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added example to README plus minor changed 

example regarding computing many points quickly with numpy arrays
pull/7/merge
Andy 2017-03-30 02:55:40 -07:00
parent dcd4896fd6
commit 3ad65aa3c5
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45
README.ipynb
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@ -86,7 +86,7 @@
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@ -305,7 +305,7 @@
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@ -346,8 +346,8 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Tangent vectors and Bezier curves as numpy polynomial objects\n", "### Bezier curves as NumPy polynomial objects\n",
"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. \n", "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. \n",
"There's also a ``polynomial2bezier()`` function in the pathtools.py submodule to convert polynomials back to Bezier curves. \n", "There's also a ``polynomial2bezier()`` function in the pathtools.py submodule to convert polynomials back to Bezier curves. \n",
"\n", "\n",
"**Note:** cubic Bezier curves are parameterized as $$\\mathcal{B}(t) = P_0(1-t)^3 + 3P_1(1-t)^2t + 3P_2(1-t)t^2 + P_3t^3$$\n", "**Note:** cubic Bezier curves are parameterized as $$\\mathcal{B}(t) = P_0(1-t)^3 + 3P_1(1-t)^2t + 3P_2(1-t)t^2 + P_3t^3$$\n",
@ -363,12 +363,12 @@
"\\end{bmatrix}\n", "\\end{bmatrix}\n",
"\\begin{bmatrix}P_0\\\\P_1\\\\P_2\\\\P_3\\end{bmatrix}$$ \n", "\\begin{bmatrix}P_0\\\\P_1\\\\P_2\\\\P_3\\end{bmatrix}$$ \n",
"\n", "\n",
"QuadraticBezier.poly() and Line.poly() are defined similarly." "`QuadraticBezier.poly()` and `Line.poly()` are [defined similarly](https://en.wikipedia.org/wiki/B%C3%A9zier_curve#General_definition)."
] ]
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@ -409,14 +409,23 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"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.\n", "The ability to convert between Bezier objects to NumPy polynomial objects is very useful. For starters, we can take turn a list of Bézier segments into a NumPy array \n",
"### Numpy Array operations on Bézier path segments\n",
"[Example available here](https://github.com/mathandy/svgpathtools/blob/master/examples/compute-many-points-quickly-using-numpy-arrays.py)"
]
},
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"source": [
"To further illustrate the power 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.\n",
"\n", "\n",
"### Tangent vectors (and more on polynomials)" "### Tangent vectors (and more on NumPy polynomials)"
] ]
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64
README.rst
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@ -1,3 +1,4 @@
svgpathtools svgpathtools
============ ============
@ -37,11 +38,6 @@ Some included tools:
- compute **inverse arc length** - compute **inverse arc length**
- convert RGB color tuples to hexadecimal color strings and back - convert RGB color tuples to hexadecimal color strings and back
Note on Python 3
----------------
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.
Prerequisites Prerequisites
------------- -------------
@ -85,8 +81,6 @@ 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 module <https://github.com/regebro/svg.path>`__. Interested svg.path
users should see the compatibility notes at bottom of this readme. 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 <http://pomax.github.io/bezierinfo/>`_, an outstanding resource for learning about Bézier curves and Bézier curve-related algorithms.
Basic Usage Basic Usage
----------- -----------
@ -117,11 +111,11 @@ information on what each parameter means.
on discontinuous Path objects. A simple workaround is provided, however, on discontinuous Path objects. A simple workaround is provided, however,
by the ``Path.continuous_subpaths()`` method. `↩ <#a1>`__ by the ``Path.continuous_subpaths()`` method. `↩ <#a1>`__
.. code:: python .. code:: ipython2
from __future__ import division, print_function from __future__ import division, print_function
.. code:: python .. code:: ipython2
# Coordinates are given as points in the complex plane # Coordinates are given as points in the complex plane
from svgpathtools import Path, Line, QuadraticBezier, CubicBezier, Arc from svgpathtools import Path, Line, QuadraticBezier, CubicBezier, Arc
@ -158,7 +152,7 @@ The ``Path`` class is a mutable sequence, so it behaves much like a
list. So segments can **append**\ ed, **insert**\ ed, set by index, list. So segments can **append**\ ed, **insert**\ ed, set by index,
**del**\ eted, **enumerate**\ d, **slice**\ d out, etc. **del**\ eted, **enumerate**\ d, **slice**\ d out, etc.
.. code:: python .. code:: ipython2
# Let's append another to the end of it # Let's append another to the end of it
path.append(CubicBezier(250+350j, 275+350j, 250+225j, 200+100j)) path.append(CubicBezier(250+350j, 275+350j, 250+225j, 200+100j))
@ -225,7 +219,7 @@ Reading SVGSs
| Note: Line, Polyline, Polygon, and Path SVG elements can all be | Note: Line, Polyline, Polygon, and Path SVG elements can all be
converted to Path objects using this function. converted to Path objects using this function.
.. code:: python .. code:: ipython2
# Read SVG into a list of path objects and list of dictionaries of attributes # Read SVG into a list of path objects and list of dictionaries of attributes
from svgpathtools import svg2paths, wsvg from svgpathtools import svg2paths, wsvg
@ -262,7 +256,7 @@ convenience function **disvg()** (or set 'openinbrowser=True') to
automatically attempt to open the created svg file in your default SVG automatically attempt to open the created svg file in your default SVG
viewer. viewer.
.. code:: python .. code:: ipython2
# Let's make a new SVG that's identical to the first # Let's make a new SVG that's identical to the first
wsvg(paths, attributes=attributes, svg_attributes=svg_attributes, filename='output1.svg') wsvg(paths, attributes=attributes, svg_attributes=svg_attributes, filename='output1.svg')
@ -294,7 +288,7 @@ over the domain 0 <= t <= 1.
that ``path.point(T)=path[k].point(t)``. that ``path.point(T)=path[k].point(t)``.
| There is also a ``Path.t2T()`` method to solve the inverse problem. | There is also a ``Path.t2T()`` method to solve the inverse problem.
.. code:: python .. code:: ipython2
# Example: # Example:
@ -324,11 +318,11 @@ over the domain 0 <= t <= 1.
True True
Tangent vectors and Bezier curves as numpy polynomial objects Bezier curves as NumPy polynomial objects
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
| Another great way to work with the parameterizations for Line, | Another great way to work with the parameterizations for ``Line``,
QuadraticBezier, and CubicBezier objects is to convert them to ``QuadraticBezier``, and ``CubicBezier`` objects is to convert them to
``numpy.poly1d`` objects. This is done easily using the ``numpy.poly1d`` objects. This is done easily using the
``Line.poly()``, ``QuadraticBezier.poly()`` and ``CubicBezier.poly()`` ``Line.poly()``, ``QuadraticBezier.poly()`` and ``CubicBezier.poly()``
methods. methods.
@ -360,9 +354,10 @@ form
\end{bmatrix} \end{bmatrix}
\begin{bmatrix}P_0\\P_1\\P_2\\P_3\end{bmatrix} \begin{bmatrix}P_0\\P_1\\P_2\\P_3\end{bmatrix}
QuadraticBezier.poly() and Line.poly() are defined similarly. ``QuadraticBezier.poly()`` and ``Line.poly()`` are `defined
similarly <https://en.wikipedia.org/wiki/B%C3%A9zier_curve#General_definition>`__.
.. code:: python .. code:: ipython2
# Example: # Example:
b = CubicBezier(300+100j, 100+100j, 200+200j, 200+300j) b = CubicBezier(300+100j, 100+100j, 200+200j, 200+300j)
@ -392,15 +387,21 @@ QuadraticBezier.poly() and Line.poly() are defined similarly.
(-400 + -100j) t + (900 + 300j) t - 600 t + (300 + 100j) (-400 + -100j) t + (900 + 300j) t - 600 t + (300 + 100j)
To illustrate the awesomeness of being able to convert our Bezier curve The ability to convert between Bezier objects to NumPy polynomial
objects to numpy.poly1d objects and back, lets compute the unit tangent objects is very useful. For starters, we can take turn a list of Bézier
vector of the above CubicBezier object, b, at t=0.5 in four different segments into a NumPy array ### Numpy Array operations on Bézier path
ways. segments `Example available
here <https://github.com/mathandy/svgpathtools/blob/master/examples/compute-many-points-quickly-using-numpy-arrays.py>`__
Tangent vectors (and more on polynomials) To further illustrate the power 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.
.. code:: python Tangent vectors (and more on NumPy polynomials)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: ipython2
t = 0.5 t = 0.5
### Method 1: the easy way ### Method 1: the easy way
@ -442,7 +443,7 @@ Tangent vectors (and more on polynomials)
Translations (shifts), reversing orientation, and normal vectors Translations (shifts), reversing orientation, and normal vectors
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
# Speaking of tangents, let's add a normal vector to the picture # Speaking of tangents, let's add a normal vector to the picture
n = b.normal(t) n = b.normal(t)
@ -472,7 +473,7 @@ Translations (shifts), reversing orientation, and normal vectors
Rotations and Translations Rotations and Translations
~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
# Let's take a Line and an Arc and make some pictures # 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) top_half = Arc(start=-1, radius=1+2j, rotation=0, large_arc=1, sweep=1, end=1)
@ -505,7 +506,7 @@ midpoints of the paths from ``test.svg``. We'll need to compute use the
``CubicBezier.length()``, and ``Arc.length()`` methods, as well as the ``CubicBezier.length()``, and ``Arc.length()`` methods, as well as the
related inverse arc length methods ``.ilength()`` function to do this. related inverse arc length methods ``.ilength()`` function to do this.
.. code:: python .. code:: ipython2
# First we'll load the path data from the file test.svg # First we'll load the path data from the file test.svg
paths, attributes = svg2paths('test.svg') paths, attributes = svg2paths('test.svg')
@ -547,7 +548,7 @@ related inverse arc length methods ``.ilength()`` function to do this.
Intersections between Bezier curves Intersections between Bezier curves
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. code:: python .. code:: ipython2
# Let's find all intersections between redpath and the other # Let's find all intersections between redpath and the other
redpath = paths[0] redpath = paths[0]
@ -571,7 +572,7 @@ An Advanced Application: Offsetting Paths
Here we'll find the `offset Here we'll find the `offset
curve <https://en.wikipedia.org/wiki/Parallel_curve>`__ for a few paths. curve <https://en.wikipedia.org/wiki/Parallel_curve>`__ for a few paths.
.. code:: python .. code:: ipython2
from svgpathtools import parse_path, Line, Path, wsvg from svgpathtools import parse_path, Line, Path, wsvg
def offset_curve(path, offset_distance, steps=1000): def offset_curve(path, offset_distance, steps=1000):
@ -628,3 +629,4 @@ Licence
------- -------
This module is under a MIT License. This module is under a MIT License.