Code:Vectors
This interactive code demp plots three vectors using matplotlib. The "zero" vector, x[0], is colored blue because it is recomputed from the other two vectors, x[1] and x[2].
If you drag them around, you can see that x[0] always shows the sum,
x[1] + x[2]
By changing the "def update_vec" function, you can implement dot products, projections, and reflections.
<source lang="python"> import numpy as np import matplotlib.path as mpath import matplotlib.patches as mpatches import matplotlib.pyplot as plt
Path = mpath.Path
- fig, ax = plt.subplots()
ax = plt.gca()
- arrows = np.array([[[0.0, 0.0], [0.0, 2.0]]])
arrows = np.array([[0.0, 2.0], [-1,-1], [3,-0.5]])
codes = [Path.MOVETO, Path.LINETO, Path.LINETO,
Path.LINETO, Path.LINETO, Path.LINETO]
def path_from_vec(x,y,dx,dy):
r = (dx*dx+dy*dy)**0.5
a = 0.5
c = 0.2*dx/r
s = 0.2*dy/r
x1 = x + (r-0.2)*dx/r
y1 = y + (r-0.2)*dy/r
pathdata = [(x,y),
(x1,y1),
(x1+s-a*c, y1-c-a*s),
(x1+c, y1+s),
(x1-s-a*c, y1+c-a*s),
(x1,y1)]
return pathdata
def to_path(v, color='green'):
verts = path_from_vec(0., 0., *v) path = mpath.Path(verts, codes) patch = mpatches.PathPatch(path, facecolor=color, edgecolor='k', alpha=0.5) ax.add_patch(patch) return patch
class PathInteractor(object):
showverts = True epsilon = 10 # max pixel distance to count as a vertex hit
def __init__(self, vecs):
self.paths = []
color = 'blue'
vecs[0] = update_vec(vecs)
for i,v in enumerate(vecs):
if i > 0:
color = 'green'
path = to_path(v, color)
self.paths.append(path)
path.set_animated(True)
self.ax = self.paths[0].axes
canvas = self.ax.figure.canvas
self.vecs = vecs
self._ind = None # the active vert
canvas.mpl_connect('draw_event', self.draw_callback)
canvas.mpl_connect('button_press_event', self.button_press_callback)
canvas.mpl_connect('key_press_event', self.key_press_callback)
canvas.mpl_connect('button_release_event', self.button_release_callback)
canvas.mpl_connect('motion_notify_event', self.motion_notify_callback)
self.canvas = canvas
def draw_callback(self, event):
self.background = self.canvas.copy_from_bbox(self.ax.bbox)
for path in self.paths:
self.ax.draw_artist(path)
self.canvas.blit(self.ax.bbox)
def get_ind_under_point(self, event):
'get the index of the vertex under point if within epsilon tolerance'
# display coords
r = np.sqrt(sum(self.vecs*self.vecs,1))
r += (0.1 - r)*(r < 0.1)
xy = self.vecs*(r-0.1)/r # move location to arrow head
xyt = self.paths[0].get_transform().transform(xy)
xt, yt = xyt[:, 0], xyt[:, 1]
d = np.sqrt((xt - event.x)**2 + (yt - event.y)**2)
ind = d.argmin()
if d[ind] >= self.epsilon:
ind = None
return ind
def button_press_callback(self, event):
'whenever a mouse button is pressed'
if not self.showverts:
return
if event.inaxes is None:
return
if event.button != 1:
return
self._ind = self.get_ind_under_point(event)
def button_release_callback(self, event):
'whenever a mouse button is released'
if not self.showverts:
return
if event.button != 1:
return
self._ind = None
def key_press_callback(self, event):
'whenever a key is pressed'
if not event.inaxes:
return
#if event.key == 't':
# self.showverts = not self.showverts
# self.line.set_visible(self.showverts)
# if not self.showverts:
# self._ind = None
#self.canvas.draw()
def motion_notify_callback(self, event):
'on mouse movement'
if not self.showverts:
return
if self._ind is None:
return
if event.inaxes is None:
return
if event.button != 1:
return
x, y = event.xdata, event.ydata
self.vecs[self._ind] = x, y
self.paths[self._ind].get_path().vertices[:] = \
path_from_vec(0., 0., *self.vecs[self._ind])
# update vec 0 based on callback
if self._ind != 0:
self.vecs[0] = update_vec(self.vecs)
self.paths[0].get_path().vertices[:] = \
path_from_vec(0., 0., *self.vecs[0])
self.canvas.restore_region(self.background)
for path in self.paths:
self.ax.draw_artist(path)
self.canvas.blit(self.ax.bbox)
def update_vec(x):
return x[1]+x[2]
interactor = PathInteractor(arrows) ax.set_title('drag vertices to update path') ax.set_xlim(-3, 4) ax.set_ylim(-3, 4)
plt.show() </source>
