math::real latX, Math::real lonX, Math::real aziX, Math::real latY, Math::real lonY, Math::real aziY, Math::real maxdist, std::vector< int > &c, const Point &p0=Point(0, 0)) const
Definition Intersect.cpp:115
GeographicLib::Intersect::Next
Point Next(Math::real latX, Math::real lonX, Math::real aziX, Math::real aziY, int *c=nullptr) const
Definition Intersect.cpp:91
GeographicLib::Intersect::Intersect
Intersect(const Geodesic &geod)
Definition Intersect.cpp:20
GeographicLib::Math
Mathematical functions needed by GeographicLib.
Definition Math.hpp:77
GeographicLib::Math::infinity
static T infinity()
Definition Math.cpp:289
GeographicLib::Math::sincosde
static void sincosde(T x, T t, T &sinx, T &cosx)
Definition Math.cpp:128
GeographicLib::Math::pi
static T pi()
Definition Math.hpp:199
GeographicLib::Math::AngDiff
static T AngDiff(T x, T y, T &e)
Definition Math.cpp:77
GeographicLib::Math::real
double real
Definition Math.hpp:110
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12
std
Definition NearestNeighbor.hpp:806
std::swap
void swap(GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &a, GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &b)
Definition NearestNeighbor.hpp:819