A collection of tools for manipulating and analyzing SVG Path objects and Bezier curves.

Project Description
## Features

## Note on Python 3

## Prerequisites

## Setup

### Alternative Setup

## Credit where credit’s due

## Basic Usage

### Classes

### Reading SVGSs

### Writing SVGSs (and some geometric functions and methods)

### The .point() method and transitioning between path and path segment parameterizations

**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).
### Tangent vectors and Bezier curves as numpy polynomial objects

### Tangent vectors (and more on polynomials)

### Translations (shifts), reversing orientation, and normal vectors

### Rotations and Translations

### arc length and inverse arc length

### Intersections between Bezier curves

### An Advanced Application: Offsetting Paths

## Compatibility Notes for users of svg.path (v2.0)

## Licence

Release History
Download Files
## Download Files

svgpathtools is a collection of tools for manipulating and analyzing SVG Path objects and Bézier curves.

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

While I am hopeful that this package entirely works with Python 3, it was born from a larger project coded in Python 2 and has not been thoroughly tested in Python 3. Please let me know if you find any incompatibilities.

**numpy****svgwrite**

If not already installed, you can **install the prerequisites** using
pip.

$ pip install numpy

$ pip install svgwrite

Then **install svgpathtools**:

$ pip install svgpathtools

You can download the source from Github and install by using the command (from inside the folder containing setup.py):

$ python setup.py install

Much of the core of this module was taken from the svg.path (v2.0) module. Interested svg.path users should see the compatibility notes at bottom of this readme.

Also, a big thanks to the author(s) of A Primer on Bézier Curves, an outstanding resource for learning about Bézier curves and Bézier curve-related algorithms.

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 disconnected1) 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 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. ↩

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

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.

# 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.

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.

# 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

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.

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

output1.svg

There will be many more examples of writing and displaying path data below.

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.

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.

# 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

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

\begin{equation*}
\mathcal{B}(t) = P_0(1-t)^3 + 3P_1(1-t)^2t + 3P_2(1-t)t^2 + P_3t^3
\end{equation*}

where \(P_0\), \(P_1\), \(P_2\), and \(P_3\) 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

\begin{equation*}
\mathcal{B}(t) = c_0t^3 + c_1t^2 +c_2t+c3
\end{equation*}

\begin{equation*}
where
\end{equation*}

\begin{equation*}
\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}
\end{equation*}

QuadraticBezier.poly() and Line.poly() are defined similarly.

# 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)

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.

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

# 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])

vectorframes.svg

# 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')

decorated_ellipse.svg

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.

# 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')

output2.svg

# 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))

output_intersections.svg

Here we’ll find the offset curve for a few paths.

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')

offset_curves.svg

- renamed Arc.arc attribute as Arc.large_arc
- Path.d() : For behavior similar2 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. ↩

This module is under a MIT License.

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