我正在寻找算法来减少节点的折线，线（循环或非循环）的LOD。 简单来说，我想拍摄高分辨率的海岸线数据，并能够将其LOD减少百倍或千倍以进行小规模渲染。
我发现了多边形缩减算法（但它们需要三角形）和拉普拉斯平滑，但这似乎不是我需要的。
答案 0 :(得分：14)
我修改了culebrón's answer中的代码，不需要Vec2D / Line类，而是将这些点作为元组列表处理。
代码稍微整洁一点，但更短，更快一点（对于900点，原始代码需要2966ms，这个版本需要500ms - 仍然比我想要的慢一点，但是有所改进）
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:])
答案 1 :(得分：13)
我发现并且很可能会使用的解决方案是Ramer-Douglas-Peucker算法。它在PostGIS
中使用我发布了my own implementation in Python（网站目前已关闭，以下是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 ),
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])
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)
答案 2 :(得分：4)
当我看到将Bezier曲线转换成直线段时，我最终做的是定义曲线与曲线两点之间的直线之间的最大距离。从一个点作为一个终点开始，沿着曲线滑动另一端，直到再滑动它将超过最大距离。然后再次使用第二个（依此类推）点，直到覆盖整个曲线。
您应该能够通过简单地增加线段和折线之间的距离来生成多个LOD。
答案 3 :(得分：2)
我开发了一个非常简单的算法，使用给定点到以下点的距离来决定将它们包含在渲染中是否有意义。根据当前比例，您可以关联转换模型所需的点之间的最小距离。
答案 4 :(得分：2)
我喜欢根据片段在点的任一侧产生的角度对点进行排序，然后迭代地移除具有最浅角度的点，直到达到某个阈值。我认为O（n log（n））与RDP方法的O（n ^ 2）相比，并且具有较小的常量来引导。 ：）
如果你想为更长的段提供更多的权重（合意性），角度甚至可以通过段长度来缩放（实际上它更容易以这种方式计算）。
给定p0，p1，p2，p1的权重为（（p0-p1）dot（p2-p1）），如果你不想按长度加权，则将差异标准化。 （相比之下，距离线距离要便宜得多，结果可能相同。）
答案 5 :(得分：1)
晚会，但这是道格拉斯peucker算法的Java实现。
答案 6 :(得分：1)
添加大量答案。我在这个github repo发现了一个javascript实现：https://github.com/mourner/simplify-js
还有一系列不同语言的Ramer-Douglas-Peucker算法的不同实现。
答案 7 :(得分：0)
关于culebron's answer，递归调用是否正确？据我所知，RDP将一行划分为两行：从最大开始到最大结束。
但是看看这个电话，其中pos是列表中max dist的索引...
return (ramerdouglas(line[:pos + 2], dist) +
ramerdouglas(line[pos + 1:], dist)[1:])
return (ramerdouglas(line[:pos + 1], dist) +
ramerdouglas(line[pos:], dist)[1:])