问题
I'm searching for algorithms to reduce the LOD of polylines, lines (looped or not) of nodes. In simple words, I want to take hi-resolution coastline data and be able to reduce its LOD hundred- or thousandfold to render it in small-scale.
I found polygon reduction algorithms (but they require triangles) and Laplacian smoothing, but that doesn't seem exactly what I need.
回答1:
I've modified the code in culebrón's answer, removing the need for the Vec2D/Line classes, instead handling the points as a list of tuples.
The code is slightly less tidy, but shorter, and a bit quicker (for 900 points, the original code took 2966ms, and this version takes 500ms - still a bit slower than I'd like, but an improvement)
def _vec2d_dist(p1, p2):
return (p1[0] - p2[0])**2 + (p1[1] - p2[1])**2
def _vec2d_sub(p1, p2):
return (p1[0]-p2[0], p1[1]-p2[1])
def _vec2d_mult(p1, p2):
return p1[0]*p2[0] + p1[1]*p2[1]
def ramerdouglas(line, dist):
"""Does Ramer-Douglas-Peucker simplification of a curve with `dist`
threshold.
`line` is a list-of-tuples, where each tuple is a 2D coordinate
Usage is like so:
>>> myline = [(0.0, 0.0), (1.0, 2.0), (2.0, 1.0)]
>>> simplified = ramerdouglas(myline, dist = 1.0)
"""
if len(line) < 3:
return line
(begin, end) = (line[0], line[-1]) if line[0] != line[-1] else (line[0], line[-2])
distSq = []
for curr in line[1:-1]:
tmp = (
_vec2d_dist(begin, curr) - _vec2d_mult(_vec2d_sub(end, begin), _vec2d_sub(curr, begin)) ** 2 / _vec2d_dist(begin, end))
distSq.append(tmp)
maxdist = max(distSq)
if maxdist < dist ** 2:
return [begin, end]
pos = distSq.index(maxdist)
return (ramerdouglas(line[:pos + 2], dist) +
ramerdouglas(line[pos + 1:], dist)[1:])
回答2:
The solution that I've found and quite probably will use, is Ramer-Douglas-Peucker algorithm. It's used in PostGIS
I've published my own implementation in Python (site currently down, the following was pulled from archive.org)
#!/usr/bin/python
"""Ramer-Douglas-Peucker line simplification demo.
Dmitri Lebedev, detail@ngs.ru
http://ryba4.com/python/ramer-douglas-peucker
2010-04-17"""
def ramerdouglas(line, dist):
"""Does Ramer-Douglas-Peucker simplification of
a line with `dist` threshold.
`line` must be a list of Vec objects,
all of the same type (either 2d or 3d)."""
if len(line) < 3:
return line
begin, end = line[0], line[-1]
distSq = [begin.distSq(curr) -
((end - begin) * (curr - begin)) ** 2 /
begin.distSq(end) for curr in line[1:-1]]
maxdist = max(distSq)
if maxdist < dist ** 2:
return [begin, end]
pos = distSq.index(maxdist)
return (ramerdouglas(line[:pos + 2], dist) +
ramerdouglas(line[pos + 1:], dist)[1:])
class Line:
"""Polyline. Contains a list of points and outputs
a simplified version of itself."""
def __init__(self, points):
pointclass = points[0].__class__
for i in points[1:]:
if i.__class__ != pointclass:
raise TypeError("""All points in a Line
must have the same type""")
self.points = points
def simplify(self, dist):
if self.points[0] != self.points[-1]:
points = ramerdouglas(self.points, dist)
else:
points = ramerdouglas(
self.points[:-1], dist) + self.points[-1:]
return self.__class__(points)
def __repr__(self):
return '{0}{1}'.format(self.__class__.__name__,
tuple(self.points))
class Vec:
"""Generic vector class for n-dimensional vectors
for any natural n."""
def __eq__(self, obj):
"""Equality check."""
if self.__class__ == obj.__class__:
return self.coords == obj.coords
return False
def __repr__(self):
"""String representation. The string is executable as Python
code and makes the same vector."""
return '{0}{1}'.format(self.__class__.__name__, self.coords)
def __add__(self, obj):
"""Add a vector."""
if not isinstance(obj, self.__class__):
raise TypeError
return self.__class__(*map(sum, zip(self.coords, obj.coords)))
def __neg__(self):
"""Reverse the vector."""
return self.__class__(*[-i for i in self.coords])
def __sub__(self, obj):
"""Substract object from self."""
if not isinstance(obj, self.__class__):
raise TypeError
return self + (- obj)
def __mul__(self, obj):
"""If obj is scalar, scales the vector.
If obj is vector returns the scalar product."""
if isinstance(obj, self.__class__):
return sum([a * b for (a, b) in zip(self.coords, obj.coords)])
return self.__class__(*[i * obj for i in self.coords])
def dist(self, obj = None):
"""Distance to another object. Leave obj empty to get
the length of vector from point 0."""
return self.distSq(obj) ** 0.5
def distSq(self, obj = None):
""" Square of distance. Use this method to save
calculations if you don't need to calculte an extra square root."""
if obj is None:
obj = self.__class__(*[0]*len(self.coords))
elif not isinstance(obj, self.__class__):
raise TypeError('Parameter must be of the same class')
# simple memoization to save extra calculations
if obj.coords not in self.distSqMem:
self.distSqMem[obj.coords] = sum([(s - o) ** 2 for (s, o) in
zip(self.coords, obj.coords)])
return self.distSqMem[obj.coords]
class Vec3D(Vec):
"""3D vector"""
def __init__(self, x, y, z):
self.coords = x, y, z
self.distSqMem = {}
class Vec2D(Vec):
"""2D vector"""
def __init__(self, x, y):
self.coords = x, y
self.distSqMem = {}
if __name__ == '__main__':
coast = Line([
Vec2D( 6.247872 , 11.316756 ),
Vec2D( 6.338566 , 11.316756 ),
Vec2D( 6.633323 , 11.205644 ),
Vec2D( 6.724018 , 11.205644 ),
Vec2D( 6.792039 , 11.205644 ),
Vec2D( 7.154817 , 11.372311 ),
Vec2D( 7.313532 , 11.400089 ),
Vec2D( 7.381553 , 11.344533 ),
Vec2D( 7.336206 , 11.288978 ),
Vec2D( 7.200164 , 11.288978 ),
Vec2D( 7.154817 , 11.261200 ),
Vec2D( 7.132143 , 11.233422 ),
Vec2D( 7.154817 , 11.150089 ),
Vec2D( 7.268185 , 11.177867 ),
Vec2D( 7.313532 , 11.122311 ),
Vec2D( 7.404227 , 11.150089 ),
Vec2D( 7.472248 , 11.094533 ),
Vec2D( 7.767005 , 10.900089 ),
Vec2D( 7.758951 , 10.864989 ),
Vec2D( 7.752684 , 10.837656 ),
Vec2D( 7.426900 , 10.927867 ),
Vec2D( 6.519955 , 10.927867 ),
Vec2D( 6.429261 , 10.900089 ),
Vec2D( 6.315893 , 10.955644 ),
Vec2D( 6.270545 , 10.955644 ),
Vec2D( 6.247872 , 10.927867 ),
Vec2D( 6.111830 , 11.011200 ),
Vec2D( 6.066483 , 11.066756 ),
Vec2D( 5.862420 , 11.038978 ),
Vec2D( 5.817073 , 10.955644 ),
Vec2D( 5.771726 , 10.900089 ),
Vec2D( 5.862420 , 10.761200 ),
Vec2D( 5.975788 , 10.733422 ),
Vec2D( 6.157177 , 10.566756 ),
Vec2D( 6.247872 , 10.511200 ),
Vec2D( 6.293219 , 10.427867 ),
Vec2D( 6.315893 , 10.233422 ),
Vec2D( 6.315893 , 10.177867 ),
Vec2D( 6.542629 , 9.844533 ),
Vec2D( 6.587976 , 9.761200 ),
Vec2D( 6.610650 , 9.288978 ),
Vec2D( 6.542629 , 9.066756 ),
Vec2D( 6.565303 , 8.900089 ),
Vec2D( 6.519955 , 8.816756 ),
Vec2D( 6.542629 , 8.761200 ),
Vec2D( 6.565303 , 8.733422 ),
Vec2D( 6.429261 , 8.427867 ),
Vec2D( 6.474608 , 8.316756 ),
Vec2D( 6.724018 , 8.288978 ),
Vec2D( 6.882733 , 8.538978 ),
Vec2D( 6.973428 , 8.594533 ),
Vec2D( 6.996101 , 8.622311 ),
Vec2D( 7.200164 , 8.650089 ),
Vec2D( 7.290859 , 8.650089 ),
Vec2D( 7.426900 , 8.483422 ),
Vec2D( 7.404227 , 8.455644 ),
Vec2D( 7.245511 , 8.511200 ),
Vec2D( 6.996101 , 8.427867 ),
Vec2D( 7.041449 , 8.372311 ),
Vec2D( 7.154817 , 8.455644 ),
Vec2D( 7.200164 , 8.455644 ),
Vec2D( 7.245511 , 8.455644 ),
Vec2D( 7.381553 , 8.316756 ),
Vec2D( 7.381553 , 8.261200 ),
Vec2D( 7.404227 , 8.233422 ),
Vec2D( 7.494921 , 8.205644 ),
Vec2D( 7.767005 , 8.288978 ),
Vec2D( 7.948394 , 8.233422 ),
Vec2D( 8.016415 , 8.261200 ),
Vec2D( 8.197804 , 8.094533 ),
Vec2D( 8.084435 , 7.816756 ),
Vec2D( 8.152456 , 7.733422 ),
Vec2D( 8.175130 , 7.650089 ),
Vec2D( 8.175130 , 7.511200 ),
Vec2D( 8.311172 , 7.427867 ),
Vec2D( 8.311172 , 7.372311 ),
Vec2D( 8.651276 , 7.372311 ),
Vec2D( 8.923360 , 7.316756 ),
Vec2D( 8.900686 , 7.261200 ),
Vec2D( 8.809991 , 7.261200 ),
Vec2D( 8.472735 , 7.171122 ),
Vec2D( 8.333845 , 7.038978 ),
Vec2D( 8.282022 , 6.981100 ),
Vec2D( 8.254778 , 6.848911 ),
Vec2D( 8.265824 , 6.816756 ),
Vec2D( 8.239206 , 6.711211 ),
Vec2D( 8.219743 , 6.612067 ),
Vec2D( 8.130227 , 6.433044 ),
Vec2D( 8.084435 , 6.316756 ),
Vec2D( 8.107109 , 6.288978 ),
Vec2D( 7.948394 , 6.177867 ),
Vec2D( 7.925720 , 5.983422 ),
Vec2D( 7.857699 , 5.816756 ),
Vec2D( 7.835026 , 5.788978 ),
Vec2D( 7.857699 , 5.511200 ),
Vec2D( 7.812352 , 5.400089 ),
Vec2D( 7.812352 , 5.344533 ),
Vec2D( 7.812352 , 5.177867 ),
Vec2D( 8.084435 , 4.733422 ),
Vec2D( 8.107109 , 4.622311 ),
Vec2D( 7.857699 , 4.344533 ),
Vec2D( 7.630963 , 4.261200 ),
Vec2D( 7.540268 , 4.177867 ),
Vec2D( 7.494921 , 4.150089 ),
Vec2D( 7.449574 , 4.150089 ),
Vec2D( 7.404227 , 4.150089 ),
Vec2D( 7.336206 , 4.094533 ),
Vec2D( 7.313532 , 4.066756 ),
Vec2D( 7.041449 , 4.011200 ),
Vec2D( 6.905407 , 3.955644 ),
Vec2D( 6.950754 , 3.900089 ),
Vec2D( 7.200164 , 3.927867 ),
Vec2D( 7.630963 , 3.872311 ),
Vec2D( 7.721657 , 3.872311 ),
Vec2D( 7.948394 , 3.788978 ),
Vec2D( 7.993741 , 3.705644 ),
Vec2D( 7.971067 , 3.677867 ),
Vec2D( 7.925720 , 3.622311 ),
Vec2D( 8.175130 , 3.705644 ),
Vec2D( 8.401866 , 3.650089 ),
Vec2D( 8.492561 , 3.650089 ),
Vec2D( 8.605929 , 3.538978 ),
Vec2D( 8.651276 , 3.566756 ),
Vec2D( 8.855339 , 3.372311 ),
Vec2D( 8.900686 , 3.316756 ),
Vec2D( 8.900686 , 3.150089 ),
Vec2D( 8.787318 , 2.900089 ),
Vec2D( 8.787318 , 2.844533 ),
Vec2D( 8.946033 , 2.816756 ),
Vec2D( 8.991380 , 2.788978 ),
Vec2D( 9.014054 , 2.705644 ),
Vec2D( 8.886928 , 2.524989 ),
Vec2D( 8.832665 , 2.538978 ),
Vec2D( 8.809991 , 2.455644 ),
Vec2D( 8.923360 , 2.538978 ),
Vec2D( 9.014054 , 2.400089 ),
Vec2D( 9.308811 , 2.288978 ),
Vec2D( 9.399506 , 2.261200 ),
Vec2D( 9.512874 , 2.122311 ),
Vec2D( 9.535548 , 1.983422 ),
Vec2D( 9.512874 , 1.955644 ),
Vec2D( 9.467527 , 1.816756 ),
Vec2D( 9.036728 , 1.816756 ),
Vec2D( 8.991380 , 1.927867 ),
Vec2D( 8.946033 , 1.955644 ),
Vec2D( 8.900686 , 1.983422 ),
Vec2D( 8.946033 , 2.122311 ),
Vec2D( 8.968707 , 2.150089 ),
Vec2D( 9.195443 , 1.927867 ),
Vec2D( 9.354158 , 1.955644 ),
Vec2D( 9.376832 , 2.038978 ),
Vec2D( 9.376832 , 2.094533 ),
Vec2D( 9.240790 , 2.205644 ),
Vec2D( 9.195443 , 2.205644 ),
Vec2D( 9.263464 , 2.150089 ),
Vec2D( 9.240790 , 2.122311 ),
Vec2D( 9.195443 , 2.122311 ),
Vec2D( 9.104749 , 2.122311 ),
Vec2D( 8.900686 , 2.316756 ),
Vec2D( 8.787318 , 2.344533 ),
Vec2D( 8.696623 , 2.372311 ),
Vec2D( 8.651276 , 2.427867 ),
Vec2D( 8.719297 , 2.455644 ),
Vec2D( 8.787318 , 2.650089 ),
Vec2D( 8.832665 , 2.705644 ),
Vec2D( 8.605929 , 2.677867 ),
Vec2D( 8.537908 , 2.788978 ),
Vec2D( 8.333845 , 2.788978 ),
Vec2D( 7.925720 , 2.316756 ),
Vec2D( 7.925720 , 2.261200 ),
Vec2D( 7.903046 , 2.233422 ),
Vec2D( 7.857699 , 2.233422 ),
Vec2D( 7.857699 , 2.177867 ),
Vec2D( 7.789678 , 1.983422 ),
Vec2D( 7.812352 , 1.788978 ),
Vec2D( 7.948394 , 1.538978 ),
Vec2D( 7.971067 , 1.511200 ),
Vec2D( 8.129783 , 1.511200 ),
Vec2D( 8.243151 , 1.594533 ),
Vec2D( 8.333845 , 1.594533 ),
Vec2D( 8.424540 , 1.622311 ),
Vec2D( 8.515234 , 1.566756 ),
Vec2D( 8.673950 , 1.400089 ),
Vec2D( 8.771174 , 1.291756 ),
Vec2D( 8.828938 , 1.119878 ),
Vec2D( 8.762504 , 0.972544 ),
Vec2D( 9.238614 , 0.759633 ),
Vec2D( 9.492323 , 0.627022 ),
Vec2D( 9.820891 , 0.644711 ),
Vec2D( 10.376567 , 0.800622 ),
Vec2D( 10.651961 , 1.085978 ),
Vec2D( 10.762173 , 1.132022 ),
Vec2D( 10.943045 , 1.095989 ),
Vec2D( 11.256739 , 0.999878 ),
Vec2D( 11.576074 , 0.761611 ),
Vec2D( 11.768247 , 0.425211 ),
Vec2D( 11.960165 , 0.074778 ),
Vec2D( 11.953907 , 0.000000 ),
Vec2D( 11.629411 , 0.258767 ),
Vec2D( 11.229920 , 0.582278 ),
Vec2D( 11.001633 , 0.564300 ),
Vec2D( 10.868476 , 0.447478 ),
Vec2D( 10.633849 , 0.541833 ),
Vec2D( 10.513370 , 0.672133 ),
Vec2D( 11.188700 , 0.820078 ),
Vec2D( 11.194014 , 0.859656 ),
Vec2D( 11.118212 , 0.905822 ),
Vec2D( 10.874860 , 0.930311 ),
Vec2D( 10.427319 , 0.716522 ),
Vec2D( 10.023620 , 0.374211 ),
Vec2D( 9.434614 , 0.360144 ),
Vec2D( 8.455131 , 0.859544 ),
Vec2D( 8.180481 , 0.920500 ),
Vec2D( 7.902529 , 1.115078 ),
Vec2D( 7.823108 , 1.269800 ),
Vec2D( 7.830482 , 1.403778 ),
Vec2D( 7.791937 , 1.496744 ),
Vec2D( 7.767005 , 1.538978 ),
Vec2D( 7.676310 , 1.622311 ),
Vec2D( 7.653637 , 1.650089 ),
Vec2D( 7.585616 , 1.955644 ),
Vec2D( 7.562942 , 1.983422 ),
Vec2D( 7.562942 , 2.233422 ),
Vec2D( 7.608289 , 2.400089 ),
Vec2D( 7.630963 , 2.427867 ),
Vec2D( 7.608289 , 2.538978 ),
Vec2D( 7.585616 , 2.566756 ),
Vec2D( 7.653637 , 2.705644 ),
Vec2D( 7.630963 , 2.816756 ),
Vec2D( 7.336206 , 3.011200 ),
Vec2D( 7.290859 , 3.011200 ),
Vec2D( 7.245511 , 3.011200 ),
Vec2D( 7.041449 , 2.955644 ),
Vec2D( 6.928081 , 2.816756 ),
Vec2D( 6.928081 , 2.733422 ),
Vec2D( 6.905407 , 2.622311 ),
Vec2D( 6.860060 , 2.677867 ),
Vec2D( 6.814712 , 2.677867 ),
Vec2D( 6.678671 , 2.677867 ),
Vec2D( 6.678671 , 2.733422 ),
Vec2D( 6.769365 , 2.733422 ),
Vec2D( 6.814712 , 2.733422 ),
Vec2D( 6.792039 , 2.788978 ),
Vec2D( 6.293219 , 3.066756 ),
Vec2D( 6.225198 , 3.122311 ),
Vec2D( 6.202525 , 3.233422 ),
Vec2D( 6.134504 , 3.344533 ),
Vec2D( 5.907767 , 3.261200 ),
Vec2D( 5.862420 , 3.288978 ),
Vec2D( 6.043809 , 3.427867 ),
Vec2D( 6.021136 , 3.483422 ),
Vec2D( 5.975788 , 3.483422 ),
Vec2D( 5.930441 , 3.511200 ),
Vec2D( 5.953115 , 3.566756 ),
Vec2D( 5.975788 , 3.594533 ),
Vec2D( 5.749052 , 3.788978 ),
Vec2D( 5.703705 , 3.788978 ),
Vec2D( 5.635684 , 3.788978 ),
Vec2D( 5.703705 , 3.844533 ),
Vec2D( 5.703705 , 4.011200 ),
Vec2D( 5.499642 , 4.011200 ),
Vec2D( 5.862420 , 4.372311 ),
Vec2D( 5.975788 , 4.427867 ),
Vec2D( 6.021136 , 4.427867 ),
Vec2D( 6.089156 , 4.538978 ),
Vec2D( 6.111830 , 4.566756 ),
Vec2D( 6.089156 , 4.650089 ),
Vec2D( 5.998462 , 4.650089 ),
Vec2D( 5.817073 , 4.788978 ),
Vec2D( 5.771726 , 4.816756 ),
Vec2D( 5.681031 , 4.816756 ),
Vec2D( 5.749052 , 4.927867 ),
Vec2D( 5.749052 , 5.038978 ),
Vec2D( 5.839747 , 5.177867 ),
Vec2D( 5.998462 , 5.233422 ),
Vec2D( 6.225198 , 5.233422 ),
Vec2D( 6.270545 , 5.233422 ),
Vec2D( 6.383914 , 5.288978 ),
Vec2D( 6.406587 , 5.372311 ),
Vec2D( 6.429261 , 5.400089 ),
Vec2D( 6.587976 , 5.483422 ),
Vec2D( 6.670626 , 5.490000 ),
Vec2D( 6.700845 , 5.564100 ),
Vec2D( 6.860060 , 5.927867 ),
Vec2D( 6.860060 , 6.038978 ),
Vec2D( 6.950754 , 6.205644 ),
Vec2D( 6.973428 , 6.316756 ),
Vec2D( 7.041449 , 6.344533 ),
Vec2D( 7.064122 , 6.455644 ),
Vec2D( 7.116072 , 6.541989 ),
Vec2D( 7.114313 , 6.603667 ),
Vec2D( 7.025305 , 6.741422 ),
Vec2D( 6.736924 , 6.701367 ),
Vec2D( 6.641658 , 6.741467 ),
Vec2D( 6.500574 , 6.761389 ),
Vec2D( 6.435410 , 6.733422 ),
Vec2D( 6.224291 , 6.728556 ),
Vec2D( 6.191759 , 6.738989 ),
Vec2D( 6.099124 , 6.755000 ),
Vec2D( 6.041805 , 6.749733 ),
Vec2D( 6.001672 , 6.742967 ),
Vec2D( 5.905382 , 6.718300 ),
Vec2D( 5.817073 , 6.677867 ),
Vec2D( 5.611713 , 6.686622 ),
Vec2D( 5.401366 , 6.864333 ),
Vec2D( 5.386274 , 6.927867 ),
Vec2D( 5.356608 , 6.981811 ),
Vec2D( 5.404095 , 7.111822 ),
Vec2D( 5.561958 , 7.216133 ),
Vec2D( 5.660643 , 7.244722 ),
Vec2D( 5.366149 , 7.489478 ),
Vec2D( 5.340927 , 7.511200 ),
Vec2D( 5.114998 , 7.592867 ),
Vec2D( 4.870667 , 7.692033 ),
Vec2D( 4.746560 , 7.781856 ),
Vec2D( 4.708060 , 7.760867 ),
Vec2D( 4.692225 , 7.802500 ),
Vec2D( 4.607090 , 7.849044 ),
Vec2D( 4.481324 , 7.879711 ),
Vec2D( 4.340031 , 8.093378 ),
Vec2D( 4.181171 , 8.158044 ),
Vec2D( 4.116415 , 8.200800 ),
Vec2D( 4.081135 , 8.195278 ),
Vec2D( 4.090912 , 8.272500 ),
Vec2D( 4.032232 , 8.378311 ),
Vec2D( 3.779566 , 8.791278 ),
Vec2D( 3.769654 , 8.849022 ),
Vec2D( 3.598177 , 8.955178 ),
Vec2D( 3.576828 , 9.059633 ),
Vec2D( 3.527037 , 9.066756 ),
Vec2D( 3.498069 , 9.082022 ),
Vec2D( 3.541865 , 9.174211 ),
Vec2D( 3.542409 , 9.234411 ),
Vec2D( 3.576275 , 9.262711 ),
Vec2D( 3.582279 , 9.287744 ),
Vec2D( 3.390995 , 9.316756 ),
Vec2D( 3.209606 , 9.344533 ),
Vec2D( 3.100836 , 9.367511 ),
Vec2D( 2.957466 , 9.370756 ),
Vec2D( 2.870844 , 9.366222 ),
Vec2D( 2.777211 , 9.285222 ),
Vec2D( 2.744851 , 9.285900 ),
Vec2D( 2.775397 , 9.294867 ),
Vec2D( 2.832661 , 9.341156 ),
Vec2D( 2.868114 , 9.373300 ),
Vec2D( 2.869502 , 9.400089 ),
Vec2D( 2.794434 , 9.420178 ),
Vec2D( 2.714423 , 9.440078 ),
Vec2D( 2.641124 , 9.441944 ),
Vec2D( 2.572096 , 9.428378 ),
Vec2D( 2.548379 , 9.418600 ),
Vec2D( 2.573130 , 9.388211 ),
Vec2D( 2.563126 , 9.333567 ),
Vec2D( 2.535855 , 9.320067 ),
Vec2D( 2.517670 , 9.282778 ),
Vec2D( 2.479488 , 9.260278 ),
Vec2D( 2.483125 , 9.239067 ),
Vec2D( 2.464034 , 9.224278 ),
Vec2D( 2.468586 , 9.180556 ),
Vec2D( 2.443129 , 9.168989 ),
Vec2D( 2.439084 , 9.147456 ),
Vec2D( 2.448389 , 9.129344 ),
Vec2D( 2.444897 , 9.109600 ),
Vec2D( 2.450720 , 9.097256 ),
Vec2D( 2.444897 , 9.080389 ),
Vec2D( 2.447808 , 9.045822 ),
Vec2D( 2.424536 , 9.024011 ),
Vec2D( 2.415811 , 9.000133 ),
Vec2D( 2.442457 , 8.957422 ),
Vec2D( 2.429887 , 8.946567 ),
Vec2D( 2.455028 , 8.894556 ),
Vec2D( 2.435936 , 8.879078 ),
Vec2D( 2.413136 , 8.853411 ),
Vec2D( 2.410805 , 8.836944 ),
Vec2D( 2.412202 , 8.822133 ),
Vec2D( 2.387533 , 8.789544 ),
Vec2D( 2.386608 , 8.776044 ),
Vec2D( 2.398706 , 8.757278 ),
Vec2D( 2.373103 , 8.739511 ),
Vec2D( 2.387070 , 8.769467 ),
Vec2D( 2.375434 , 8.784611 ),
Vec2D( 2.358674 , 8.785922 ),
Vec2D( 2.337270 , 8.793167 ),
Vec2D( 2.365195 , 8.790533 ),
Vec2D( 2.399169 , 8.821478 ),
Vec2D( 2.396376 , 8.837933 ),
Vec2D( 2.408946 , 8.879078 ),
Vec2D( 2.432218 , 8.894878 ),
Vec2D( 2.414995 , 8.963022 ),
Vec2D( 2.390961 , 8.983722 ),
Vec2D( 2.340091 , 8.969389 ),
Vec2D( 2.332091 , 8.946244 ),
Vec2D( 2.340091 , 8.927722 ),
Vec2D( 2.332091 , 8.912289 ),
Vec2D( 2.316093 , 8.904067 ),
Vec2D( 2.311730 , 8.874744 ),
Vec2D( 2.288975 , 8.861244 ),
Vec2D( 2.247727 , 8.856233 ),
Vec2D( 2.233180 , 8.861889 ),
Vec2D( 2.209436 , 8.859233 ),
Vec2D( 2.231003 , 8.871144 ),
Vec2D( 2.265911 , 8.873200 ),
Vec2D( 2.277548 , 8.869600 ),
Vec2D( 2.290635 , 8.873711 ),
Vec2D( 2.299360 , 8.904578 ),
Vec2D( 2.268088 , 8.909622 ),
Vec2D( 2.247727 , 8.925256 ),
Vec2D( 2.225734 , 8.920756 ),
Vec2D( 2.208747 , 8.909622 ),
Vec2D( 2.203768 , 8.921811 ),
Vec2D( 2.214352 , 8.931822 ),
Vec2D( 2.197138 , 8.933811 ),
Vec2D( 2.148725 , 8.907478 ),
Vec2D( 2.134577 , 8.904844 ),
Vec2D( 2.113354 , 8.917222 ),
Vec2D( 2.095107 , 8.918800 ),
Vec2D( 2.079961 , 8.912944 ),
Vec2D( 2.060761 , 8.913356 ),
Vec2D( 2.034577 , 8.902656 ),
Vec2D( 1.983589 , 8.895400 ),
Vec2D( 2.033997 , 8.913356 ),
Vec2D( 2.062502 , 8.918700 ),
Vec2D( 2.092758 , 8.929811 ),
Vec2D( 2.148090 , 8.928756 ),
Vec2D( 2.168397 , 8.937878 ),
Vec2D( 2.146421 , 8.965533 ),
Vec2D( 2.182173 , 8.943933 ),
Vec2D( 2.201537 , 8.951311 ),
Vec2D( 2.239138 , 8.938400 ),
Vec2D( 2.267063 , 8.944989 ),
Vec2D( 2.284939 , 8.925767 ),
Vec2D( 2.306887 , 8.926022 ),
Vec2D( 2.311086 , 8.936356 ),
Vec2D( 2.296312 , 8.952489 ),
Vec2D( 2.317254 , 8.981122 ),
Vec2D( 2.334939 , 9.003844 ),
Vec2D( 2.374500 , 9.014044 ),
Vec2D( 2.386136 , 9.034778 ),
Vec2D( 2.401962 , 9.044656 ),
Vec2D( 2.418723 , 9.044889 ),
Vec2D( 2.426287 , 9.054878 ),
Vec2D( 2.411739 , 9.063522 ),
Vec2D( 2.426867 , 9.099311 ),
Vec2D( 2.398362 , 9.125233 ),
Vec2D( 2.373339 , 9.121944 ),
Vec2D( 2.403595 , 9.134289 ),
Vec2D( 2.417680 , 9.165778 ),
Vec2D( 2.425860 , 9.192778 ),
Vec2D( 2.423783 , 9.231400 ),
Vec2D( 2.400330 , 9.237022 ),
Vec2D( 2.419494 , 9.243567 ),
Vec2D( 2.429815 , 9.246711 ),
Vec2D( 2.449495 , 9.245489 ),
Vec2D( 2.457676 , 9.289856 ),
Vec2D( 2.481311 , 9.298211 ),
Vec2D( 2.488585 , 9.334211 ),
Vec2D( 2.520255 , 9.353822 ),
Vec2D( 2.520400 , 9.369944 ),
Vec2D( 2.494960 , 9.432511 ),
Vec2D( 2.463671 , 9.469200 ),
Vec2D( 2.406950 , 9.500578 ),
Vec2D( 2.240907 , 9.536433 ),
Vec2D( 2.129969 , 9.569467 ),
Vec2D( 2.031530 , 9.607422 ),
Vec2D( 1.932328 , 9.658044 ),
Vec2D( 1.835167 , 9.695656 ),
Vec2D( 1.746196 , 9.760744 ),
Vec2D( 1.667446 , 9.789667 ),
Vec2D( 1.575400 , 9.797622 ),
Vec2D( 1.562104 , 9.828722 ),
Vec2D( 1.531422 , 9.846800 ),
Vec2D( 1.415859 , 9.888744 ),
Vec2D( 1.315206 , 9.942167 ),
Vec2D( 1.175573 , 10.083667 ),
Vec2D( 1.147394 , 10.090267 ),
Vec2D( 1.118064 , 10.086567 ),
Vec2D( 0.990883 , 9.998400 ),
Vec2D( 0.778930 , 9.990856 ),
Vec2D( 0.592924 , 10.033144 ),
Vec2D( 0.507490 , 10.125422 ),
Vec2D( 0.419562 , 10.320811 ),
Vec2D( 0.375403 , 10.344533 ),
Vec2D( 0.276464 , 10.431189 ),
Vec2D( 0.220170 , 10.534911 ),
Vec2D( 0.181271 , 10.571000 ),
Vec2D( 0.153745 , 10.620156 ),
Vec2D( 0.114973 , 10.653889 ),
Vec2D( 0.103274 , 10.707756 ),
Vec2D( 0.097914 , 10.761511 ),
Vec2D( 0.076256 , 10.811522 ),
Vec2D( 0.061935 , 10.867833 ),
Vec2D( 0.000000 , 10.960167 )
])
distances = (0, .05, .1, .25) # threshold sizes in kilometres
import csv
for d in distances:
simple = coast.simplify(d) if d > 0 else coast
with open('poly-{0}.csv'.format(d), 'w') as output_doc:
writer = csv.writer(output_doc, dialect='excel')
for pt in simple.points:
writer.writerow(pt.coords)
回答3:
When I was looking at turning a Bezier curve into straight line segments, what I ended up doing was defining a maximum distance between the curve and a straight line between two points of the curve. Start with one point being one end-point, slide the other end along the curve, until sliding it any further would exceed the maximum distance. Then do it again, using the second (and so on) point, until you've covered the whole curve.
You should be able to generate multiple LODs by simply increasing the distance allowed between the line segments and your poly-line.
回答4:
I developed a very simple algorithm, using the distance of a given point to the following points to decide whether it makes sense to include them in the rendering. Depending on current scale you could associate a minimum distance between points required for a transformed model.
回答5:
I'm a fan of sorting the points based on the angle that the segments make on either side of the point, then removing the points with the shallowest angle iteratively until you hit some threshold. O(n log(n)) I think, versus the RDP method's O(n^2), and with smaller constants to boot. :)
The angle can even be scaled by the segment lengths (indeed it's easier to compute it this way) if you want to give more weight (desirability) to longer segments.
Given p0, p1, p2, p1's weight would be ((p0 - p1) dot (p2 - p1)), normalize the differences if you don't want to weight by length. (Contrast this to distance-to-line, it is much cheaper, and the results may be identical.)
回答6:
Late to the party, but here's a Java implementation of the douglas peucker algorithm.
https://github.com/MKergall/osmbonuspack/blob/0310258c53244a485fda0ff0dd7829e5557b531b/OSMBonusPack/src/main/java/org/osmdroid/bonuspack/utils/DouglasPeuckerReducer.java
回答7:
Adding to the slew of answers. I found a javascript implementation at this github repo: https://github.com/mourner/simplify-js
There's also a list of different implementations of the Ramer-Douglas-Peucker algorithm in different languages.
回答8:
In regards to culebron's answer, is the recursive call correct? From what I understand, RDP breaks up a a line into two different lines: start to max, and max to end.
But looking at the call, where pos is the index of the max dist in the list...
return (ramerdouglas(line[:pos + 2], dist) +
ramerdouglas(line[pos + 1:], dist)[1:])
is instead doing start to max+1, max+1 to end. Shouldn't it be...
return (ramerdouglas(line[:pos + 1], dist) +
ramerdouglas(line[pos:], dist)[1:])
来源：https://stackoverflow.com/questions/2573997/reduce-number-of-points-in-line