GeographicLib: Intersect.cpp Source File

GeographicLib 2.5

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Intersect.cpp
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1/**
2 * \file Intersect.cpp
3 * \brief Implementation for GeographicLib::Intersect class
4 *
5 * Copyright (c) Charles Karney (2023) <karney@alum.mit.edu> and licensed under
6 * the MIT/X11 License. For more information, see
7 * https://geographiclib.sourceforge.io/
8 **********************************************************************/
9
10#include <GeographicLib/Intersect.hpp>
11#include <limits>
12#include <utility>
13#include <algorithm>
14#include <set>
15
16using namespace std;
17
18namespace GeographicLib {
19
20 Intersect::Intersect(const Geodesic& geod)
21 : _geod(geod)
22 , _a(_geod.EquatorialRadius())
23 , _f(_geod.Flattening())
24 , _rR(sqrt(_geod.EllipsoidArea() / (4 * Math::pi())))
25 , _d(_rR * Math::pi()) // Used to normalize intersection points
26 , _eps(3 * numeric_limits<real>::epsilon())
27 , _tol(_d * pow(numeric_limits<real>::epsilon(), 3/real(4)))
28 , _delta(_d * pow(numeric_limits<real>::epsilon(), 1/real(5)))
29 , _comp(_delta)
30 , _cnt0(0)
31 , _cnt1(0)
32 , _cnt2(0)
33 , _cnt3(0)
34 , _cnt4(0)
35 {
36 _t1 = _t4 = _a * (1 - _f) * Math::pi();
37 _t2 = 2 * distpolar(90);
38 _geod.Inverse(0, 0, 90, 0, _t5); _t5 *= 2;
39 if (_f > 0) {
40 _t3 = distoblique();
41 _t4 = _t1;
42 } else {
43 _t3 = _t5;
44 _t4 = polarb();
45 swap(_t1, _t2);
46 }
47 _d1 = _t2 / 2;
48 _d2 = 2 * _t3 / 3;
49 _d3 = _t4 - _delta;
50 if (! (_d1 < _d3 && _d2 < _d3 && _d2 < 2 * _t1) )
51 throw GeographicErr("Ellipsoid too eccentric for Closest");
52 }
53
54 Intersect::Point
55 Intersect::Closest(Math::real latX, Math::real lonX, Math::real aziX,
56 Math::real latY, Math::real lonY, Math::real aziY,
57 const Intersect::Point& p0, int* c) const {
58 return Closest(_geod.Line(latX, lonX, aziX, LineCaps),
59 _geod.Line(latY, lonY, aziY, LineCaps),
60 p0, c);
61 }
62
63 Intersect::Point
64 Intersect::Closest(const GeodesicLine& lineX, const GeodesicLine& lineY,
65 const Intersect::Point& p0, int* c) const {
66 XPoint p = ClosestInt(lineX, lineY, XPoint(p0));
67 if (c) *c = p.c;
68 return p.data();
69 }
70
71 Intersect::Point
72 Intersect::Segment(Math::real latX1, Math::real lonX1,
73 Math::real latX2, Math::real lonX2,
74 Math::real latY1, Math::real lonY1,
75 Math::real latY2, Math::real lonY2,
76 int& segmode, int* c) const {
77 return Segment(_geod.InverseLine(latX1, lonX1, latX2, lonX2, LineCaps),
78 _geod.InverseLine(latY1, lonY1, latY2, lonY2, LineCaps),
79 segmode, c);
80 }
81
82 Intersect::Point
83 Intersect::Segment(const GeodesicLine& lineX,
84 const GeodesicLine& lineY, int& segmode, int* c) const {
85 XPoint p = SegmentInt(lineX, lineY, segmode);
86 if (c) *c = p.c;
87 return p.data();
88 }
89
90 Intersect::Point
91 Intersect::Next(Math::real latX, Math::real lonX,
92 Math::real aziX, Math::real aziY, int* c) const {
93 return Next(_geod.Line(latX, lonX, aziX, LineCaps),
94 _geod.Line(latX, lonX, aziY, LineCaps), c);
95 }
96
97 Intersect::Point
98 Intersect::Next(const GeodesicLine& lineX, const GeodesicLine& lineY,
99 int* c) const {
100 XPoint p = NextInt(lineX, lineY);
101 if (c) *c = p.c;
102 return p.data();
103 }
104
105 std::vector<Intersect::Point>
106 Intersect::All(Math::real latX, Math::real lonX, Math::real aziX,
107 Math::real latY, Math::real lonY, Math::real aziY,
108 Math::real maxdist, const Point& p0) const {
109 return All(_geod.Line(latX, lonX, aziX, LineCaps),
110 _geod.Line(latY, lonY, aziY, LineCaps),
111 maxdist, p0);
112 }
113
114 std::vector<Intersect::Point>
115 Intersect::All(Math::real latX, Math::real lonX, Math::real aziX,
116 Math::real latY, Math::real lonY, Math::real aziY,
117 Math::real maxdist, std::vector<int>& c, const Point& p0)
118 const {
119 return All(_geod.Line(latX, lonX, aziX, LineCaps),
120 _geod.Line(latY, lonY, aziY, LineCaps),
121 maxdist, c, p0);
122 }
123
124 std::vector<Intersect::Point>
125 Intersect::All(const GeodesicLine& lineX, const GeodesicLine& lineY,
126 Math::real maxdist, const Point& p0) const {
127 vector<int> c;
128 return AllInternal(lineX, lineY, maxdist, p0, c, false);
129 }
130
131 std::vector<Intersect::Point>
132 Intersect::All(const GeodesicLine& lineX, const GeodesicLine& lineY,
133 Math::real maxdist, std::vector<int>& c, const Point& p0)
134 const {
135 return AllInternal(lineX, lineY, maxdist, p0, c, true);
136 }
137
138 Intersect::XPoint
139 Intersect::Spherical(const GeodesicLine& lineX, const GeodesicLine& lineY,
140 const Intersect::XPoint& p) const {
141 // threshold for coincident geodesics and intersections; this corresponds
142 // to about 4.3 nm on WGS84.
143 real latX, lonX, aziX, latY, lonY, aziY;
144 lineX.Position(p.x , latX, lonX, aziX);
145 lineY.Position(p.y, latY, lonY, aziY);
146 real z, aziXa, aziYa;
147 _geod.Inverse(latX, lonX, latY, lonY, z, aziXa, aziYa);
148 real sinz = sin(z/_rR), cosz = cos(z/_rR);
149 // X = interior angle at X, Y = exterior angle at Y
150 real dX, dY, dXY,
151 X = Math::AngDiff(aziX, aziXa, dX), Y = Math::AngDiff(aziY, aziYa, dY),
152 XY = Math::AngDiff(X, Y, dXY);
153 real s = copysign(real(1), XY + (dXY + dY - dX)); // inverted triangle
154 // For z small, sinz -> z, cosz -> 1
155 // ( sinY*cosX*cosz - cosY*sinX) =
156 // (-sinX*cosY*cosz + cosX*sinY) -> sin(Y-X)
157 // for z = pi, sinz -> 0, cosz -> -1
158 // ( sinY*cosX*cosz - cosY*sinX) -> -sin(Y+X)
159 // (-sinX*cosY*cosz + cosX*sinY) -> sin(Y+X)
160 real sinX, cosX; Math::sincosde(s*X, s*dX, sinX, cosX);
161 real sinY, cosY; Math::sincosde(s*Y, s*dY, sinY, cosY);
162 real sX, sY;
163 int c;
164 if (z <= _eps * _rR) {
165 sX = sY = 0; // Already at intersection
166 // Determine whether lineX and lineY are parallel or antiparallel
167 if (fabs(sinX - sinY) <= _eps && fabs(cosX - cosY) <= _eps)
168 c = 1;
169 else if (fabs(sinX + sinY) <= _eps && fabs(cosX + cosY) <= _eps)
170 c = -1;
171 else
172 c = 0;
173 } else if (fabs(sinX) <= _eps && fabs(sinY) <= _eps) {
174 c = cosX * cosY > 0 ? 1 : -1;
175 // Coincident geodesics, place intersection at midpoint
176 sX = cosX * z/2; sY = -cosY * z/2;
177 // alt1: sX = cosX * z; sY = 0;
178 // alt2: sY = -cosY * z; sX = 0;
179 } else {
180 // General case. [SKIP: Divide args by |sinz| to avoid possible
181 // underflow in {sinX,sinY}*sinz; this is probably not necessary].
182 // Definitely need to treat sinz < 0 (z > pi*R) correctly. Without
183 // this we have some convergence failures in Basic.
184 sX = _rR * atan2(sinY * sinz, sinY * cosX * cosz - cosY * sinX);
185 sY = _rR * atan2(sinX * sinz, -sinX * cosY * cosz + cosX * sinY);
186 c = 0;
187 }
188 return XPoint(sX, sY, c);
189 }
190
191 Intersect::XPoint
192 Intersect::Basic(const GeodesicLine& lineX, const GeodesicLine& lineY,
193 const Intersect::XPoint& p0) const {
194 ++_cnt1;
195 XPoint q = p0;
196 for (int n = 0;
197 n < numit_ ||
198 GEOGRAPHICLIB_PANIC("Convergence failure in Intersect");
199 ++n) {
200 ++_cnt0;
201 XPoint dq = Spherical(lineX, lineY, q);
202 q += dq;
203 if (q.c || !(dq.Dist() > _tol)) break; // break if nan
204 }
205 return q;
206 }
207
208 Intersect::XPoint
209 Intersect::ClosestInt(const GeodesicLine& lineX, const GeodesicLine& lineY,
210 const Intersect::XPoint& p0) const {
211 const int num = 5;
212 const int ix[num] = { 0, 1, -1, 0, 0 };
213 const int iy[num] = { 0, 0, 0, 1, -1 };
214 bool skip[num] = { 0, 0, 0, 0, 0 };
215 XPoint q; // Best intersection so far
216 for (int n = 0; n < num; ++n) {
217 if (skip[n]) continue;
218 XPoint qx = Basic(lineX, lineY, p0 + XPoint(ix[n] * _d1, iy[n] * _d1));
219 qx = fixcoincident(p0, qx);
220 if (_comp.eq(q, qx)) continue;
221 if (qx.Dist(p0) < _t1) { q = qx; ++_cnt2; break; }
222 if (n == 0 || qx.Dist(p0) < q.Dist(p0)) { q = qx; ++_cnt2; }
223 for (int m = n + 1; m < num; ++m)
224 skip[m] = skip[m] ||
225 qx.Dist(p0 + XPoint(ix[m]*_d1, iy[m]*_d1)) < 2*_t1 - _d1 - _delta;
226 }
227 return q;
228 }
229
230 Intersect::XPoint
231 Intersect::NextInt(const GeodesicLine& lineX, const GeodesicLine& lineY)
232 const {
233 const int num = 8;
234 const int ix[num] = { -1, -1, 1, 1, -2, 0, 2, 0 };
235 const int iy[num] = { -1, 1, -1, 1, 0, 2, 0, -2 };
236 bool skip[num] = { 0, 0, 0, 0, 0, 0, 0, 0 };
237 XPoint z(0,0), // for excluding the origin
238 q(Math::infinity(), 0); // Best intersection so far
239 for (int n = 0; n < num; ++n) {
240 if (skip[n]) continue;
241 XPoint qx = Basic(lineX, lineY, XPoint(ix[n] * _d2, iy[n] * _d2));
242 qx = fixcoincident(z, qx);
243 bool zerop = _comp.eq(z, qx);
244 if (qx.c == 0 && zerop) continue;
245 if (qx.c && zerop) {
246 for (int sgn = -1; sgn <= 1; sgn+=2) {
247 real s = ConjugateDist(lineX, sgn * _d, false);
248 XPoint qa(s, qx.c*s, qx.c);
249 if (qa.Dist() < q.Dist()) { q = qa; ++_cnt2; }
250 }
251 } else {
252 if (qx.Dist() < q.Dist()) { q = qx; ++_cnt2; }
253 }
254 for (int sgn = -1; sgn <= 1; ++sgn) {
255 // if qx.c == 0 only process sgn == 0
256 // if zerop skip sgn == 0
257 if ((qx.c == 0 && sgn != 0) || (zerop && sgn == 0)) continue;
258 XPoint qy = qx.c ? qx + Point(sgn * _d2, qx.c * sgn *_d2) : qx;
259 for (int m = n + 1; m < num; ++m)
260 skip[m] = skip[m] ||
261 qy.Dist(XPoint(ix[m]*_d2, iy[m]*_d2)) < 2*_t1 - _d2 - _delta;
262 }
263 }
264 return q;
265 }
266
267 Intersect::XPoint
268 Intersect::SegmentInt(const GeodesicLine& lineX, const GeodesicLine& lineY,
269 int& segmode) const {
270 // The conjecture is that whenever two geodesic segments intersect, the
271 // intersection is the one that is closest to the midpoints of segments.
272 // If this is proven, set conjectureproved to true.
273 const bool conjectureproved = false;
274 real sx = lineX.Distance(), sy = lineY.Distance();
275 // p0 is center of [sx,sy] rectangle, q is intersection closest to p0
276 XPoint p0 = XPoint(sx/2, sy/2), q = ClosestInt(lineX, lineY, p0);
277 q = fixsegment(sx, sy, q);
278 segmode = segmentmode(sx, sy, q);
279 // Are corners of [sx,sy] rectangle further from p0 than q?
280 if (!conjectureproved && segmode != 0 && p0.Dist() >= p0.Dist(q)) {
281 int segmodex = 1;
282 XPoint qx;
283 // Cycle through 4 corners of [sx,sy] rectangle
284 for (int ix = 0; ix < 2 && segmodex != 0; ++ix) {
285 for (int iy = 0; iy < 2 && segmodex != 0; ++iy) {
286 XPoint t(ix * sx, iy * sy); // corner point
287 // Is corner outside next intersection exclusion circle?
288 if (q.Dist(t) >= 2 * _t1) {
289 ++_cnt3;
290 qx = Basic(lineX, lineY, t);
291 // fixsegment is not needed because the coincidence line must just
292 // slice off a corner of the sx x sy rectangle.
293 qx = fixcoincident(t, qx);
294 // No need to check if equal to q, because result is only accepted
295 // if segmode != 0 && segmodex == 0.
296 segmodex = segmentmode(sx, sy, qx);
297 }
298 }
299 }
300 if (segmodex == 0) { ++_cnt4; segmode = 0; q = qx; }
301 }
302 return q;
303 }
304
305 std::vector<Intersect::XPoint>
306 Intersect::AllInt0(const GeodesicLine& lineX,
307 const GeodesicLine& lineY,
308 Math::real maxdist, const XPoint& p0) const {
309 real maxdistx = maxdist + _delta;
310 const int m = int(ceil(maxdistx / _d3)), // process m x m set of tiles
311 m2 = m*m + (m - 1) % 2, // add center tile if m is even
312 n = m - 1; // Range of i, j = [-n:2:n]
313 real d3 = maxdistx/m; // d3 <= _d3
314 vector<XPoint> start(m2);
315 vector<bool> skip(m2, false);
316 int h = 0, c0 = 0;
317 start[h++] = p0;
318 for (int i = -n; i <= n; i += 2)
319 for (int j = -n; j <= n; j += 2) {
320 if (!(i == 0 && j == 0))
321 start[h++] = p0 + XPoint( d3 * (i + j) / 2, d3 * (i - j) / 2);
322 }
323 // assert(h == m2);
324 set<XPoint, SetComp> r(_comp); // Intersections found
325 set<XPoint, SetComp> c(_comp); // Closest coincident intersections
326 vector<XPoint> added;
327 for (int k = 0; k < m2; ++k) {
328 if (skip[k]) continue;
329 XPoint q = Basic(lineX, lineY, start[k]);
330 if (r.find(q) != r.end() // intersection already found
331 // or it's on a line of coincident intersections already processed
332 || (c0 != 0 && c.find(fixcoincident(p0, q)) != c.end()))
333 continue;
334 added.clear();
335 if (q.c != 0) {
336 // This value of q.c must be constitent with c0
337 // assert(c0 == 0 || c0 == q.c);
338 c0 = q.c;
339 // Process coincident intersections
340 q = fixcoincident(p0, q);
341 c.insert(q);
342 // Elimate all existing intersections on this line (which
343 // didn't set c0).
344 for (auto qp = r.begin(); qp != r.end(); ) {
345 if (_comp.eq(fixcoincident(p0, *qp, c0), q)) {
346 qp = r.erase(qp);
347 }
348 else
349 ++qp;
350 }
351 real s0 = q.x;
352 XPoint qc;
353 real t, m12, M12, M21;
354 lineX.GenPosition(false, s0,
355 GeodesicLine::REDUCEDLENGTH |
356 GeodesicLine::GEODESICSCALE,
357 t, t, t, t, m12, M12, M21, t);
358 // Compute line of conjugate points
359 for (int sgn = -1; sgn <= 1; sgn += 2) {
360 real sa = 0;
361 do {
362 sa = ConjugateDist(lineX, s0 + sa + sgn*_d, false, m12, M12, M21)
363 - s0;
364 qc = q + XPoint(sa, c0*sa);
365 added.push_back(qc);
366 r.insert(qc);
367 } while (qc.Dist(p0) <= maxdistx);
368 }
369 }
370 added.push_back(q);
371 r.insert(q);
372 for (auto qp = added.cbegin(); qp != added.cend(); ++qp) {
373 for (int l = k + 1; l < m2; ++l)
374 skip[l] = skip[l] || qp->Dist(start[l]) < 2*_t1 - d3 - _delta;
375 }
376 }
377 // Trim intersections to maxdist
378 for (auto qp = r.begin(); qp != r.end(); ) {
379 if (!(qp->Dist(p0) <= maxdist))
380 qp = r.erase(qp);
381 else
382 ++qp;
383 }
384 vector<XPoint> v(r.size());
385 int i = 0;
386 for (auto p = r.cbegin(); p != r.cend(); ++p)
387 v[i++] = *p;
388 sort(v.begin(), v.end(), RankPoint(p0));
389 return v;
390 }
391
392 std::vector<Intersect::Point>
393 Intersect::AllInternal(const GeodesicLine& lineX, const GeodesicLine& lineY,
394 Math::real maxdist, const Point& p0,
395 std::vector<int>& c, bool cp) const {
396 const vector<XPoint>
397 v = AllInt0(lineX, lineY, fmax(real(0), maxdist), XPoint(p0));
398 int i = int(v.size());
399 vector<Point> u(i);
400 if (cp) c.resize(i);
401 for (int j = 0; j < i; ++j) {
402 u[j] = v[j].data();
403 if (cp) c[j] = v[j].c;
404 }
405 return u;
406 }
407
408 Math::real Intersect::distpolar(Math::real lat1, Math::real* lat2)
409 const {
410 GeodesicLine line = _geod.Line(lat1, 0, 0,
411 GeodesicLine::REDUCEDLENGTH |
412 GeodesicLine::GEODESICSCALE |
413 GeodesicLine::DISTANCE_IN);
414 real s = ConjugateDist(line, (1 + _f/2) * _a * Math::pi() / 2, true);
415 if (lat2) {
416 real t;
417 line.GenPosition(false, s, GeodesicLine::LATITUDE,
418 *lat2, t, t, t, t, t, t, t);
419 }
420 return s;
421 }
422
423 Math::real Intersect::polarb(Math::real* lata, Math::real* latb) const {
424 if (_f == 0) {
425 if (lata) *lata = 64;
426 if (latb) *latb = 90-64;
427 return _d;
428 }
429 real
430 lat0 = 63, s0 = distpolar(lat0),
431 lat1 = 65, s1 = distpolar(lat1),
432 lat2 = 64, s2 = distpolar(lat2),
433 latx = lat2, sx = s2;
434 // Solve for ds(lat)/dlat = 0 with a quadratic fit
435 for (int i = 0; i < 10; ++i) {
436 real den = (lat1-lat0)*s2 + (lat0-lat2)*s1 + (lat2-lat1)*s0;
437 if (!(den < 0 || den > 0)) break; // Break if nan
438 real latn = ((lat1-lat0)*(lat1+lat0)*s2 + (lat0-lat2)*(lat0+lat2)*s1 +
439 (lat2-lat1)*(lat2+lat1)*s0) / (2*den);
440 lat0 = lat1; s0 = s1;
441 lat1 = lat2; s1 = s2;
442 lat2 = latn; s2 = distpolar(lat2);
443 if (_f < 0 ? (s2 < sx) : (s2 > sx)) {
444 sx = s2;
445 latx = lat2;
446 }
447 }
448 if (lata) *lata = latx;
449 if (latb) distpolar(latx, latb);
450 return 2 * sx;
451 }
452
453 // Find {semi-,}conjugate point relative to s0 which is close to s1.
454 Math::real Intersect::ConjugateDist(const GeodesicLine& line, Math::real s3,
455 bool semi, Math::real m12,
456 Math::real M12, Math::real M21) const {
457 // semi = false: solve for m23 = 0 using dm23/ds3 = M32
458 // semi = true : solve for M23 = 0 using dM23/ds3 = - (1 - M23*M32)/m23
459 // Here 2 is point with given m12, M12, M21 and default values s.t. point 2
460 // = point 1.
461 real s = s3;
462 for (int i = 0; i < 100; ++i) {
463 real t, m13, M13, M31;
464 line.GenPosition(false, s,
465 GeodesicLine::REDUCEDLENGTH |
466 GeodesicLine::GEODESICSCALE,
467 t, t, t, t, m13, M13, M31, t);
468 real
469 // See "Algorithms for geodesics", eqs. 31, 32, 33.
470 m23 = m13 * M12 - m12 * M13,
471 // when m12 -> eps, (1 - M12 * M21) -> eps^2, I suppose.
472 M23 = M13 * M21 + (m12 == 0 ? 0 : (1 - M12 * M21) * m13/m12),
473 M32 = M31 * M12 + (m13 == 0 ? 0 : (1 - M13 * M31) * m12/m13);
474 real ds = semi ? m23 * M23 / (1 - M23*M32) : -m23 / M32;
475 s = s + ds;
476 if (!(fabs(ds) > _tol)) break;
477 }
478 return s;
479 }
480
481 Math::real Intersect::conjdist(Math::real azi,
482 Math::real* ds,
483 Math::real* sp, Math::real* sm) const {
484 GeodesicLine line = _geod.Line(0, 0, azi, LineCaps);
485 real s = ConjugateDist(line, _d, false);
486 if (ds) {
487 XPoint p = Basic(line, line, XPoint(s/2, -3*s/2));
488 if (sp) *sp = p.x;
489 if (sm) *sm = p.y;
490 *ds = p.Dist() - 2*s;
491 }
492 return s;
493 }
494
495 Math::real Intersect::distoblique(Math::real* azi,
496 Math::real* sp,
497 Math::real* sm) const {
498 if (_f == 0) {
499 if (azi) *azi = 45;
500 if (sp) *sp = 0.5;
501 if (sm) *sm = -1.5;
502 return _d;
503 }
504 real sa, sb,
505 azi0 = 46, ds0, s0 = conjdist(azi0, &ds0, &sa, &sb),
506 azi1 = 44, ds1, s1 = conjdist(azi1, &ds1, &sa, &sb),
507 azix = azi1, dsx = fabs(ds1), sx = s1, sax = sa, sbx = sb;
508 // find ds(azi) = 0 by secant method
509 (void) s0;
510 for (int i = 0; i < 10 && ds1 != ds0; ++i) {
511 real azin = (azi0*ds1-azi1*ds0)/(ds1-ds0);
512 azi0 = azi1; s0 = s1; ds0 = ds1;
513 azi1 = azin; s1 = conjdist(azi1, &ds1, &sa, &sb);
514 if (fabs(ds1) < dsx) {
515 azix = azi1, sx = s1, dsx = fabs(ds1);
516 sax = sa; sbx = sb;
517 if (ds1 == 0) break;
518 }
519 }
520 if (azi) *azi = azix;
521 if (sp) *sp = sax;
522 if (sm) *sm = sbx;
523 return sx;
524 }
525
526 Intersect::XPoint
527 Intersect::fixcoincident(const Intersect::XPoint& p0,
528 const Intersect::XPoint& p) {
529 return fixcoincident(p0, p, p.c);
530 }
531
532 Intersect::XPoint
533 Intersect::fixcoincident(const Intersect::XPoint& p0,
534 const Intersect::XPoint& p, int c) {
535 if (c == 0) return p;
536 // eqs : [p0x-p1x = -c*(p0y-p1y), p1x = px+s, p1y = py+c*s]$
537 // sol : solve(eqs,[s,p1x,p1y]);
538 // =>
539 // sol:[ s = ((p0x+c*p0y) - (px+c*py))/2,
540 // p1x = px + ((p0x+c*p0y) - (px+c*py))/2,
541 // p1y = py + c * ((p0x+c*p0y) - (px+c*py))/2
542 // ];
543 real s = ((p0.x + c * p0.y) - (p.x + c * p.y))/2;
544 return p + XPoint(s, c*s);
545 }
546
547 Intersect::XPoint
548 Intersect::fixsegment(Math::real sx, Math::real sy,
549 const Intersect::XPoint& p) {
550 if (p.c == 0) return p;
551 // eq0: [p1x = px+s, p1y = py+f*s]$
552 // solx0:linsolve(cons(p1x=0 ,eq0),[s,p1x,p1y]);
553 // solx1:linsolve(cons(p1x=sx,eq0),[s,p1x,p1y]);
554 // soly0:linsolve(cons(p1y=0 ,eq0),[s,p1x,p1y]);
555 // soly1:linsolve(cons(p1y=sy,eq0),[s,p1x,p1y]);
556 // solx0:[s = -px ,p1x = 0 ,p1y = py-f*px ];
557 // solx1:[s = sx-px ,p1x = sx,p1y = py-f*(px-sx)];
558 // soly0:[s = -f*py ,p1x = px-f*py ,p1y = 0 ];
559 // soly1:[s = f*(sy-py),p1x = px-f*(py-sy),p1y = sy];
560 real
561 pya = p.y - p.c * p.x, sa = -p.x, // pxa = 0
562 pyb = p.y - p.c * (p.x-sx), sb = sx - p.x, // pxb = sx
563 pxc = p.x - p.c * p.y, sc = p.c * -p.y, // pyc = 0
564 pxd = p.x - p.c * (p.y-sy), sd = p.c * (sy - p.y); // pyd = sy
565 bool
566 ga = 0 <= pya && pya <= sy,
567 gb = 0 <= pyb && pyb <= sy,
568 gc = 0 <= pxc && pxc <= sx,
569 gd = 0 <= pxd && pxd <= sx;
570 real s;
571 // Test opposite sides of the rectangle first
572 if (ga && gb) s = (sa + sb) / 2;
573 else if (gc && gd) s = (sc + sd) / 2;
574 else if (ga && gc) s = (sa + sc) / 2;
575 else if (ga && gd) s = (sa + sd) / 2;
576 else if (gb && gc) s = (sb + sc) / 2;
577 else if (gb && gd) s = (sb + sd) / 2;
578 else {
579 // Intersection not within segments; place intersection in smallest gap.
580 if (p.c > 0) {
581 // distance from p to corner p0 is abs( (px - py) - (p0x - p0y) )
582 // consider corners p0 = [0, sy] and p0 = [sx, 0]
583 if (fabs((p.x - p.y) + sy) < fabs((p.x - p.y) - sx))
584 s = (sy - (p.x + p.y))/2;
585 else
586 s = (sx - (p.x + p.y))/2;
587 } else {
588 // distance from p to corner p0 is abs( (px + p.y) - (p0x + p0y) )
589 // consider corners p0 = [0, 0] and p0 = [sx, sy]
590 if (fabs(p.x + p.y) < fabs((p.x + p.y) - (sx + sy)))
591 s = (0 - (p.x - p.y))/2;
592 else
593 s = ((sx - sy) - (p.x - p.y))/2;
594 }
595 }
596 return p + XPoint(s, p.c*s);
597 }
598
599}
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::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