File: trace.pyx

package info (click to toggle)
python-cartopy 0.18.0%2Bdfsg-2
  • links: PTS, VCS
  • area: main
  • in suites: bullseye
  • size: 18,204 kB
  • sloc: python: 15,593; makefile: 160; javascript: 65; sh: 6
file content (644 lines) | stat: -rw-r--r-- 24,188 bytes parent folder | download
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
# (C) British Crown Copyright 2011 - 2019, Met Office
#
# This file is part of cartopy.
#
# cartopy is free software: you can redistribute it and/or modify it under
# the terms of the GNU Lesser General Public License as published by the
# Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# cartopy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with cartopy.  If not, see <https://www.gnu.org/licenses/>.
#
# cython: embedsignature=True

"""
This module pulls together proj, GEOS and ``_crs.pyx`` to implement a function
to project a `~shapely.geometry.LinearRing` / `~shapely.geometry.LineString`.
In general, this should never be called manually, instead leaving the
processing to be done by the :class:`cartopy.crs.Projection` subclasses.
"""

cimport cython
from libc.math cimport HUGE_VAL, sqrt
from numpy.math cimport isfinite, isnan
from libc.stdint cimport uintptr_t as ptr
from libcpp cimport bool
from libcpp.list cimport list
from libcpp.vector cimport vector

cdef bool DEBUG = False

cdef extern from "geos_c.h":
    ctypedef void *GEOSContextHandle_t
    ctypedef struct GEOSGeometry:
        pass
    ctypedef struct GEOSCoordSequence
    ctypedef struct GEOSPreparedGeometry
    GEOSCoordSequence *GEOSCoordSeq_create_r(GEOSContextHandle_t, unsigned int, unsigned int) nogil
    GEOSGeometry *GEOSGeom_createPoint_r(GEOSContextHandle_t, GEOSCoordSequence *) nogil
    GEOSGeometry *GEOSGeom_createLineString_r(GEOSContextHandle_t, GEOSCoordSequence *) nogil
    GEOSGeometry *GEOSGeom_createCollection_r(GEOSContextHandle_t, int, GEOSGeometry **, unsigned int) nogil
    GEOSGeometry *GEOSGeom_createEmptyCollection_r(GEOSContextHandle_t, int) nogil
    void GEOSGeom_destroy_r(GEOSContextHandle_t, GEOSGeometry *) nogil
    GEOSCoordSequence *GEOSGeom_getCoordSeq_r(GEOSContextHandle_t, GEOSGeometry *) nogil
    int GEOSCoordSeq_getSize_r(GEOSContextHandle_t handle, const GEOSCoordSequence* s, unsigned int *size) nogil
    int GEOSCoordSeq_getX_r(GEOSContextHandle_t, GEOSCoordSequence *, int, double *) nogil
    int GEOSCoordSeq_getY_r(GEOSContextHandle_t, GEOSCoordSequence *, int, double *) nogil
    int GEOSCoordSeq_setX_r(GEOSContextHandle_t, GEOSCoordSequence *, int, double) nogil
    int GEOSCoordSeq_setY_r(GEOSContextHandle_t, GEOSCoordSequence *, int, double) nogil
    const GEOSPreparedGeometry *GEOSPrepare_r(GEOSContextHandle_t handle, const GEOSGeometry* g) nogil
    char GEOSPreparedCovers_r(GEOSContextHandle_t, const GEOSPreparedGeometry*, const GEOSGeometry*) nogil
    char GEOSPreparedDisjoint_r(GEOSContextHandle_t, const GEOSPreparedGeometry*, const GEOSGeometry*) nogil
    void GEOSPreparedGeom_destroy_r(GEOSContextHandle_t handle, const GEOSPreparedGeometry* g) nogil
    cdef int GEOS_MULTILINESTRING

from cartopy._crs cimport CRS
from cartopy._crs import PROJ4_VERSION
from ._proj4 cimport (projPJ, projLP, pj_get_spheroid_defn, pj_transform,
                      pj_strerrno, DEG_TO_RAD)
from .geodesic._geodesic cimport (geod_geodesic, geod_geodesicline,
                                  geod_init, geod_geninverse,
                                  geod_lineinit, geod_genposition,
                                  GEOD_ARCMODE, GEOD_LATITUDE, GEOD_LONGITUDE)


import shapely.geometry as sgeom
from shapely.geos import lgeos


cdef GEOSContextHandle_t get_geos_context_handle():
    cdef ptr handle = lgeos.geos_handle
    return <GEOSContextHandle_t>handle


cdef GEOSGeometry *geos_from_shapely(shapely_geom) except *:
    """Get the GEOS pointer from the given shapely geometry."""
    cdef ptr geos_geom = shapely_geom._geom
    return <GEOSGeometry *>geos_geom


cdef shapely_from_geos(GEOSGeometry *geom):
    """Turn the given GEOS geometry pointer into a shapely geometry."""
    return sgeom.base.geom_factory(<ptr>geom)


ctypedef struct Point:
    double x
    double y

ctypedef list[Point] Line


cdef bool degenerate_line(const Line &value):
    return value.size() < 2


cdef bool close(double a, double b):
    return abs(a - b) <= (1e-8 + 1e-5 * abs(b))


@cython.final
cdef class LineAccumulator:
    cdef list[Line] lines

    def __init__(self):
        self.new_line()

    cdef void new_line(self):
        cdef Line line
        self.lines.push_back(line)

    cdef void add_point(self, const Point &point):
        self.lines.back().push_back(point)

    cdef void add_point_if_empty(self, const Point &point):
        if self.lines.back().empty():
            self.add_point(point)

    cdef GEOSGeometry *as_geom(self, GEOSContextHandle_t handle):
        from cython.operator cimport dereference, preincrement
        # self.lines.remove_if(degenerate_line) is not available in Cython.
        cdef list[Line].iterator it = self.lines.begin()
        while it != self.lines.end():
            if degenerate_line(dereference(it)):
                it = self.lines.erase(it)
            else:
                preincrement(it)

        cdef Point first, last
        if self.lines.size() > 1:
            first = self.lines.front().front()
            last = self.lines.back().back()
            if close(first.x, last.x) and close(first.y, last.y):
                self.lines.front().pop_front()
                self.lines.back().splice(self.lines.back().end(),
                                         self.lines.front())
                self.lines.pop_front()

        cdef Line ilines
        cdef Point ipoints
        cdef vector[GEOSGeometry *] geoms
        cdef int i
        cdef GEOSCoordSequence *coords
        for ilines in self.lines:
            coords = GEOSCoordSeq_create_r(handle, ilines.size(), 2)
            for i, ipoints in enumerate(ilines):
                GEOSCoordSeq_setX_r(handle, coords, i, ipoints.x)
                GEOSCoordSeq_setY_r(handle, coords, i, ipoints.y)

            geoms.push_back(GEOSGeom_createLineString_r(handle, coords))

        cdef GEOSGeometry *geom
        if geoms.empty():
            geom = GEOSGeom_createEmptyCollection_r(handle,
                                                    GEOS_MULTILINESTRING)
        else:
            geom = GEOSGeom_createCollection_r(handle, GEOS_MULTILINESTRING,
                                               &geoms[0], geoms.size())
        return geom

    cdef size_t size(self):
        return self.lines.size()


cdef class Interpolator:
    cdef Point start
    cdef Point end
    cdef projPJ src_proj
    cdef projPJ dest_proj
    cdef double src_scale
    cdef double dest_scale

    def __cinit__(self):
        self.src_scale = 1
        self.dest_scale = 1

    cdef void init(self, projPJ src_proj, projPJ dest_proj):
        self.src_proj = src_proj
        self.dest_proj = dest_proj

    cdef void set_line(self, const Point &start, const Point &end):
        self.start = start
        self.end = end

    cdef Point interpolate(self, double t):
        raise NotImplementedError

    cdef Point project(self, const Point &point):
        raise NotImplementedError


cdef class CartesianInterpolator(Interpolator):
    cdef Point interpolate(self, double t):
        cdef Point xy
        xy.x = self.start.x + (self.end.x - self.start.x) * t
        xy.y = self.start.y + (self.end.y - self.start.y) * t
        return self.project(xy)

    cdef Point project(self, const Point &src_xy):
        cdef Point dest_xy
        cdef projLP xy

        xy.u = src_xy.x * self.src_scale
        xy.v = src_xy.y * self.src_scale

        cdef int status = pj_transform(self.src_proj, self.dest_proj,
                                       1, 1, &xy.u, &xy.v, NULL)
        if status in (-14, -20):
            # -14 => "latitude or longitude exceeded limits"
            # -20 => "tolerance condition error"
            xy.u = xy.v = HUGE_VAL
        elif status != 0:
            raise Exception('pj_transform failed: %d\n%s' % (
                status,
                pj_strerrno(status)))

        dest_xy.x = xy.u * self.dest_scale
        dest_xy.y = xy.v * self.dest_scale
        return dest_xy


cdef class SphericalInterpolator(Interpolator):
    cdef geod_geodesic geod
    cdef geod_geodesicline geod_line
    cdef double a13

    cdef void init(self, projPJ src_proj, projPJ dest_proj):
        self.src_proj = src_proj
        self.dest_proj = dest_proj

        cdef double major_axis
        cdef double eccentricity_squared
        pj_get_spheroid_defn(self.src_proj, &major_axis, &eccentricity_squared)
        geod_init(&self.geod, major_axis, 1 - sqrt(1 - eccentricity_squared))

    cdef void set_line(self, const Point &start, const Point &end):
        cdef double azi1
        self.a13 = geod_geninverse(&self.geod,
                                   start.y, start.x, end.y, end.x,
                                   NULL, &azi1, NULL, NULL, NULL, NULL, NULL)
        geod_lineinit(&self.geod_line, &self.geod, start.y, start.x, azi1,
                      GEOD_LATITUDE | GEOD_LONGITUDE);

    cdef Point interpolate(self, double t):
        cdef Point lonlat

        geod_genposition(&self.geod_line, GEOD_ARCMODE, self.a13 * t,
                         &lonlat.y, &lonlat.x, NULL, NULL, NULL, NULL, NULL,
                         NULL)

        return self.project(lonlat)

    cdef Point project(self, const Point &lonlat):
        cdef Point xy
        cdef projLP dest

        dest.u = (lonlat.x * DEG_TO_RAD) * self.src_scale
        dest.v = (lonlat.y * DEG_TO_RAD) * self.src_scale

        cdef int status = pj_transform(self.src_proj, self.dest_proj,
                                       1, 1, &dest.u, &dest.v, NULL)
        if status in (-14, -20):
            # -14 => "latitude or longitude exceeded limits"
            # -20 => "tolerance condition error"
            dest.u = dest.v = HUGE_VAL
        elif status != 0:
            raise Exception('pj_transform failed: %d\n%s' % (
                status,
                pj_strerrno(status)))

        xy.x = dest.u * self.dest_scale
        xy.y = dest.v * self.dest_scale
        return xy


cdef enum State:
    POINT_IN = 1,
    POINT_OUT,
    POINT_NAN


cdef State get_state(const Point &point, const GEOSPreparedGeometry *gp_domain,
                     GEOSContextHandle_t handle):
    cdef State state
    cdef GEOSCoordSequence *coords
    cdef GEOSGeometry *g_point

    if isfinite(point.x) and isfinite(point.y):
        # TODO: Avoid create-destroy
        coords = GEOSCoordSeq_create_r(handle, 1, 2)
        GEOSCoordSeq_setX_r(handle, coords, 0, point.x)
        GEOSCoordSeq_setY_r(handle, coords, 0, point.y)
        g_point = GEOSGeom_createPoint_r(handle, coords)
        state = (POINT_IN
                 if GEOSPreparedCovers_r(handle, gp_domain, g_point)
                 else POINT_OUT)
        GEOSGeom_destroy_r(handle, g_point)
    else:
        state = POINT_NAN
    return state


@cython.cdivision(True)  # Want divide-by-zero to produce NaN.
cdef bool straightAndDomain(double t_start, const Point &p_start,
                            double t_end, const Point &p_end,
                            Interpolator interpolator, double threshold,
                            GEOSContextHandle_t handle,
                            const GEOSPreparedGeometry *gp_domain,
                            bool inside):
    """
    Return whether the given line segment is suitable as an
    approximation of the projection of the source line.

    t_start: Interpolation parameter for the start point.
    p_start: Projected start point.
    t_end: Interpolation parameter for the end point.
    p_start: Projected end point.
    interpolator: Interpolator for current source line.
    threshold: Lateral tolerance in target projection coordinates.
    handle: Thread-local context handle for GEOS.
    gp_domain: Prepared polygon of target map domain.
    inside: Whether the start point is within the map domain.

    """
    # Straight and in-domain (de9im[7] == 'F')
    cdef bool valid
    cdef double t_mid
    cdef Point p_mid
    cdef double seg_dx, seg_dy
    cdef double mid_dx, mid_dy
    cdef double seg_hypot_sq
    cdef double along
    cdef double separation
    cdef double hypot
    cdef GEOSCoordSequence *coords
    cdef GEOSGeometry *g_segment

    # This could be optimised out of the loop.
    if not (isfinite(p_start.x) and isfinite(p_start.y)):
        valid = False
    elif not (isfinite(p_end.x) and isfinite(p_end.y)):
        valid = False
    else:
        # Find the projected mid-point
        t_mid = (t_start + t_end) * 0.5
        p_mid = interpolator.interpolate(t_mid)

        # Determine the closest point on the segment to the midpoint, in
        # normalized coordinates. We could use GEOSProjectNormalized_r
        # here, but since it's a single line segment, it's much easier to
        # just do the math ourselves:
        #     ○̩ (x1, y1) (assume that this is not necessarily vertical)
        #     │
        #     │   D
        #    ╭├───────○ (x, y)
        #    ┊│┘     ╱
        #    ┊│     ╱
        #    ┊│    ╱
        #    L│   ╱
        #    ┊│  ╱
        #    ┊│θ╱
        #    ┊│╱
        #    ╰̍○̍
        #  (x0, y0)
        # The angle θ can be found by arctan2:
        #     θ = arctan2(y1 - y0, x1 - x0) - arctan2(y - y0, x - x0)
        # and the projection onto the line is simply:
        #     L = hypot(x - x0, y - y0) * cos(θ)
        # with the normalized form being:
        #     along = L / hypot(x1 - x0, y1 - y0)
        #
        # Plugging those into SymPy and .expand().simplify(), we get the
        # following equations (with a slight refactoring to reuse some
        # intermediate values):
        seg_dx = p_end.x - p_start.x
        seg_dy = p_end.y - p_start.y
        mid_dx = p_mid.x - p_start.x
        mid_dy = p_mid.y - p_start.y
        seg_hypot_sq = seg_dx*seg_dx + seg_dy*seg_dy

        along = (seg_dx*mid_dx + seg_dy*mid_dy) / seg_hypot_sq

        if isnan(along):
            valid = True
        else:
            valid = 0.0 < along < 1.0
            if valid:
                # For the distance of the point from the line segment, using
                # the same geometry above, use sin instead of cos:
                #     D = hypot(x - x0, y - y0) * sin(θ)
                # and then simplify with SymPy again:
                separation = (abs(mid_dx*seg_dy - mid_dy*seg_dx) /
                              sqrt(seg_hypot_sq))
                if inside:
                    # Scale the lateral threshold by the distance from
                    # the nearest end. I.e. Near the ends the lateral
                    # threshold is much smaller; it only has its full
                    # value in the middle.
                    valid = (separation <=
                             threshold * 2.0 * (0.5 - abs(0.5 - along)))
                else:
                    # Check if the mid-point makes less than ~11 degree
                    # angle with the straight line.
                    # sin(11') => 0.2
                    # To save the square-root we just use the square of
                    # the lengths, hence:
                    # 0.2 ^ 2 => 0.04
                    hypot = mid_dx*mid_dx + mid_dy*mid_dy
                    valid = ((separation * separation) / hypot) < 0.04

        if valid:
            # TODO: Re-use geometries, instead of create-destroy!

            # Create a LineString for the current end-point.
            coords = GEOSCoordSeq_create_r(handle, 2, 2)
            GEOSCoordSeq_setX_r(handle, coords, 0, p_start.x)
            GEOSCoordSeq_setY_r(handle, coords, 0, p_start.y)
            GEOSCoordSeq_setX_r(handle, coords, 1, p_end.x)
            GEOSCoordSeq_setY_r(handle, coords, 1, p_end.y)
            g_segment = GEOSGeom_createLineString_r(handle, coords)

            if inside:
                valid = GEOSPreparedCovers_r(handle, gp_domain, g_segment)
            else:
                valid = GEOSPreparedDisjoint_r(handle, gp_domain, g_segment)

            GEOSGeom_destroy_r(handle, g_segment)

    return valid


cdef void bisect(double t_start, const Point &p_start, const Point &p_end,
                 GEOSContextHandle_t handle,
                 const GEOSPreparedGeometry *gp_domain, const State &state,
                 Interpolator interpolator, double threshold,
                 double &t_min, Point &p_min, double &t_max, Point &p_max):
    cdef double t_current
    cdef Point p_current
    cdef bool valid

    # Initialise our bisection range to the start and end points.
    (&t_min)[0] = t_start
    (&p_min)[0] = p_start
    (&t_max)[0] = 1.0
    (&p_max)[0] = p_end

    # Start the search at the end.
    t_current = t_max
    p_current = p_max

    # TODO: See if we can convert the 't' threshold into one based on the
    # projected coordinates - e.g. the resulting line length.

    while abs(t_max - t_min) > 1.0e-6:
        if DEBUG:
            print("t: ", t_current)

        if state == POINT_IN:
            # Straight and entirely-inside-domain
            valid = straightAndDomain(t_start, p_start, t_current, p_current,
                                      interpolator, threshold,
                                      handle, gp_domain, True)

        elif state == POINT_OUT:
            # Straight and entirely-outside-domain
            valid = straightAndDomain(t_start, p_start, t_current, p_current,
                                      interpolator, threshold,
                                      handle, gp_domain, False)
        else:
            valid = not isfinite(p_current.x) or not isfinite(p_current.y)

        if DEBUG:
            print("   => valid: ", valid)

        if valid:
            (&t_min)[0] = t_current
            (&p_min)[0] = p_current
        else:
            (&t_max)[0] = t_current
            (&p_max)[0] = p_current

        t_current = (t_min + t_max) * 0.5
        p_current = interpolator.interpolate(t_current)


cdef void _project_segment(GEOSContextHandle_t handle,
                           const GEOSCoordSequence *src_coords,
                           unsigned int src_idx_from, unsigned int src_idx_to,
                           Interpolator interpolator,
                           const GEOSPreparedGeometry *gp_domain,
                           double threshold, LineAccumulator lines):
    cdef Point p_current, p_min, p_max, p_end
    cdef double t_current, t_min, t_max
    cdef State state

    GEOSCoordSeq_getX_r(handle, src_coords, src_idx_from, &p_current.x)
    GEOSCoordSeq_getY_r(handle, src_coords, src_idx_from, &p_current.y)
    GEOSCoordSeq_getX_r(handle, src_coords, src_idx_to, &p_end.x)
    GEOSCoordSeq_getY_r(handle, src_coords, src_idx_to, &p_end.y)
    if DEBUG:
        print("Setting line:")
        print("   ", p_current.x, ", ", p_current.y)
        print("   ", p_end.x, ", ", p_end.y)

    interpolator.set_line(p_current, p_end)
    p_current = interpolator.project(p_current)
    p_end = interpolator.project(p_end)
    if DEBUG:
        print("Projected as:")
        print("   ", p_current.x, ", ", p_current.y)
        print("   ", p_end.x, ", ", p_end.y)

    t_current = 0.0
    state = get_state(p_current, gp_domain, handle)

    cdef size_t old_lines_size = lines.size()
    while t_current < 1.0 and (lines.size() - old_lines_size) < 100:
        if DEBUG:
            print("Bisecting from: ", t_current, " (")
            if state == POINT_IN:
                print("IN")
            elif state == POINT_OUT:
                print("OUT")
            else:
                print("NAN")
            print(")")
            print("   ", p_current.x, ", ", p_current.y)
            print("   ", p_end.x, ", ", p_end.y)

        bisect(t_current, p_current, p_end, handle, gp_domain, state,
               interpolator, threshold,
               t_min, p_min, t_max, p_max)
        if DEBUG:
            print("   => ", t_min, "to", t_max)
            print("   => (", p_min.x, ", ", p_min.y, ") to (",
                  p_max.x, ", ", p_max.y, ")")

        if state == POINT_IN:
            lines.add_point_if_empty(p_current)
            if t_min != t_current:
                lines.add_point(p_min)
                t_current = t_min
                p_current = p_min
            else:
                t_current = t_max
                p_current = p_max
                state = get_state(p_current, gp_domain, handle)
                if state == POINT_IN:
                    lines.new_line()

        elif state == POINT_OUT:
            if t_min != t_current:
                t_current = t_min
                p_current = p_min
            else:
                t_current = t_max
                p_current = p_max
                state = get_state(p_current, gp_domain, handle)
                if state == POINT_IN:
                    lines.new_line()

        else:
            t_current = t_max
            p_current = p_max
            state = get_state(p_current, gp_domain, handle)
            if state == POINT_IN:
                lines.new_line()


def project_linear(geometry not None, CRS src_crs not None,
                   dest_projection not None):
    """
    Project a geometry from one projection to another.

    Parameters
    ----------
    geometry : `shapely.geometry.LineString` or `shapely.geometry.LinearRing`
        A geometry to be projected.
    src_crs : cartopy.crs.CRS
        The coordinate system of the line to be projected.
    dest_projection : cartopy.crs.Projection
        The projection for the resulting projected line.

    Returns
    -------
    `shapely.geometry.MultiLineString`
        The result of projecting the given geometry from the source projection
        into the destination projection.

    """
    cdef:
        double threshold = dest_projection.threshold
        GEOSContextHandle_t handle = get_geos_context_handle()
        GEOSGeometry *g_linear = geos_from_shapely(geometry)
        Interpolator interpolator
        GEOSGeometry *g_domain
        const GEOSCoordSequence *src_coords
        unsigned int src_size, src_idx
        const GEOSPreparedGeometry *gp_domain
        LineAccumulator lines
        GEOSGeometry *g_multi_line_string

    g_domain = geos_from_shapely(dest_projection.domain)

    if src_crs.is_geodetic():
        interpolator = SphericalInterpolator()
    else:
        interpolator = CartesianInterpolator()
    interpolator.init(src_crs.proj4, (<CRS>dest_projection).proj4)
    if (6, 1, 1) <= PROJ4_VERSION < (6, 3, 0):
        # Workaround bug in Proj 6.1.1+ with +to_meter on +proj=ob_tran.
        # See https://github.com/OSGeo/proj#1782.
        lonlat = ('latlon', 'latlong', 'lonlat', 'longlat')
        if (src_crs.proj4_params.get('proj', '') == 'ob_tran' and
                src_crs.proj4_params.get('o_proj', '') in lonlat and
                'to_meter' in src_crs.proj4_params):
            interpolator.src_scale = src_crs.proj4_params['to_meter']
        if (dest_projection.proj4_params.get('proj', '') == 'ob_tran' and
                dest_projection.proj4_params.get('o_proj', '') in lonlat and
                'to_meter' in dest_projection.proj4_params):
            interpolator.dest_scale = 1 / dest_projection.proj4_params['to_meter']

    src_coords = GEOSGeom_getCoordSeq_r(handle, g_linear)
    gp_domain = GEOSPrepare_r(handle, g_domain)

    GEOSCoordSeq_getSize_r(handle, src_coords, &src_size)  # check exceptions

    lines = LineAccumulator()
    for src_idx in range(1, src_size):
        _project_segment(handle, src_coords, src_idx - 1, src_idx,
                         interpolator, gp_domain, threshold, lines);

    GEOSPreparedGeom_destroy_r(handle, gp_domain)

    g_multi_line_string = lines.as_geom(handle)

    del lines, interpolator
    multi_line_string = shapely_from_geos(g_multi_line_string)
    return multi_line_string