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Svg Elements Parsing

Project description


Parsing for SVG File, Path, Matrix, Angle, Distance, Color, Point and other SVG Elements. The SVG spec defines not only paths by a variety of classes. In order to have a robust experience with SVGs we must be able to deal with the parsing and interactions of these elements.


pip install svg.elements

Then in a script:

from svg.elements import *




svg.elements is compatible with Python 2.7 and Python 3.6. Support for 2.7 will be dropped at Python 2 End-Of-Life January 1, 2020.


The goal of this project is to provide svg spec-like objects and structures. The svg standard 1.1 and elements of 2.0 will be used to provide much of the decisions making for implementation objects. If there is a question on implementation and the SVG documentation has a methodology, that is the preferred methodology.

The primary goal is to make a more robust version of svg.path including other elements like Point and Matrix with clear emphasis on conforming to the SVG spec in all ways that realworld uses for SVG demands.

svg.elements should conform to the SVG Conforming Interpretor class (2.5.4. Conforming SVG Interpreters):

An SVG interpreter is a program which can parse and process SVG document fragments. Examples of SVG interpreters are server-side transcoding tools or optimizers (e.g., a tool which converts SVG content into modified SVG content) or analysis tools (e.g., a tool which extracts the text content from SVG content, or a validity checker).

For real world functionality we must correctly and reasonably provide the ability to do transcoding of svg as well as accessing and modifying content.

This project began as part of meerK40t which does svg loading of files for laser cutting. It attempts to more fully map out the svg spec, objects, and paths, while remaining easy to use and highly backwards compatible.

Example Usages

The usability has greatly increased with dunder methods and various extensions. Points, PathSegments, Paths can be multiplied by a matrix. Functionally understandable parsable elements are parsed and used.

Parse an svg file:

>>> svg = SVG(file)
>>> list(svg.nodes())

Make a PathSegment

>>> Line((20,20), (40,40))
Line(start=Point(20,20), end=Point(40,40))

Rotate a PathSegment:

>>> Line((20,20), (40,40)) * Matrix.rotate(Angle.degrees(45))
Line(start=Point(0,28.284271247462), end=Point(0,56.568542494924))

Rotate a PathSegment with a parsed matrix:

>>> Line((20,20), (40,40)) * Matrix("Rotate(45)")
Line(start=Point(0,28.284271247462), end=Point(0,56.568542494924))

Rotate a PathSegment with an implied parsed matrix:

>>> Line((20,20), (40,40)) * "Rotate(45)"
Line(start=Point(0,28.284271247462), end=Point(0,56.568542494924))

Rotate a Partial Path with an implied matrix: (Note: The SVG does not allow us to specify a start point for the invalid path)

>>> Path("L 40,40") * "Rotate(45)"

Prepend a move to the rotated partial path: (Note: This rotates the partial path, then adds the start point)

>>> Move((20,20)) + Path("L 40,40") * "Rotate(45)"
Path(Move(end=Point(20,20)), Line(start=Point(20,20), end=Point(0,56.568542494924)))

Prepend a move to the partial path, and rotate:

>>> (Move((20,20)) + Path("L 40,40")) * "Rotate(45)"
Path(Move(end=Point(0,28.284271247462)), Line(start=Point(0,28.284271247462), end=Point(0,56.568542494924)))

Since Move() is a qualified element we can postpend the SVG text:

>>> (Move((20,20)) + "L 40,40") * "Rotate(45)"
Path(Move(end=Point(0,28.284271247462)), Line(start=Point(0,28.284271247462), end=Point(0,56.568542494924)))

Define the entire qualified path and rotate:

>>> Path("M 20,20 L 40,40") * "Rotate(45)"
Path(Move(end=Point(0,28.284271247462)), Line(start=Point(0,28.284271247462), end=Point(0,56.568542494924)))

Combine individual PathSegments together:

>>> Move((2,2)) + Close()
Path(Move(end=Point(2,2)), Close())

Write that as SVG text:

>>> print(Move((2,2)) + Close())
M 2,2 Z

Scale a path:

>>> Path("M1,1 1,2 2,2 2,1z") * "scale(2)"
Path(Move(end=Point(2,2)), Line(start=Point(2,2), end=Point(2,4)), Line(start=Point(2,4), end=Point(4,4)), Line(start=Point(4,4), end=Point(4,2)), Close(start=Point(4,2), end=Point(2,2)))

Print that:

>>> print(Path("M1,1 1,2 2,2 2,1z") * "scale(2)")
M 2,2 L 2,4 L 4,4 L 4,2 Z

Reverse a scaled path:

>>> p = (Path("M1,1 1,2 2,2 2,1z") * "scale(2)")
>>> p.reverse()
>>> print(p)
M 4,2 L 4,4 L 2,4 L 2,2 Z

Query length of paths:

>>> QuadraticBezier("0,0", "50,50", "100,0").length()

Apply a translations:

>>> Path('M 0,0 Q 50,50 100,0') * "translate(40,40)"
Path(Move(end=Point(40,40)), QuadraticBezier(start=Point(40,40), control=Point(90,90), end=Point(140,40)))

Query lengths of translated paths:

>>> (Path('M 0,0 Q 50,50 100,0') * "translate(40,40)").length()
>>> Path('M 0,0 Q 50,50 100,0').length()

Query a subpaths:

>>> Path('M 0,0 Q 50,50 100,0 M 20,20 v 20 h 20 v-20 h-20 z').subpath(1).d()
'M 20,20 L 20,40 L 40,40 L 40,20 L 20,20 Z'

Reverse subpaths:

>>> p = Path('M 0,0 Q 50,50 100,0 M 20,20 v 20 h 20 v-20 h-20 z')
>>> print(p)
M 0,0 Q 50,50 100,0 M 20,20 L 20,40 L 40,40 L 40,20 L 20,20 Z
>>> p.subpath(1).reverse()
>>> print(p)
M 0,0 Q 50,50 100,0 M 20,20 L 40,20 L 40,40 L 20,40 L 20,20 Z

Query a bounding box:

>>> QuadraticBezier("0,0", "50,50", "100,0").bbox()
(0.0, 0.0, 100.0, 50.0)

Query a translated bounding box:

>>> (Path('M 0,0 Q 50,50 100,0') * "translate(40,40)").bbox()
(40.0, 40.0, 140.0, 90.0)



The core functionality of this class are the elements. These are svg-based objects which interact in coherent ways.


The element is Path this is based on regebro's code and methods from the svg.path project. The primary methods use different PathSegment classes for the various elements within a pathd code. These should always have a high degree of backwards compatibility. And for most purposes importing the relevant classes from svg.elements should be highly compatible with any existing code.

For this reason the test code and functionality from svg.path is included in this project. The Point class takes and works like a complex while not actually being one. This permits any other code from other projects to quickly port without requiring a rewrite. But, also allows for corrections like making the Matrix object easy.

  • Path(*segments)

The Path class is a mutable sequence, so it behaves like a list. You can add to it and replace path segments etc:

>>> path = Path(Line(100+100j,300+100j), Line(100+100j,300+100j))
>>> path.append(QuadraticBezier(300+100j, 200+200j, 200+300j))
>>> print(path)
L 300,100 L 300,100 Q 200,200 200,300

>>> path[1] = Line(200+100j,300+100j)
>>> print(path)
L 300,100 L 300,100 Q 200,200 200,300

>>> del path[1]
>>> print(path)
L 300,100 Q 200,200 200,300

>>> path = path = Move() + path
>>> print(path)
M 100,100 L 300,100 Q 200,200 200,300

The path object also has a d() method that will return the SVG representation of the Path segments:

>>> path.d()
'M 100,100 L 300,100 Q 200,200 200,300'

The d() parameter also takes a value for relative:

>>> path.d(relative=True)
'm 100,100 l 200,0 q -100,100 -100,200'

A Path object that is a collection of the PathSegment objects. These can be defined by combining a PathSegment with another PathSegment initializing it with Path() or Path(*segments) or Path(<svg_text>).


Subpaths provide a window into a Path object. These are backed by the path and consequently operations performed on them apply to that part of the path.

>>> p = Path('M 0,0 Q 50,50 100,0 M 20,20 v 20 h 20 v-20 h-20 z')
>>> print(p)
M 0,0 Q 50,50 100,0 M 20,20 L 20,40 L 40,40 L 40,20 L 20,20 Z
>>> q = p.subpath(1) 
>>> q *= "scale(2)"
>>> print(p)
M 0,0 Q 50,50 100,0 M 40,40 L 40,80 L 80,80 L 80,40 L 40,40 Z

or likewise .reverse() (notice the path will go 80,40 first rather than 40,80.)

>>> q.reverse()
>>> print(p)
M 0,0 Q 50,50 100,0 M 40,40 L 80,40 L 80,80 L 40,80 L 40,40 Z


There are 6 PathSegment objects: Line, Arc, CubicBezier, QuadraticBezier, Move and Close. These have a 1:1 correspondence to the commands in a pathd.

>>> from svg.elements import Path, Line, Arc, CubicBezier, QuadraticBezier, Close

All of these objects have a .point() function which will return the coordinates of a point on the path, where the point is given as a floating point value where 0.0 is the start of the path and 1.0 is end.

You can calculate the length of a Path or its segments with the .length() function. For CubicBezier and Arc segments this is done by geometric approximation and for this reason may be very slow. You can make it faster by passing in an error option to the method. If you don't pass in error, it defaults to 1e-12::

>>> CubicBezier(300+100j, 100+100j, 200+200j, 200+300j).length(error=1e-5)

CubicBezier and Arc also has a min_depth option that specifies the minimum recursion depth. This is set to 5 by default, resulting in using a minimum of 32 segments for the calculation. Setting it to 0 is a bad idea for CubicBeziers, as they may become approximated to a straight line.

Line.length() and QuadraticBezier.length() also takes these parameters, but they unneeded as direct values rather than approximations are returned.

CubicBezier and QuadraticBezier also have is_smooth_from(previous) methods, that check if the segment is a "smooth" segment compared to the given segment.

Unlike svg.path the preferred method of getting a Path from a pathd string is as an argument:

>>> from svg.elements import Path
>>> Path('M 100 100 L 300 100')
Path(Move(end=Point(100,100)), Line(start=Point(100,100), end=Point(300,100)))

PathSegment Classes

These are the SVG PathSegment classes. See the SVG specifications <>_ for more information on what each parameter means.

  • Move(start, end) The move object describes a move to the start of the next subpath. It may lack a start position but not en end position.

  • Close(start, end) The close object describes a close path element. It will have a length if and only if the end point is not equal to the subpath start point. Neither the start point or end point is required.

  • Line(start, end) The line object describes a line moving straight from one point to the next point.

  • Arc(start, radius, rotation, arc, sweep, end) The arc object describes an arc across a circular path. This supports multiple types of parameterizations. The given default there is compatible with svg.path and has a complex radius. It is also valid to divide radius into rx and ry or Arc(start, end, center, prx, pry, sweep) where start, end, center, prx, pry are points and sweep is the radians value of the arc distance traveled.

  • QuadraticBezier(start, control, end) the quadraticbezier object describes a single control point bezier curve.

  • CubicBezier(start, control1, control2, end) the cubic bezier curve object describes a two control point bezier curve.


This SVG path example draws a triangle:

>>> path1 = Path('M 100 100 L 300 100 L 200 300 z')

You can format SVG paths in many different ways, all valid paths should be accepted::

>>> path2 = Path('M100,100L300,100L200,300z')

And these paths should be equal:

>>> path1 == path2

You can also build a path from objects:

>>> path3 = Path(Move(100 + 100j), Line(100 + 100j, 300 + 100j), Line(300 + 100j, 200 + 300j), Close(200 + 300j, 100 + 100j))

And it should again be equal to the first path::

>>> path1 == path3

Paths are mutable sequences, you can slice and append::

>>> path1.append(QuadraticBezier(300+100j, 200+200j, 200+300j))
>>> len(path1[2:]) == 3

Note that there is no protection against you creating paths that are invalid. You can for example have a Close command that doesn't end at the path start:

>>> wrong = Path(Line(100+100j,200+100j), Close(200+300j, 0))

Matrix (Transformations)

SVG 1.1, 7.15.3 defines the matrix form as:

[a c  e]
[b d  f]

Since we are delegating to SVG spec for such things, this is how it is implemented in elements.

To be compatible with SGV 1.1 and SVG 2.0 the matrix class provided has all the SVG functions as well as the CSS functions:

  • translate(x,[y])
  • translateX(x)
  • translateY(y)
  • scale(x,[y])
  • scaleX(x)
  • scaleY(y)
  • skew(x,[y])
  • skewX(x)
  • skewY(y)

Since we have compatibility with CSS for the SVG 2.0 spec compatibility we can perform length translations: (Note this converts based on the default PPI of 96)

>>> Point(0,0) * Matrix("Translate(1cm,1cm)")

We can also rotate by turns, grad, deg, rad which are permitted CSS angles:

>>> Point(10,0) * Matrix("Rotate(1turn)")
>>> Point(10,0) * Matrix("Rotate(400grad)")
>>> Point(10,0) * Matrix("Rotate(360deg)")

A large goal of this project is to provide a more robust modifications of Path objects including matrix transformations. This is done by three major shifts from svg.paths methods.

  • Points are not stored as complex numbers. These are stored as Point objects, which have backwards compatibility with complex numbers, without the data actually being backed by a complex.
  • A matrix is added which conforms to the SVGMatrix Element. The matrix contains valid versions of all the affline transformations elements required by the SVG Spec.
  • The Arc object is fundamentally backed by a different point-based parameterization.

The objects themselves have robust dunder methods. So if you have a path object you may simply multiply it by a matrix.

>>> Path(Line(0+0j, 100+100j)) * Matrix.scale(2)
>>> Path(Line(start=Point(0.000000000000,0.000000000000), end=Point(200.000000000000,200.000000000000)))

Or rotate a parsed path.

>>> Path("M0,0L100,100") * Matrix.rotate(30)
Path(Move(end=Point(0,0)), Line(start=Point(0,0), end=Point(114.228307398045,-83.378017420528)))

Or modify an svg path.

>>> str(Path("M0,0L100,100") * Matrix.rotate(30))
'M 0,0 L 114.228,-83.378'

The Matrix objects can be used to modify points:

>>> Point(100,100) * Matrix("scale(2)")

>>> Point(100,100) * (Matrix("scale(2)") * Matrix("Translate(40,40)"))

Do note that the order of operations for matrices matters:

>>> Point(100,100) * (Matrix("Translate(40,40)") * Matrix("scale(2)"))

The first version is:

>>> (Matrix("scale(2)") * Matrix("Translate(40,40)"))
Matrix(2.000000, 0.000000, 0.000000, 2.000000, 40.000000, 40.000000)

The second is:

>>>> (Matrix("Translate(40,40)") * Matrix("scale(2)"))
Matrix(2.000000, 0.000000, 0.000000, 2.000000, 80.000000, 80.000000)

This is:

>>>> Point(100,100) * Matrix("Matrix(2,0,0,2,80,80)")

SVG Transform Parsing

Within the SVG.nodes() schema where objects svg nodes are dictionaries. The transform tags within objects are combined together. This means that if you get a the d object from an end-node in the SVG you can choose to apply the transformations. This list of transformations complies with the SVG spec. They merely applied automatically in the call for nodes().

>>> node = { 'd': "M0,0 100,0, 0,100 z", 'transform': "scale(0.5)"}
>>> print(Path(node['d']) * Matrix(node['transform']))
M 0,0 L 50,0 L 0,50 Z

SVG Viewport Scaling, Unit Scaling

There is need in many applications to append a transformation for the viewbox, height, width. So as to prevent a variety of errors where the expected size is far vastly different from the actual size. If we have a viewbox of "0 0 100 100" but the height and width show that to be 50cm wide, then a path "M25,50L75,50" within that viewbox has a real size of length of 25cm which can be quite different from 50 (unitless value).

parse_viewbox_transform performs this operation. It uses the conversion of the width and height to real world units. With a variable setting of ppi or pixels_per_inch. The standard default value for this is 96. Though other values have been used in other places. And this property can be configured.

This can be easily invoked calling the nodes generator on the SVG object. If called with viewport_transform=True it will parse this viewport appending the required transformation to the SVG root object, which will be passed to all the child nodes. If you then apply the transform to the path object it will be scaled to the real size.

The parse_viewbox_transform code conforms to the algorithm given in SVG 1.1 7.2, SVG 2.0 8.2 'equivalent transform of an SVG viewport.' This will also fully implement the preserveAspectRatio, xMidYMid, and meetOrSlice values.

SVG Shapes

One of the elements within SVG are the shapes. While all of these can be converted to paths. They can serve some usages in their original form. There are methods to deform a rectangle that simple don't exist in the path form of that object.

  • Rect
  • Ellipse
  • Circle
  • Line (SimpleLine)
  • Polyline
  • Polygon

The Line shape is converted into a shape called SimpleLine to not interfere with the Line(PathSegment).


Rectangles are defined by x,y and height and width. Within SVG there are also rounded corners defined with rx and ry.

>>> Rect(10,10,8,4).d()
'M10 10 L 18 10 L 18 14 L 10 14 z'

Much like all the paths these shapes also contain a .d() function that produces the path data for them. This could then be wrapped into a Path().

>>> print(Path(Rect(10,10,8,4).d()) * "rotate(0.5turns)")
M -10,-10 L -18,-10 L -18,-14 L -10,-14 Z

Matrices can be applied to Rect objects directly.

>>> from svg.elements import *
>>> Rect(10,10,8,4) * "rotate(0.5turns)"
Rect(x=-18, y=-14, w=8, h=4)

>>> Rect(10,10,8,4) * "rotate(0.25turns)"
Rect(x=-14, y=10, w=4, h=8)

With a caveat that rectangles only actually make sense when parallel so the results can be strange:

>>> Rect(10,10,8,4) * "rotate(14deg)"
Rect(x=6.316050724365, y=12.122176218757, w=8.730053392607, h=5.816558069901)

This also works with rx and ry:

>>> Rect(10,10,8,4, 2, 1) * "rotate(0.25turns)"
Rect(x=-14, y=10, w=4, h=8, rx=-1, ry=2)


>>> Rect(10,10,8,4, 2, 1) * "rotate(14deg)"
Rect(x=6.316050724365, y=12.122176218757, w=8.730053392607, h=5.816558069901, rx=1.698669556952, ry=1.454139517475)

And the matrix forms should work correctly with most matrices:

>>> Rect(10,10,8,4, 2, 1) * "translate(50)"
Rect(x=60, y=10, w=8, h=4, rx=2, ry=1)

If you want a form that deforms the rectangle-ness of the shape you'll be better off just converting it to a Path.

Ellipse & Circle

Ellipses and Circles are different shapes but since a circle is a particular kind of Ellipse much of the functionality here is duplicated.

While the objects are different they can be checked for equivolency:

>>> Ellipse(center=(0,0), rx=10, ry=10) == Circle(center="0,0", r=10.0)

Also, when circles are changed with a matrix they become ellipses:

>>> Circle(center="0,0", r=10.0) * "scale(2,1)"
Ellipse(center=Point(0,0), rx=20, ry=10, rotation=0)

And they will become a circle again if they are a circle:

>>> Ellipse(center=Point(0,0), rx=20, ry=10, rotation=0) * "scale(0.5,1)"
Circle(center=Point(0,0), r=10, rotation=0)

They won't change if they don't deform.

>>> Circle(center="0,0", r=10.0) * "rotate(20deg)"
Circle(center=Point(0,0), r=10, rotation=0.349065850399)

However, currently the rotations aren't taken into account for the path transformations.

>>>(Ellipse(center=Point(0,0), rx=20, ry=10, rotation=0) * "rotate(45)").d()
'M -20.000000, 0.000000 a20.000000,10.000000 0 1,0 40.000000,0 a20.000000,10.000000 0 1,0 -40.000000,0'


SimpleLine is renamed from the SVG form of Line since we already have Line objects as PathSegments.

>>> s = SimpleLine(0,0,200,200)
>>> s
SimpleLine(start=Point(0,0), end=Point(200,200))
>>> s *= "rotate(45)"
>>> s
SimpleLine(start=Point(0,0), end=Point(0,282.842712474619))
>>> s.d()
'M 0,0 L 2.84217E-14,282.843'

Polyline and Polygon

The difference here is polylines are not closed while Polygons are closed.

>>> p = Polygon(0,0, 100,0, 100,100, 0,100)
>>> p *= "scale(2)"
>>> p.d()
'M 0,0, 200,0, 200,200, 0,200z'

and the same for Polyline:

>>> p = Polyline(0,0, 100,0, 100,100, 0,100)
>>> p *= "scale(2)"
>>> p.d()
'M 0,0, 200,0, 200,200, 0,200'

CSS Distance

The conversion of distances to utilizes another element Distance It's a minor element and is a backed by a float. As such you can call and it will convert 25mm to pixels with the default 96 pixels per inch. It provides conversions for mm, cm, in, px, pt, pc. You can also parse an element like the string '25mm' calling Distance.parse('25mm') and get the expected results. You can also call Distance.parse('25mm').as_inch which will return 25mm in inches.

>>> Distance.parse('25mm').as_inch


Color is another important element it is back by int in the form of an ARGB 32-bit integer. It will parse all the SVG color functions.

If we get the fill or stroke of an object from a node be a text element. This needs to be converted to a consistent form. We could have a 3, 4, 6, or 8 digit hex. rgb(r,g,b) value, a static dictionary name or percent rgb(r,g,b). And must be properly parsed according to the spec.

>>> Color.parse("red").hex


Angle is backed by a 'float' and contains all the CSS angle values. 'deg', 'rad', 'grad', 'turn'.

>>> Angle.degrees(360).as_radians

The Angle element is used automatically with the Skew and Rotate for matrix.

>>> Point(100,100) * Matrix("SkewX(0.05turn)")


Point is used in all the SVG path segment objects. With regard to svg.path it is not back by, but implements all the same functionality as a complex and will take a complex as an input. So older svg.path code will remain valid. While also allowing for additional functionality like finding a distance.

>>> Point(0+100j).distance_to([0,0])

The class supports complex subscriptable elements, .x and .y methods, and .imag and .real. As well as providing several of these indexing methods.

It includes a number of point functions like:

  • move_towards(point,float): Move this point towards the other point. with an amount [0,1]
  • distance_to(point): Calculate the Euclidean distance to the other point.
  • angle_to(point): Calculate the angle to the given point.
  • polar_to(angle,distance): Return a point via polar coords at the angle and distance.
  • reflected_across(point): Returns a point reflected across another point. (Smooth bezier curves use this).

This for example takes the 0,0 point turns 1/8th of a turn, and moves forward by 5cm.

>>> Point(0).polar_to(Angle.turns(0.125),


The Path element of this project is based in part on the regebro/svg.path ( ) project. It is also may be based, in part, on some elements of mathandy/svgpathtools ( ).

The Zingl-Bresenham plotting algorithms are from Alois Zingl's "The Beauty of Bresenham's Algorithm" ( ). They are all MIT Licensed and this library is also MIT licensed. In the case of Zingl's work this isn't explicit from his website, however from personal correspondence "'Free and open source' means you can do anything with it like the MIT licence[sic]."


This module is under a MIT License.

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