Defining paths in your **Matplotlib Visualization**.

The object underlying all of the matplotlib.patch objects is the Path, which supports the standard set of moveto, lineto, curveto commands to draw simple and compound outlines consisting of line segments and splines. The Path is instantiated with an (N,2) array of (x,y) vertices, and an N-length array of path codes. For example, to draw the unit rectangle from (0,0) to (1,1), we could use this code.

```
import matplotlib.pyplot as plt
from matplotlib.path import Path
import matplotlib.patches as patches
verts = [
(0., 0.), # left, bottom
(0., 1.), # left, top
(1., 1.), # right, top
(1., 0.), # right, bottom
(0., 0.), # ignored
]
codes = [
Path.MOVETO,
Path.LINETO,
Path.LINETO,
Path.LINETO,
Path.CLOSEPOLY,
]
path = Path(verts, codes)
fig, ax = plt.subplots()
patch = patches.PathPatch(path, facecolor='red', lw=2)
ax.add_patch(patch)
ax.set_xlim(-2, 2)
ax.set_ylim(-2, 2)
plt.show()
```

- Code Vertices Description
- STOP 1 (ignored) A marker for the end of the entire path (currently not required and ignored)
- MOVETO 1 Pick up the pen and move to the given vertex.
- LINETO 1 Draw a line from the current position to the given vertex.
- CURVE3 2 (1 control point, 1 endpoint) Draw a quadratic Bézier curve from the current position, with the given control point, to the given endpoint.
- CURVE4 3 (2 control points, 1 endpoint) Draw a cubic Bézier curve from the current position, with the given control points, to the given endpoint.
- CLOSEPOLY 1 (point itself is ignored) Draw a line segment to the start point of the current polyline.

Some of the path components require multiple vertices to specify them: for example CURVE 3 is a bézier curve with one control point and one endpoint, and CURVE4 has three vertices for the two control points and the endpoint. The example below shows a CURVE4 Bézier spline -- the bézier curve will be contained in the convex hull of the start point, the two control points, and the endpoint.

```
verts = [
(0., 0.), # P0
(0.2, 1.), # P1
(1., 0.8), # P2
(0.8, 0.), # P3
]
codes = [
Path.MOVETO,
Path.CURVE4,
Path.CURVE4,
Path.CURVE4,
]
path = Path(verts, codes)
fig, ax = plt.subplots()
patch = patches.PathPatch(path, facecolor='none', lw=2)
ax.add_patch(patch)
xs, ys = zip(*verts)
ax.plot(xs, ys, 'x--', lw=2, color='black', ms=10)
ax.text(-0.05, -0.05, 'P0')
ax.text(0.15, 1.05, 'P1')
ax.text(1.05, 0.85, 'P2')
ax.text(0.85, -0.05, 'P3')
ax.set_xlim(-0.1, 1.1)
ax.set_ylim(-0.1, 1.1)
plt.show()
```

All of the simple patch primitives in matplotlib, Rectangle, Circle, Polygon, etc, are implemented with a simple path. Plotting functions like hist() and bar(), which create a number of primitives, e.g., a bunch of Rectangles, can usually be implemented more efficiently using a compound path. The reason bar creates a list of rectangles and not a compound path is largely historical: the Path code is comparatively new and the bar predates it. While we could change it now, it would break old code, so here we will cover how to create compound paths, replacing the functionality in the bar, in case you need to do so in your own code for efficiency reasons, e.g., you are creating an animated bar plot.

We will make the histogram chart by creating a series of rectangles for each histogram bar: the rectangle width is the bin width and the rectangle height is the number of data points in that bin. First, we'll create some random normally distributed data and compute the histogram. Because numpy returns the bin edges and not centers, the length of bins is 1 greater than the length of n in the example below:

```
import numpy as np
import matplotlib.patches as patches
import matplotlib.path as path
fig, ax = plt.subplots()
# Fixing random state for reproducibility
np.random.seed(19680801)
# histogram our data with numpy
data = np.random.randn(1000)
n, bins = np.histogram(data, 100)
# get the corners of the rectangles for the histogram
left = np.array(bins[:-1])
right = np.array(bins[1:])
bottom = np.zeros(len(left))
top = bottom + n
nrects = len(left)
nverts = nrects*(1+3+1)
verts = np.zeros((nverts, 2))
codes = np.ones(nverts, int) * path.Path.LINETO
codes[0::5] = path.Path.MOVETO
codes[4::5] = path.Path.CLOSEPOLY
verts[0::5, 0] = left
verts[0::5, 1] = bottom
verts[1::5, 0] = left
verts[1::5, 1] = top
verts[2::5, 0] = right
verts[2::5, 1] = top
verts[3::5, 0] = right
verts[3::5, 1] = bottom
barpath = path.Path(verts, codes)
patch = patches.PathPatch(barpath, facecolor='green',
edgecolor='black', alpha=0.5)
ax.add_patch(patch)
ax.set_xlim(left[0], right[-1])
ax.set_ylim(bottom.min(), top.max())
plt.show()
```

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