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# (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
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