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svgpathtools
============
svgpathtools is a collection of tools for manipulating and analyzing SVG
Path objects and Bézier curves.
Features
--------
svgpathtools contains functions designed to **easily read, write and
display SVG files** as well as *a large selection of
geometrically-oriented tools* to **transform and analyze path
elements**.
Additionally, the submodule *bezier.py* contains tools for for working
with general **nth order Bezier curves stored as n-tuples**.
Some included tools:
- **read**, **write**, and **display** SVG files containing Path (and
other) SVG elements
- convert Bézier path segments to **numpy.poly1d** (polynomial) objects
- convert polynomials (in standard form) to their Bézier form
- compute **tangent vectors** and (right-hand rule) **normal vectors**
- compute **curvature**
- break discontinuous paths into their **continuous subpaths**.
- efficiently compute **intersections** between paths and/or segments
- find a **bounding box** for a path or segment
- **reverse** segment/path orientation
- **crop** and **split** paths and segments
- **smooth** paths (i.e. smooth away kinks to make paths
differentiable)
- **transition maps** from path domain to segment domain and back (T2t
and t2T)
- compute **area** enclosed by a closed path
- compute **arc length**
- compute **inverse arc length**
- convert RGB color tuples to hexadecimal color strings and back
Prerequisites
-------------
- **numpy**
- **svgwrite**
Setup
-----
If not already installed, you can **install the prerequisites** using
pip.
.. code:: bash
$ pip install numpy
.. code:: bash
$ pip install svgwrite
Then **install svgpathtools**:
.. code:: bash
$ pip install svgpathtools
Alternative Setup
~~~~~~~~~~~~~~~~~
You can download the source from Github and install by using the command
(from inside the folder containing setup.py):
.. code:: bash
$ python setup.py install
Credit where credit's due
-------------------------
Much of the core of this module was taken from `the svg.path (v2.0)
module <https://github.com/regebro/svg.path>`__. Interested svg.path
users should see the compatibility notes at bottom of this readme.
Also, a big thanks to the author(s) of `http://pomax.github.io/bezierinfo/ <http://pomax.github.io/bezierinfo/>`_, an outstanding resource for learning about Bézier curves and Bézier curve-related algorithms.
Basic Usage
-----------
Classes
~~~~~~~
The svgpathtools module is primarily structured around four path segment
classes: ``Line``, ``QuadraticBezier``, ``CubicBezier``, and ``Arc``.
There is also a fifth class, ``Path``, whose objects are sequences of
(connected or disconnected\ `1 <#f1>`__\ ) path segment objects.
- ``Line(start, end)``
- ``Arc(start, radius, rotation, large_arc, sweep, end)`` Note: See
docstring for a detailed explanation of these parameters
- ``QuadraticBezier(start, control, end)``
- ``CubicBezier(start, control1, control2, end)``
- ``Path(*segments)``
See the relevant docstrings in *path.py* or the `official SVG
specifications <http://www.w3.org/TR/SVG/paths.html>`__ for more
information on what each parameter means.
1 Warning: Some of the functionality in this library has not been tested
on discontinuous Path objects. A simple workaround is provided, however,
by the ``Path.continuous_subpaths()`` method. `↩ <#a1>`__
.. code:: python
from __future__ import division, print_function
.. code:: python
# 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)
.. parsed-literal::
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
The ``Path`` class is a mutable sequence, so it behaves much like a
list. So segments can **append**\ ed, **insert**\ ed, set by index,
**del**\ eted, **enumerate**\ d, **slice**\ d out, etc.
.. code:: python
# 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)))
.. parsed-literal::
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.
Reading SVGSs
~~~~~~~~~~~~~
| The **svg2paths()** function converts an svgfile to a list of Path
objects and a separate list of dictionaries containing the attributes
of each said path.
| Note: Line, Polyline, Polygon, and Path SVG elements can all be
converted to Path objects using this function.
.. code:: python
# 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'])
.. parsed-literal::
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
Writing SVGSs (and some geometric functions and methods)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The **wsvg()** function creates an SVG file from a list of path. This
function can do many things (see docstring in *paths2svg.py* for more
information) and is meant to be quick and easy to use. Note: Use the
convenience function **disvg()** (or set 'openinbrowser=True') to
automatically attempt to open the created svg file in your default SVG
viewer.
.. code:: python
# Let's make a new SVG that's identical to the first
wsvg(paths, attributes=attributes, svg_attributes=svg_attributes, filename='output1.svg')
.. figure:: https://cdn.rawgit.com/mathandy/svgpathtools/master/output1.svg
:alt: output1.svg
output1.svg
There will be many more examples of writing and displaying path data
below.
The .point() method and transitioning between path and path segment parameterizations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SVG Path elements and their segments have official parameterizations.
These parameterizations can be accessed using the ``Path.point()``,
``Line.point()``, ``QuadraticBezier.point()``, ``CubicBezier.point()``,
and ``Arc.point()`` methods. All these parameterizations are defined
over the domain 0 <= t <= 1.
| **Note:** In this document and in inline documentation and doctrings,
I use a capital ``T`` when referring to the parameterization of a Path
object and a lower case ``t`` when referring speaking about path
segment objects (i.e. Line, QaudraticBezier, CubicBezier, and Arc
objects).
| Given a ``T`` value, the ``Path.T2t()`` method can be used to find the
corresponding segment index, ``k``, and segment parameter, ``t``, such
that ``path.point(T)=path[k].point(t)``.
| There is also a ``Path.t2T()`` method to solve the inverse problem.
.. code:: python
# 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))
.. parsed-literal::
True
True
False
True
Tangent vectors and Bezier curves as numpy polynomial objects
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
| Another great way to work with the parameterizations for Line,
QuadraticBezier, and CubicBezier objects is to convert them to
``numpy.poly1d`` objects. This is done easily using the
``Line.poly()``, ``QuadraticBezier.poly()`` and ``CubicBezier.poly()``
methods.
| There's also a ``polynomial2bezier()`` function in the pathtools.py
submodule to convert polynomials back to Bezier curves.
**Note:** cubic Bezier curves are parameterized as
.. math:: \mathcal{B}(t) = P_0(1-t)^3 + 3P_1(1-t)^2t + 3P_2(1-t)t^2 + P_3t^3
where :math:`P_0`, :math:`P_1`, :math:`P_2`, and :math:`P_3` are the
control points ``start``, ``control1``, ``control2``, and ``end``,
respectively, that svgpathtools uses to define a CubicBezier object. The
``CubicBezier.poly()`` method expands this polynomial to its standard
form
.. math:: \mathcal{B}(t) = c_0t^3 + c_1t^2 +c_2t+c3
where
.. math::
\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() and Line.poly() are defined similarly.
.. code:: python
# 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'))
.. parsed-literal::
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)
To illustrate the awesomeness of being able to convert our Bezier curve
objects to numpy.poly1d objects and back, lets compute the unit tangent
vector of the above CubicBezier object, b, at t=0.5 in four different
ways.
Tangent vectors (and more on polynomials)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: python
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)])
.. parsed-literal::
unit tangent check: True
Translations (shifts), reversing orientation, and normal vectors
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: python
# 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])
.. figure:: https://cdn.rawgit.com/mathandy/svgpathtools/master/vectorframes.svg
:alt: vectorframes.svg
vectorframes.svg
Rotations and Translations
~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: python
# 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')
.. figure:: https://cdn.rawgit.com/mathandy/svgpathtools/master/decorated_ellipse.svg
:alt: decorated\_ellipse.svg
decorated\_ellipse.svg
arc length and inverse arc length
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Here we'll create an SVG that shows off the parametric and geometric
midpoints of the paths from ``test.svg``. We'll need to compute use the
``Path.length()``, ``Line.length()``, ``QuadraticBezier.length()``,
``CubicBezier.length()``, and ``Arc.length()`` methods, as well as the
related inverse arc length methods ``.ilength()`` function to do this.
.. code:: python
# 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')
.. figure:: https://cdn.rawgit.com/mathandy/svgpathtools/master/output2.svg
:alt: output2.svg
output2.svg
Intersections between Bezier curves
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: python
# 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))
.. figure:: https://cdn.rawgit.com/mathandy/svgpathtools/master/output_intersections.svg
:alt: output\_intersections.svg
output\_intersections.svg
An Advanced Application: Offsetting Paths
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Here we'll find the `offset
curve <https://en.wikipedia.org/wiki/Parallel_curve>`__ for a few paths.
.. code:: python
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))
# Note: This will take a few moments
wsvg(paths + offset_paths, 'g'*len(paths) + 'r'*len(offset_paths), filename='offset_curves.svg')
.. figure:: https://cdn.rawgit.com/mathandy/svgpathtools/master/offset_curves.svg
:alt: offset\_curves.svg
offset\_curves.svg
Compatibility Notes for users of svg.path (v2.0)
------------------------------------------------
- renamed Arc.arc attribute as Arc.large\_arc
- Path.d() : For behavior similar\ `2 <#f2>`__\ to svg.path (v2.0),
set both useSandT and use\_closed\_attrib to be True.
2 The behavior would be identical, but the string formatting used in
this method has been changed to use default format (instead of the
General format, {:G}), for inceased precision. `↩ <#a2>`__
Licence
-------
This module is under a MIT License.
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