svgpathtools

svgpathtools是一套用于操作和分析SVG路径对象和贝塞尔曲线的工具。

功能

svgpathtools包含旨在轻松读取、写入和显示SVG文件的功能，以及大量面向几何的工具，用于转换和分析路径元素。

此外，子模块bezier.py包含用于处理以n元组形式存储的通用n次贝塞尔曲线的工具。

一些包含的工具

• 读取、写入和显示包含路径（和其他）SVG元素的SVG文件
• 将贝塞尔路径段转换为numpy.poly1d（多项式）对象
• 将多项式（以标准形式）转换为它们的贝塞尔形式
• 计算切向量
• 计算曲率
• 将不连续路径分解为其连续子路径。
• 高效计算路径和/或段之间的交集。
• 为路径或段找到一个边界框。
• 反转段/路径的方向。
• 裁剪和分割路径和段。
• 平滑路径（即平滑拐角以使路径可微）。
• 过渡映射从路径域到段域及其返回（T2t和t2T）。
• 计算封闭路径所围成的面积。
• 计算弧长。
• 计算逆弧长。
• 将RGB颜色元组转换为十六进制颜色字符串及其返回。

先决条件

• numpy
• svgwrite
• scipy（可选，但推荐以提高性能）

设置

$ pip install svgpathtools

备用设置

您可以从Github下载源代码，并使用以下命令安装（在包含setup.py的文件夹内）：

$ python setup.py install

致谢

此模块的大部分核心代码来自svg.path（v2.0）模块。感兴趣的svg.path用户应查看此readme底部的兼容性说明。

基本用法

类

svgpathtools模块主要围绕四个路径段类构建：Line、QuadraticBezier、CubicBezier和Arc。还有一个第五个类，Path，其对象是（连接或不连接¹）路径段对象的序列。

• Line(start, end)

• Arc(start, radius, rotation, large_arc, sweep, end) 注意：请参阅文档字符串以获取这些参数的详细解释

• QuadraticBezier(start, control, end)

• CubicBezier(start, control1, control2, end)

• Path(*segments)

有关每个参数含义的更多信息，请参阅path.py中的相关文档字符串或官方SVG规范。

1 警告：此库中的一些功能尚未在断续路径对象上测试。然而，提供了一个简单的解决方案，即通过Path.continuous_subpaths()方法。 ↩

from __future__ import division, print_function

# Coordinates are given as points in the complex plane
from svgpathtools import Path, Line, QuadraticBezier, CubicBezier, Arc
seg1 = CubicBezier(300+100j, 100+100j, 200+200j, 200+300j)  # A cubic beginning at (300, 100) and ending at (200, 300)
seg2 = Line(200+300j, 250+350j)  # A line beginning at (200, 300) and ending at (250, 350)
path = Path(seg1, seg2)  # A path traversing the cubic and then the line

# We could alternatively created this Path object using a d-string
from svgpathtools import parse_path
path_alt = parse_path('M 300 100 C 100 100 200 200 200 300 L 250 350')

# Let's check that these two methods are equivalent
print(path)
print(path_alt)
print(path == path_alt)

# On a related note, the Path.d() method returns a Path object's d-string
print(path.d())
print(parse_path(path.d()) == path)

Path(CubicBezier(start=(300+100j), control1=(100+100j), control2=(200+200j), end=(200+300j)),
     Line(start=(200+300j), end=(250+350j)))
Path(CubicBezier(start=(300+100j), control1=(100+100j), control2=(200+200j), end=(200+300j)),
     Line(start=(200+300j), end=(250+350j)))
True
M 300.0,100.0 C 100.0,100.0 200.0,200.0 200.0,300.0 L 250.0,350.0
True

Path类是一个可变序列，因此它的工作方式与列表非常相似。因此，可以对其进行append、insert、通过索引设置、del、enumerate、slice等操作。

# Let's append another to the end of it
path.append(CubicBezier(250+350j, 275+350j, 250+225j, 200+100j))
print(path)

# Let's replace the first segment with a Line object
path[0] = Line(200+100j, 200+300j)
print(path)

# You may have noticed that this path is connected and now is also closed (i.e. path.start == path.end)
print("path is continuous? ", path.iscontinuous())
print("path is closed? ", path.isclosed())

# The curve the path follows is not, however, smooth (differentiable)
from svgpathtools import kinks, smoothed_path
print("path contains non-differentiable points? ", len(kinks(path)) > 0)

# If we want, we can smooth these out (Experimental and only for line/cubic paths)
# Note:  smoothing will always works (except on 180 degree turns), but you may want 
# to play with the maxjointsize and tightness parameters to get pleasing results
# Note also: smoothing will increase the number of segments in a path
spath = smoothed_path(path)
print("spath contains non-differentiable points? ", len(kinks(spath)) > 0)
print(spath)

# Let's take a quick look at the path and its smoothed relative
# The following commands will open two browser windows to display path and spaths
from svgpathtools import disvg
from time import sleep
disvg(path) 
sleep(1)  # needed when not giving the SVGs unique names (or not using timestamp)
disvg(spath)
print("Notice that path contains {} segments and spath contains {} segments."
      "".format(len(path), len(spath)))

Path(CubicBezier(start=(300+100j), control1=(100+100j), control2=(200+200j), end=(200+300j)),
     Line(start=(200+300j), end=(250+350j)),
     CubicBezier(start=(250+350j), control1=(275+350j), control2=(250+225j), end=(200+100j)))
Path(Line(start=(200+100j), end=(200+300j)),
     Line(start=(200+300j), end=(250+350j)),
     CubicBezier(start=(250+350j), control1=(275+350j), control2=(250+225j), end=(200+100j)))
path is continuous?  True
path is closed?  True
path contains non-differentiable points?  True
spath contains non-differentiable points?  False
Path(Line(start=(200+101.5j), end=(200+298.5j)),
     CubicBezier(start=(200+298.5j), control1=(200+298.505j), control2=(201.057124638+301.057124638j), end=(201.060660172+301.060660172j)),
     Line(start=(201.060660172+301.060660172j), end=(248.939339828+348.939339828j)),
     CubicBezier(start=(248.939339828+348.939339828j), control1=(249.649982143+349.649982143j), control2=(248.995+350j), end=(250+350j)),
     CubicBezier(start=(250+350j), control1=(275+350j), control2=(250+225j), end=(200+100j)),
     CubicBezier(start=(200+100j), control1=(199.62675237+99.0668809257j), control2=(200+100.495j), end=(200+101.5j)))
Notice that path contains 3 segments and spath contains 6 segments.

读取SVGS

svg2paths()函数将svg文件转换为路径对象列表和包含每个路径属性的单独字典列表。
注意：Line、Polyline、Polygon和Path SVG元素都可以使用此函数转换为路径对象。

# Read SVG into a list of path objects and list of dictionaries of attributes 
from svgpathtools import svg2paths, wsvg
paths, attributes = svg2paths('test.svg')

# Update: You can now also extract the svg-attributes by setting
# return_svg_attributes=True, or with the convenience function svg2paths2
from svgpathtools import svg2paths2
paths, attributes, svg_attributes = svg2paths2('test.svg')

# Let's print out the first path object and the color it was in the SVG
# We'll see it is composed of two CubicBezier objects and, in the SVG file it 
# came from, it was red
redpath = paths[0]
redpath_attribs = attributes[0]
print(redpath)
print(redpath_attribs['stroke'])

Path(CubicBezier(start=(10.5+80j), control1=(40+10j), control2=(65+10j), end=(95+80j)),
     CubicBezier(start=(95+80j), control1=(125+150j), control2=(150+150j), end=(180+80j)))
red

写入SVGS（以及一些几何函数和方法）

wsvg()函数从路径列表创建SVG文件。此函数可以做很多事情（有关更多信息，请参阅paths2svg.py中的文档字符串），旨在快速且易于使用。注意：使用便利函数disvg()（或设置'openinbrowser=True'）自动尝试在您的默认SVG查看器中打开创建的svg文件。

# Let's make a new SVG that's identical to the first
wsvg(paths, attributes=attributes, svg_attributes=svg_attributes, filename='output1.svg')

下面将有更多关于编写和显示路径数据的示例。

.point()方法以及路径和路径段参数化之间的转换

SVG路径元素及其段具有官方参数化。可以使用Path.point()、Line.point()、QuadraticBezier.point()、CubicBezier.point()和Arc.point()方法访问这些参数化。所有这些参数化都在0 <= t <= 1的域上定义。

注意：在此文档以及内联文档和文档字符串中，我在提到Path对象的参数化时使用大写T，在提到路径段对象（即Line、QaudraticBezier、CubicBezier和Arc对象）时使用小写t。
给定一个 T 值，可以使用 Path.T2t() 方法找到对应的段索引 k 和段参数 t，使得 path.point(T)=path[k].point(t)。
还有一个 Path.t2T() 方法来解决逆问题。

# Example:

# Let's check that the first segment of redpath starts 
# at the same point as redpath
firstseg = redpath[0] 
print(redpath.point(0) == firstseg.point(0) == redpath.start == firstseg.start)

# Let's check that the last segment of redpath ends on the same point as redpath
lastseg = redpath[-1] 
print(redpath.point(1) == lastseg.point(1) == redpath.end == lastseg.end)

# This next boolean should return False as redpath is composed multiple segments
print(redpath.point(0.5) == firstseg.point(0.5))

# If we want to figure out which segment of redpoint the 
# point redpath.point(0.5) lands on, we can use the path.T2t() method
k, t = redpath.T2t(0.5)
print(redpath[k].point(t) == redpath.point(0.5))

True
True
False
True

贝塞尔曲线作为NumPy多项式对象

处理 Line、QuadraticBezier 和 CubicBezier 对象的参数化，另一个好方法是将它们转换为 numpy.poly1d 对象。这可以通过使用 Line.poly()、QuadraticBezier.poly() 和 CubicBezier.poly() 方法轻松完成。
在 pathtools.py 子模块中还有一个 polynomial2bezier() 函数，可以将多项式转换回贝塞尔曲线。

注意：三次贝塞尔曲线的参数化形式为 $$\mathcal{B}(t) = P_0(1-t)^3 + 3P_1(1-t)^2t + 3P_2(1-t)t^2 + P_3t^3$$ 其中 $P_0$、$P_1$、$P_2$ 和 $P_3$ 分别是控制点 start、control1、control2 和 end，svgpathtools 使用这些控制点来定义一个 CubicBezier 对象。CubicBezier.poly() 方法将此多项式展开为其标准形式 $$\mathcal{B}(t) = c_0t^3 + c_1t^2 +c_2t+c3$$ 其中 $$\begin{bmatrix}c_0\c_1\c_2\c_3\end{bmatrix} = \begin{bmatrix} -1 & 3 & -3 & 1\ 3 & -6 & -3 & 0\ -3 & 3 & 0 & 0\ 1 & 0 & 0 & 0\ \end{bmatrix} \begin{bmatrix}P_0\P_1\P_2\P_3\end{bmatrix}$$

QuadraticBezier.poly() 和 Line.poly() 的定义方式类似。

# Example:
b = CubicBezier(300+100j, 100+100j, 200+200j, 200+300j)
p = b.poly()

# p(t) == b.point(t)
print(p(0.235) == b.point(0.235))

# What is p(t)?  It's just the cubic b written in standard form.  
bpretty = "{}*(1-t)^3 + 3*{}*(1-t)^2*t + 3*{}*(1-t)*t^2 + {}*t^3".format(*b.bpoints())
print("The CubicBezier, b.point(x) = \n\n" + 
      bpretty + "\n\n" + 
      "can be rewritten in standard form as \n\n" +
      str(p).replace('x','t'))

True
The CubicBezier, b.point(x) = 

(300+100j)*(1-t)^3 + 3*(100+100j)*(1-t)^2*t + 3*(200+200j)*(1-t)*t^2 + (200+300j)*t^3

can be rewritten in standard form as 

                3                2
(-400 + -100j) t + (900 + 300j) t - 600 t + (300 + 100j)

在贝塞尔对象与NumPy多项式对象之间进行转换的能力非常有用。首先，我们可以将一个贝塞尔段的列表转换为一个NumPy数组

Numpy Array在贝塞尔路径段上的操作

示例在此处提供

为了进一步说明将我们的贝塞尔曲线对象转换为 numpy.poly1d 对象及其反向转换的强大功能，让我们计算上面三次贝塞尔对象 b 在 t=0.5 处的单位切向量，以四种不同的方式。

切向量（以及在NumPy多项式上的更多内容）

t = 0.5
### Method 1: the easy way
u1 = b.unit_tangent(t)

### Method 2: another easy way 
# Note: This way will fail if it encounters a removable singularity.
u2 = b.derivative(t)/abs(b.derivative(t))

### Method 2: a third easy way 
# Note: This way will also fail if it encounters a removable singularity.
dp = p.deriv() 
u3 = dp(t)/abs(dp(t))

### Method 4: the removable-singularity-proof numpy.poly1d way  
# Note: This is roughly how Method 1 works
from svgpathtools import real, imag, rational_limit
dx, dy = real(dp), imag(dp)  # dp == dx + 1j*dy 
p_mag2 = dx**2 + dy**2  # p_mag2(t) = |p(t)|**2
# Note: abs(dp) isn't a polynomial, but abs(dp)**2 is, and,
#  the limit_{t->t0}[f(t) / abs(f(t))] == 
# sqrt(limit_{t->t0}[f(t)**2 / abs(f(t))**2])
from cmath import sqrt
u4 = sqrt(rational_limit(dp**2, p_mag2, t))

print("unit tangent check:", u1 == u2 == u3 == u4)

# Let's do a visual check
mag = b.length()/4  # so it's not hard to see the tangent line
tangent_line = Line(b.point(t), b.point(t) + mag*u1)
disvg([b, tangent_line], 'bg', nodes=[b.point(t)])

unit tangent check: True

平移（位移）、反转方向和法向量

# Speaking of tangents, let's add a normal vector to the picture
n = b.normal(t)
normal_line = Line(b.point(t), b.point(t) + mag*n)
disvg([b, tangent_line, normal_line], 'bgp', nodes=[b.point(t)])

# and let's reverse the orientation of b! 
# the tangent and normal lines should be sent to their opposites
br = b.reversed()

# Let's also shift b_r over a bit to the right so we can view it next to b
# The simplest way to do this is br = br.translated(3*mag),  but let's use 
# the .bpoints() instead, which returns a Bezier's control points
br.start, br.control1, br.control2, br.end = [3*mag + bpt for bpt in br.bpoints()]  # 

tangent_line_r = Line(br.point(t), br.point(t) + mag*br.unit_tangent(t))
normal_line_r = Line(br.point(t), br.point(t) + mag*br.normal(t))
wsvg([b, tangent_line, normal_line, br, tangent_line_r, normal_line_r], 
     'bgpkgp', nodes=[b.point(t), br.point(t)], filename='vectorframes.svg', 
     text=["b's tangent", "br's tangent"], text_path=[tangent_line, tangent_line_r])

旋转和平移

# Let's take a Line and an Arc and make some pictures
top_half = Arc(start=-1, radius=1+2j, rotation=0, large_arc=1, sweep=1, end=1)
midline = Line(-1.5, 1.5)

# First let's make our ellipse whole
bottom_half = top_half.rotated(180)
decorated_ellipse = Path(top_half, bottom_half)

# Now let's add the decorations
for k in range(12):
    decorated_ellipse.append(midline.rotated(30*k))
    
# Let's move it over so we can see the original Line and Arc object next
# to the final product
decorated_ellipse = decorated_ellipse.translated(4+0j)
wsvg([top_half, midline, decorated_ellipse], filename='decorated_ellipse.svg')

弧长和逆弧长

在此，我们将创建一个SVG，显示来自 test.svg 的路径的参数和几何中点。我们需要使用 Path.length()、Line.length()、QuadraticBezier.length()、CubicBezier.length() 和 Arc.length() 方法，以及相关的逆弧长方法 .ilength() 函数来完成此操作。

# First we'll load the path data from the file test.svg
paths, attributes = svg2paths('test.svg')

# Let's mark the parametric midpoint of each segment
# I say "parametric" midpoint because Bezier curves aren't 
# parameterized by arclength 
# If they're also the geometric midpoint, let's mark them
# purple and otherwise we'll mark the geometric midpoint green
min_depth = 5
error = 1e-4
dots = []
ncols = []
nradii = []
for path in paths:
    for seg in path:
        parametric_mid = seg.point(0.5)
        seg_length = seg.length()
        if seg.length(0.5)/seg.length() == 1/2:
            dots += [parametric_mid]
            ncols += ['purple']
            nradii += [5]
        else:
            t_mid = seg.ilength(seg_length/2)
            geo_mid = seg.point(t_mid)
            dots += [parametric_mid, geo_mid]
            ncols += ['red', 'green']
            nradii += [5] * 2

# In 'output2.svg' the paths will retain their original attributes
wsvg(paths, nodes=dots, node_colors=ncols, node_radii=nradii, 
     attributes=attributes, filename='output2.svg')

贝塞尔曲线之间的交点

# Let's find all intersections between redpath and the other 
redpath = paths[0]
redpath_attribs = attributes[0]
intersections = []
for path in paths[1:]:
    for (T1, seg1, t1), (T2, seg2, t2) in redpath.intersect(path):
        intersections.append(redpath.point(T1))
        
disvg(paths, filename='output_intersections.svg', attributes=attributes,
      nodes = intersections, node_radii = [5]*len(intersections))

高级应用：偏移路径

在此，我们将找到几个路径的 偏移曲线。

from svgpathtools import parse_path, Line, Path, wsvg
def offset_curve(path, offset_distance, steps=1000):
    """Takes in a Path object, `path`, and a distance,
    `offset_distance`, and outputs an piecewise-linear approximation 
    of the 'parallel' offset curve."""
    nls = []
    for seg in path:
        ct = 1
        for k in range(steps):
            t = k / steps
            offset_vector = offset_distance * seg.normal(t)
            nl = Line(seg.point(t), seg.point(t) + offset_vector)
            nls.append(nl)
    connect_the_dots = [Line(nls[k].end, nls[k+1].end) for k in range(len(nls)-1)]
    if path.isclosed():
        connect_the_dots.append(Line(nls[-1].end, nls[0].end))
    offset_path = Path(*connect_the_dots)
    return offset_path

# Examples:
path1 = parse_path("m 288,600 c -52,-28 -42,-61 0,-97 ")
path2 = parse_path("M 151,395 C 407,485 726.17662,160 634,339").translated(300)
path3 = parse_path("m 117,695 c 237,-7 -103,-146 457,0").translated(500+400j)
paths = [path1, path2, path3]

offset_distances = [10*k for k in range(1,51)]
offset_paths = []
for path in paths:
    for distances in offset_distances:
        offset_paths.append(offset_curve(path, distances))

# Let's take a look
wsvg(paths + offset_paths, 'g'*len(paths) + 'r'*len(offset_paths), filename='offset_curves.svg')

svg.path（v2.0）用户兼容性说明

• 将Arc.arc属性重命名为Arc.large_arc

• Path.d()：要实现与svg.path（v2.0）类似的行为²，请将useSandT和use_closed_attrib都设置为True。

2 此行为将相同，但此方法中使用的字符串格式化方式已更改为使用默认格式（而不是通用格式{:G}），以提高精度。 ↩

许可证

本模块采用MIT许可证。