在matplotlib中，我如何绘制多色的线，例如彩虹 [英] In matplotlib, how can I plot a multi-colored line, like a rainbow
问题描述
我想绘制具有不同颜色的平行线.例如.而不是一条粗细为6的红线，我希望有两条粗细为3的平行线，一条为红色，一条为蓝色.
任何想法将不胜感激.
谢谢
即使使用智能偏移(如下)，在连续点之间具有锐角的视图中仍然存在问题.
智能补偿的放大视图:
不同厚度的叠加线:
绘制平行线并非易事.当然，使用简单的均匀偏移将不会显示所需的结果.这显示在下面的左图中.
可以在matplotlib中产生这样的简单偏移量，如转换教程.
方法1
一个更好的解决方案可能是使用右侧所示的想法.要计算第n个点的偏移量，我们可以使用法线向量到n-1 st点和n+1 st点之间的线，并沿该法线向量使用相同的距离来计算偏移点.
此方法的优点在于，原始线中的点数与偏移线中的点数相同.缺点是，它不能完全准确，如图片所示.
此方法在下面的代码的功能offset中实现.
为了使它对于matplotlib图有用，我们需要考虑线宽应该独立于数据单元.线宽通常以点为单位给出，而偏移量最好以相同单位给出，例如可以满足问题的要求(两条平行的宽度为3的线").
因此，该想法是使用ax.transData.transform将坐标从数据转换为显示坐标.同样，点o中的偏移也可以转换为相同的单位:使用dpi和ppi = 72的标准，显示坐标中的偏移为o*dpi/ppi.在应用了显示坐标的偏移量之后，逆变换(ax.transData.inverted().transform)允许进行逆变换.
现在问题的另一个层面是:如何确保偏移量保持不变，而与图形的缩放和大小无关? 每次调整大小事件发生时，可以通过重新计算偏移量来解决最后一个问题.
这是这种方法产生的彩虹曲线的样子.
这是生成图像的代码.
import numpy as np
import matplotlib.pyplot as plt
dpi = 100
def offset(x,y, o):
""" Offset coordinates given by array x,y by o """
X = np.c_[x,y].T
m = np.array([[0,-1],[1,0]])
R = np.zeros_like(X)
S = X[:,2:]-X[:,:-2]
R[:,1:-1] = np.dot(m, S)
R[:,0] = np.dot(m, X[:,1]-X[:,0])
R[:,-1] = np.dot(m, X[:,-1]-X[:,-2])
On = R/np.sqrt(R[0,:]**2+R[1,:]**2)*o
Out = On+X
return Out[0,:], Out[1,:]
def offset_curve(ax, x,y, o):
""" Offset array x,y in data coordinates
by o in points """
trans = ax.transData.transform
inv = ax.transData.inverted().transform
X = np.c_[x,y]
Xt = trans(X)
xto, yto = offset(Xt[:,0],Xt[:,1],o*dpi/72. )
Xto = np.c_[xto, yto]
Xo = inv(Xto)
return Xo[:,0], Xo[:,1]
# some single points
y = np.array([1,2,2,3,3,0])
x = np.arange(len(y))
#or try a sinus
x = np.linspace(0,9)
y=np.sin(x)*x/3.
fig, ax=plt.subplots(figsize=(4,2.5), dpi=dpi)
cols = ["#fff40b", "#00e103", "#ff9921", "#3a00ef", "#ff2121", "#af00e7"]
lw = 2.
lines = []
for i in range(len(cols)):
l, = plt.plot(x,y, lw=lw, color=cols[i])
lines.append(l)
def plot_rainbow(event=None):
xr = range(6); yr = range(6);
xr[0],yr[0] = offset_curve(ax, x,y, lw/2.)
xr[1],yr[1] = offset_curve(ax, x,y, -lw/2.)
xr[2],yr[2] = offset_curve(ax, xr[0],yr[0], lw)
xr[3],yr[3] = offset_curve(ax, xr[1],yr[1], -lw)
xr[4],yr[4] = offset_curve(ax, xr[2],yr[2], lw)
xr[5],yr[5] = offset_curve(ax, xr[3],yr[3], -lw)
for i in range(6):
lines[i].set_data(xr[i], yr[i])
plot_rainbow()
fig.canvas.mpl_connect("resize_event", plot_rainbow)
fig.canvas.mpl_connect("button_release_event", plot_rainbow)
plt.savefig(__file__+".png", dpi=dpi)
plt.show()
方法2
为避免线条重叠，必须使用更复杂的解决方案. 首先可以偏移垂直于其所属的两个线段的每个点(下图中的绿色点).然后通过这些偏移点计算线并找到它们的交点.
一种特殊情况是两个后续线段的斜率相等.必须注意这一点(下面的代码中的eps).
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
dpi = 100
def intersect(p1, p2, q1, q2, eps=1.e-10):
""" given two lines, first through points pn, second through qn,
find the intersection """
x1 = p1[0]; y1 = p1[1]; x2 = p2[0]; y2 = p2[1]
x3 = q1[0]; y3 = q1[1]; x4 = q2[0]; y4 = q2[1]
nomX = ((x1*y2-y1*x2)*(x3-x4)- (x1-x2)*(x3*y4-y3*x4))
denom = float( (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4) )
nomY = (x1*y2-y1*x2)*(y3-y4) - (y1-y2)*(x3*y4-y3*x4)
if np.abs(denom) < eps:
#print "intersection undefined", p1
return np.array( p1 )
else:
return np.array( [ nomX/denom , nomY/denom ])
def offset(x,y, o, eps=1.e-10):
""" Offset coordinates given by array x,y by o """
X = np.c_[x,y].T
m = np.array([[0,-1],[1,0]])
S = X[:,1:]-X[:,:-1]
R = np.dot(m, S)
norm = np.sqrt(R[0,:]**2+R[1,:]**2) / o
On = R/norm
Outa = On+X[:,1:]
Outb = On+X[:,:-1]
G = np.zeros_like(X)
for i in xrange(0, len(X[0,:])-2):
p = intersect(Outa[:,i], Outb[:,i], Outa[:,i+1], Outb[:,i+1], eps=eps)
G[:,i+1] = p
G[:,0] = Outb[:,0]
G[:,-1] = Outa[:,-1]
return G[0,:], G[1,:]
def offset_curve(ax, x,y, o, eps=1.e-10):
""" Offset array x,y in data coordinates
by o in points """
trans = ax.transData.transform
inv = ax.transData.inverted().transform
X = np.c_[x,y]
Xt = trans(X)
xto, yto = offset(Xt[:,0],Xt[:,1],o*dpi/72., eps=eps )
Xto = np.c_[xto, yto]
Xo = inv(Xto)
return Xo[:,0], Xo[:,1]
# some single points
y = np.array([1,1,2,0,3,2,1.,4,3]) *1.e9
x = np.arange(len(y))
x[3]=x[4]
#or try a sinus
#x = np.linspace(0,9)
#y=np.sin(x)*x/3.
fig, ax=plt.subplots(figsize=(4,2.5), dpi=dpi)
cols = ["r", "b"]
lw = 11.
lines = []
for i in range(len(cols)):
l, = plt.plot(x,y, lw=lw, color=cols[i], solid_joinstyle="miter")
lines.append(l)
def plot_rainbow(event=None):
xr = range(2); yr = range(2);
xr[0],yr[0] = offset_curve(ax, x,y, lw/2.)
xr[1],yr[1] = offset_curve(ax, x,y, -lw/2.)
for i in range(2):
lines[i].set_data(xr[i], yr[i])
plot_rainbow()
fig.canvas.mpl_connect("resize_event", plot_rainbow)
fig.canvas.mpl_connect("button_release_event", plot_rainbow)
plt.show()
请注意，只要直线之间的偏移量小于直线上后续点之间的距离，此方法就可以正常工作.否则，方法1可能更适合.
I would like to plot parallel lines with different colors. E.g. rather than a single red line of thickness 6, I would like to have two parallel lines of thickness 3, with one red and one blue.
Any thoughts would be appreciated.
Merci
Even with the smart offsetting (s. below), there is still an issue in a view that has sharp angles between consecutive points.
Zoomed view of smart offsetting:
Overlaying lines of varying thickness:
Plotting parallel lines is not an easy task. Using a simple uniform offset will of course not show the desired result. This is shown in the left picture below.
Such a simple offset can be produced in matplotlib as shown in the transformation tutorial.
Method1
A better solution may be to use the idea sketched on the right side. To calculate the offset of the nth point we can use the normal vector to the line between the n-1st and the n+1st point and use the same distance along this normal vector to calculate the offset point.
The advantage of this method is that we have the same number of points in the original line as in the offset line. The disadvantage is that it is not completely accurate, as can be see in the picture.
This method is implemented in the function offset in the code below.
In order to make this useful for a matplotlib plot, we need to consider that the linewidth should be independent of the data units. Linewidth is usually given in units of points, and the offset would best be given in the same unit, such that e.g. the requirement from the question ("two parallel lines of width 3") can be met.
The idea is therefore to transform the coordinates from data to display coordinates, using ax.transData.transform. Also the offset in points o can be transformed to the same units: Using the dpi and the standard of ppi=72, the offset in display coordinates is o*dpi/ppi. After the offset in display coordinates has been applied, the inverse transform (ax.transData.inverted().transform) allows a backtransformation.
Now there is another dimension of the problem: How to assure that the offset remains the same independent of the zoom and size of the figure? This last point can be addressed by recalculating the offset each time a zooming of resizing event has taken place.
Here is how a rainbow curve would look like produced by this method.
And here is the code to produce the image.
import numpy as np
import matplotlib.pyplot as plt
dpi = 100
def offset(x,y, o):
""" Offset coordinates given by array x,y by o """
X = np.c_[x,y].T
m = np.array([[0,-1],[1,0]])
R = np.zeros_like(X)
S = X[:,2:]-X[:,:-2]
R[:,1:-1] = np.dot(m, S)
R[:,0] = np.dot(m, X[:,1]-X[:,0])
R[:,-1] = np.dot(m, X[:,-1]-X[:,-2])
On = R/np.sqrt(R[0,:]**2+R[1,:]**2)*o
Out = On+X
return Out[0,:], Out[1,:]
def offset_curve(ax, x,y, o):
""" Offset array x,y in data coordinates
by o in points """
trans = ax.transData.transform
inv = ax.transData.inverted().transform
X = np.c_[x,y]
Xt = trans(X)
xto, yto = offset(Xt[:,0],Xt[:,1],o*dpi/72. )
Xto = np.c_[xto, yto]
Xo = inv(Xto)
return Xo[:,0], Xo[:,1]
# some single points
y = np.array([1,2,2,3,3,0])
x = np.arange(len(y))
#or try a sinus
x = np.linspace(0,9)
y=np.sin(x)*x/3.
fig, ax=plt.subplots(figsize=(4,2.5), dpi=dpi)
cols = ["#fff40b", "#00e103", "#ff9921", "#3a00ef", "#ff2121", "#af00e7"]
lw = 2.
lines = []
for i in range(len(cols)):
l, = plt.plot(x,y, lw=lw, color=cols[i])
lines.append(l)
def plot_rainbow(event=None):
xr = range(6); yr = range(6);
xr[0],yr[0] = offset_curve(ax, x,y, lw/2.)
xr[1],yr[1] = offset_curve(ax, x,y, -lw/2.)
xr[2],yr[2] = offset_curve(ax, xr[0],yr[0], lw)
xr[3],yr[3] = offset_curve(ax, xr[1],yr[1], -lw)
xr[4],yr[4] = offset_curve(ax, xr[2],yr[2], lw)
xr[5],yr[5] = offset_curve(ax, xr[3],yr[3], -lw)
for i in range(6):
lines[i].set_data(xr[i], yr[i])
plot_rainbow()
fig.canvas.mpl_connect("resize_event", plot_rainbow)
fig.canvas.mpl_connect("button_release_event", plot_rainbow)
plt.savefig(__file__+".png", dpi=dpi)
plt.show()
Method2
To avoid overlapping lines, one has to use a more complicated solution. One could first offset every point normal to the two line segments it is part of (green points in the picture below). Then calculate the line through those offset points and find their intersection.
A particular case would be when the slopes of two subsequent line segments equal. This has to be taken care of (eps in the code below).
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
dpi = 100
def intersect(p1, p2, q1, q2, eps=1.e-10):
""" given two lines, first through points pn, second through qn,
find the intersection """
x1 = p1[0]; y1 = p1[1]; x2 = p2[0]; y2 = p2[1]
x3 = q1[0]; y3 = q1[1]; x4 = q2[0]; y4 = q2[1]
nomX = ((x1*y2-y1*x2)*(x3-x4)- (x1-x2)*(x3*y4-y3*x4))
denom = float( (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4) )
nomY = (x1*y2-y1*x2)*(y3-y4) - (y1-y2)*(x3*y4-y3*x4)
if np.abs(denom) < eps:
#print "intersection undefined", p1
return np.array( p1 )
else:
return np.array( [ nomX/denom , nomY/denom ])
def offset(x,y, o, eps=1.e-10):
""" Offset coordinates given by array x,y by o """
X = np.c_[x,y].T
m = np.array([[0,-1],[1,0]])
S = X[:,1:]-X[:,:-1]
R = np.dot(m, S)
norm = np.sqrt(R[0,:]**2+R[1,:]**2) / o
On = R/norm
Outa = On+X[:,1:]
Outb = On+X[:,:-1]
G = np.zeros_like(X)
for i in xrange(0, len(X[0,:])-2):
p = intersect(Outa[:,i], Outb[:,i], Outa[:,i+1], Outb[:,i+1], eps=eps)
G[:,i+1] = p
G[:,0] = Outb[:,0]
G[:,-1] = Outa[:,-1]
return G[0,:], G[1,:]
def offset_curve(ax, x,y, o, eps=1.e-10):
""" Offset array x,y in data coordinates
by o in points """
trans = ax.transData.transform
inv = ax.transData.inverted().transform
X = np.c_[x,y]
Xt = trans(X)
xto, yto = offset(Xt[:,0],Xt[:,1],o*dpi/72., eps=eps )
Xto = np.c_[xto, yto]
Xo = inv(Xto)
return Xo[:,0], Xo[:,1]
# some single points
y = np.array([1,1,2,0,3,2,1.,4,3]) *1.e9
x = np.arange(len(y))
x[3]=x[4]
#or try a sinus
#x = np.linspace(0,9)
#y=np.sin(x)*x/3.
fig, ax=plt.subplots(figsize=(4,2.5), dpi=dpi)
cols = ["r", "b"]
lw = 11.
lines = []
for i in range(len(cols)):
l, = plt.plot(x,y, lw=lw, color=cols[i], solid_joinstyle="miter")
lines.append(l)
def plot_rainbow(event=None):
xr = range(2); yr = range(2);
xr[0],yr[0] = offset_curve(ax, x,y, lw/2.)
xr[1],yr[1] = offset_curve(ax, x,y, -lw/2.)
for i in range(2):
lines[i].set_data(xr[i], yr[i])
plot_rainbow()
fig.canvas.mpl_connect("resize_event", plot_rainbow)
fig.canvas.mpl_connect("button_release_event", plot_rainbow)
plt.show()
Note that this method should work well as long as the offset between the lines is smaller then the distance between subsequent points on the line. Otherwise method 1 may be better suited.
这篇关于在matplotlib中，我如何绘制多色的线，例如彩虹的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！
