Develop Reference

How to generate points within rectangle, at random locations and without overlap?

I have an image with width: 1980 and height: 1080.
Ultimately, I want to place various shapes within the image, but at random locations and in such a way that they do not overlap. The 0,0 coordinates of the image are in the center.
Before rendering the shapes into the image (I don't need help with this), I need to write an algorithm to generate the XY points/locations. I want to be able to specify the minimum distance any given point is allowed to get to any other points.
How can do this?
All I have been able to do, is to generate points at equally spaced locations and then add a bit of randomness to each point. But this is not ideal, because it means points just vary within some 'cell' within a grid, and if the randomness value is too high, they will appear outside of the rectangle. Here is my code:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
from random import randrange
def is_square(integer):
root = np.sqrt(integer)
return integer == int(root + 0.5) ** 2
def perfect_sqr(n):
nextN = np.floor(np.sqrt(n)) + 1
return int(nextN * nextN)
def generate_cells(width = 1920, height = 1080, n = 9, show_plot=False):
# If the number is not a perfect square, we need to find the next number which is
# so that we can get the root N, which will be used to determine the number of rows/columns
if not is_square(n):
n = perfect_sqr(n)
N = np.sqrt(n)
# generate x and y lists, where each represents an array of points evenly spaced between 0 and the width/height
x = np.array(list(range(0, width, int(width/N))))
y = np.array(list(range(0, height, int(height/N))))
# center the points within each 'cell'
x_centered = x+int(width/N)/2
y_centered = y+int(height/N)/2
x_centered = [a+randrange(50) for a in x_centered]
y_centered = [a+randrange(50) for a in y_centered]
# generate a grid with the points
xv, yv = np.meshgrid(x_centered, y_centered)
if(show_plot):
plt.scatter(xv,yv)
plt.gca().add_patch(Rectangle((0,0),width, height,edgecolor='red', facecolor='none', lw=1))
plt.show()
# convert the arrays to 1D
xx = xv.flatten()
yy = yv.flatten()
# Merge them side-by-side
zips = zip(xx, yy)
# convert to set of points/tuples and return
return set(zips)
coords = generate_cells(width=1920, height=1080, n=15, show_plot=True)
print(coords)

Assuming you simply want to randomly define non-overlapping coordinates within the confines of a maximum image size subject to not having images overlap, this might be a good solution.
import numpy as np
def locateImages(field_height: int, field_width: int, min_sep: int, points: int)-> np.array:
h_range = np.array(range(min_sep//2, field_height - (min_sep//2), min_sep))
w_range = np.array(range(min_sep//2, field_width-(min_sep//2), min_sep))
mx_len = max(len(h_range), len(w_range))
if len(h_range) < mx_len:
xtra = np.random.choice(h_range, mx_len - len(h_range))
h_range = np.append(h_range, xtra)
if len(w_range) < mx_len:
xtra = np.random.choice(w_range, mx_len - len(w_range))
w_range = np.append(w_range, xtra)
h_points = np.random.choice(h_range, points, replace=False)
w_points = np.random.choice(w_range, points, replace=False)
return np.concatenate((np.vstack(h_points), np.vstack(w_points)), axis= 1)
Then given:
field_height = the vertical coordinate of the Image space
field_width = the maximum horizontal coordinate of the Image space
min_sep = the minimum spacing between images
points = number of coordinates to be selected
Then:
locateImages(15, 8, 2, 5) will yield:
array([[13, 1],
[ 7, 3],
[ 1, 5],
[ 5, 5],
[11, 5]])
Render the output:
points = locateImages(1080, 1920, 100, 15)
x,y= zip(*points)
plt.scatter(x,x)
plt.gca().add_patch(Rectangle((0,0),1920, 1080,edgecolor='red', facecolor='none', lw=1))
plt.show()

Why does my functions seem to integrate and not differentiate? (pywt.cwt)

I am really confused by the function pywt.cwt, as I've not been able to get it to work. The function seems to integrate instead of differentiating. I would like to work it as the following: Example CWT, but my graph looks like this: My CWT. The idea is to integrate the raw signal (av) with cumtrapz, then differentiate with a gaussian CWT (=> S1), and then once more differentiate with gaussian CWT (=> S2).
As you can see in the pictures, the bottom peaks of the red line should line up in the valleys, but the land under the top peaks for me, and the green line should move 1/4th period to the left but moves to the right... Which makes me think it integrates for some reason.
I currently have no idea what causes this... Does anyone happen to know what is going on?
Thanks in advance!
#Get data from pandas
av = dfRange['y']
#remove gravity & turns av right way up
av = av - dfRange['y'].mean()
av = av * -1
#Filter
[b,a] = signal.butter(4, [0.9/(55.2/2), 20/(55.2/2)], 'bandpass')
av = signal.filtfilt(b,a, av)
#Integrate and differentiate av => S1
integrated_av = integrate.cumtrapz(av)
[CWT_av1, frequency1] = pywt.cwt(integrated_av, 8.8 , 'gaus1', 1/55.2)
CWT_av1 = CWT_av1[0]
CWT_av1 = CWT_av1 * 0.05
#differentiate S1 => S2
[CWT_av2, frequency2] = pywt.cwt(CWT_av1, 8.8 , 'gaus1', 1/55.2)
CWT_av2 = CWT_av2[0]
CWT_av2 = CWT_av2 * 0.8
#Find Peaks
inv_CWT_av1 = CWT_av1 * -1
av1_min, _ = signal.find_peaks(inv_CWT_av1)
av2_max, _ = signal.find_peaks(CWT_av2)
#Plot
plt.style.use('seaborn')
plt.figure(figsize=(25, 7), dpi = 300)
plt.plot_date(dfRange['recorded_naive'], av, linestyle = 'solid', marker = None, color = 'steelblue')
plt.plot_date(dfRange['recorded_naive'][:-1], CWT_av1[:], linestyle = 'solid', marker = None, color = 'red')
plt.plot(dfRange['recorded_naive'].iloc[av1_min], CWT_av1[av1_min], "ob", color = 'red')
plt.plot_date(dfRange['recorded_naive'][:-1], CWT_av2[:], linestyle = 'solid', marker = None, color = 'green')
plt.plot(dfRange['recorded_naive'].iloc[av2_max], CWT_av2[av2_max], "ob", color = 'green')
plt.gcf().autofmt_xdate()
plt.show()

I'm not sure this is your answer, but an observation from playing with pywt...
From the documentation the wavelets are basically given by the differentials of a Gaussian but there is an order dependent normalisation constant.
Plotting the differentials of a Guassian against the wavelets (extracted by putting in an impulse response) gives the following:
The interesting observation is that the order dependent normalisation constant sometimes seems to include a '-1'. In particular, it does for the first order gaus1.
So, my question is, could you actually have differentiation as you expect, but also multiplication by -1?
Code for the graph:
import numpy as np
import matplotlib.pyplot as plt
import pywt
dt = 0.01
t = dt * np.arange(100)
# Calculate the differentials of a gaussian by quadrature:
# start with the gaussian y = exp(-(x - x_0) ^ 2 / dt)
ctr = t[len(t) // 2]
gaus = np.exp(-np.power(t - ctr, 2)/dt)
gaus_quad = [np.gradient(gaus, dt)]
for i in range(7):
gaus_quad.append(np.gradient(gaus_quad[-1], dt))
# Extract the wavelets using the impulse half way through the dataset
y = np.zeros(len(t))
y[len(t) // 2] = 1
gaus_cwt = list()
for i in range(1, 9):
cwt, cwt_f = pywt.cwt(y, 10, f'gaus{i}', dt)
gaus_cwt.append(cwt[0])
fig, axs = plt.subplots(4, 2)
for i, ax in enumerate(axs.flatten()):
ax.plot(t, gaus_cwt[i] / np.max(np.abs(gaus_cwt[i])))
ax.plot(t, gaus_quad[i] / np.max(np.abs(gaus_quad[i])))
ax.set_title(f'gaus {i+1}', x=0.2, y=1.0, pad=-14)
ax.axhline(0, c='k')
ax.set_xticks([])
ax.set_yticks([])

How to smoothen 2D color map in matplotlib

My question is if there is any way to smoothen 2D color map using matplotlib? My code:
def map():
# setup parameters
j = 0
N = 719
N2 = 35
x = np.linspace(190, 800, N)
y = np.linspace(10, 360, N2) # (1,2,3), 1 - start Temp, 2- end temp + 10K, 3 - how many steps to reach it
z = []
A = np.zeros([35,719]) # [1 2], 1 - number of spectras, 2 - delta wavelength
# run
for i in range(10,360,10):
Z = []
file_no = (str(0) + str(i))[-3:]
data = np.genfromtxt('C:\\Users\\micha_000\\Desktop\\Measure\\' + '160317_LaPONd_g500_%s_radio.txt'%file_no,skip_header = 12)
for line in data:
Z.append(line[1]-6000)
A[j,:] = Z
j = j+1
X, Y = np.meshgrid(x,y)
fig, ax = plt.subplots()
cs = ax.contourf(X, Y, A, cmap=cm.viridis)
norm = colors.Normalize(vmin = 0, vmax = 1)
plt.xlabel('wavelength [nm]')
plt.ylabel('temperature [K]')
plt.title('LaPONd_g500')
cbar = fig.colorbar(cs, norm = norm)
plt.savefig('C:\\Users\\micha_000\\Desktop\\Measure\\LaPONd_g500_radio_map.png')
plt.show()
plt.close()
And here is an example of what i receive:
Is there any way to make it look better by smoothening pixels transitions?

The problem is not the palette (which are all smooth in matplotlib), but that fact that you are using contourf(), which generates a finite set of countours, each with a single color, and is therefore not smooth. The default is something like 10 countours.
One quick solution:, increase the number of contour levels by specifying levels (you can also give an array of which levels to include):
cs = ax.contourf(X, Y, A, cmap=cm.viridis, levels=100)
Better yet, since it seems your data data is already on a grid (e.g. X,Y,Z values for each pixel), you should use pcolormesh(X,Y,A) instead of contour to plot it. That will plot with fully continuous values, rather than steps.

open the png as an array, and blur it with a mean value filter. search convolution filters to learn more. I've just used a 25 pixel square averaging filter, but you could use a gaussian distribution to make it look smoother..
import numpy as np
from scipy import ndimage, signal, misc
img = ndimage.imread('C:/.../Zrj50.png')
#I used msPaint to get coords... there's probably a better way
x0, y0, x1, y1 = 87,215,764,1270 #chart area (pixel coords)
#you could use a gaussian filter to get a rounder blur pattern
kernel = np.ones((5,5),)/25 #mean value convolution
#convolve roi with averaging filter
#red
img[x0:x1, y0:y1, 0] = signal.convolve2d(img[x0:x1, y0:y1, 0], kernel, mode='same', boundary='symm')
#green
img[x0:x1, y0:y1, 1] = signal.convolve2d(img[x0:x1, y0:y1, 1], kernel, mode='same', boundary='symm')
#blue
img[x0:x1, y0:y1, 2] = signal.convolve2d(img[x0:x1, y0:y1, 2], kernel, mode='same', boundary='symm')
#do it again for ledgend area
#...
misc.imsave('C:/.../Zrj50_blurred.png', img)
Using a gaussian instead is pretty easy:
#red
img[x0:x1, y0:y1, 0] = ndimage.gaussian_filter(img[x0:x1, y0:y1, 0], 4, mode='nearest')

In matplotlib, how can I plot a multi-colored line, like a rainbow

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.

The best that I can think of is to take your data, generate a series of small offsets, and use fill_between to make bands of whatever color you like.
I wrote a function to do this. I don't know what shape you're trying to plot, so this may or may not work for you. I tested it on a parabola and got decent results. You can also play around with the list of colors.
def rainbow_plot(x, y, spacing=0.1):
fig, ax = plt.subplots()
colors = ['red', 'yellow', 'green', 'cyan','blue']
top = max(y)
lines = []
for i in range(len(colors)+1):
newline_data = y - top*spacing*i
lines.append(newline_data)
for i, c in enumerate(colors):
ax.fill_between(x, lines[i], lines[i+1], facecolor=c)
return fig, ax
x = np.linspace(0,1,51)
y = 1-(x-0.5)**2
rainbow_plot(x,y)

Find a easier way to cluster 2-d scatter data into grid array data

I have figured out a method to cluster disperse point data into structured 2-d array(like rasterize function). And I hope there are some better ways to achieve that target.
My work
1. Intro
1000 point data has there dimensions of properties (lon, lat, emission) whicn represent one factory located at (x,y) emit certain amount of CO2 into atmosphere
grid network: predefine the 2-d array in the shape of 20x20
http://i4.tietuku.com/02fbaf32d2f09fff.png
The code reproduced here:
#### define the map area
xc1,xc2,yc1,yc2 = 113.49805889531724,115.5030664238035,37.39995194888143,38.789235929357105
map = Basemap(llcrnrlon=xc1,llcrnrlat=yc1,urcrnrlon=xc2,urcrnrlat=yc2)
#### reading the point data and scatter plot by their position
df = pd.read_csv("xxxxx.csv")
px,py = map(df.lon, df.lat)
map.scatter(px, py, color = "red", s= 5,zorder =3)
#### predefine the grid networks
lon_grid,lat_grid = np.linspace(xc1,xc2,21), np.linspace(yc1,yc2,21)
lon_x,lat_y = np.meshgrid(lon_grid,lat_grid)
grids = np.zeros(20*20).reshape(20,20)
plt.pcolormesh(lon_x,lat_y,grids,cmap = 'gray', facecolor = 'none',edgecolor = 'k',zorder=3)
2. My target
Finding the nearest grid point for each factory
Add the emission data into this grid number
3. Algorithm realization
3.1 Raster grid
note: 20x20 grid points are distributed in this area represented by blue dot.
http://i4.tietuku.com/8548554587b0cb3a.png
3.2 KD-tree
Find the nearest blue dot of each red point
sh = (20*20,2)
grids = np.zeros(20*20*2).reshape(*sh)
sh_emission = (20*20)
grids_em = np.zeros(20*20).reshape(sh_emission)
k = 0
for j in range(0,yy.shape[0],1):
for i in range(0,xx.shape[0],1):
grids[k] = np.array([lon_grid[i],lat_grid[j]])
k+=1
T = KDTree(grids)
x_delta = (lon_grid[2] - lon_grid[1])
y_delta = (lat_grid[2] - lat_grid[1])
R = np.sqrt(x_delta**2 + y_delta**2)
for i in range(0,len(df.lon),1):
idx = T.query_ball_point([df.lon.iloc[i],df.lat.iloc[i]], r=R)
# there are more than one blue dot which are founded sometimes,
# So I'll calculate the distances between the factory(red point)
# and all blue dots which are listed
if (idx > 1):
distance = []
for k in range(0,len(idx),1):
distance.append(np.sqrt((df.lon.iloc[i] - grids[k][0])**2 + (df.lat.iloc[i] - grids[k][1])**2))
pos_index = distance.index(min(distance))
pos = idx[pos_index]
# Only find 1 point
else:
pos = idx
grids_em[pos] += df.so2[i]
4. Result
co2 = grids_em.reshape(20,20)
plt.pcolormesh(lon_x,lat_y,co2,cmap =plt.cm.Spectral_r,zorder=3)
http://i4.tietuku.com/6ded65c4ac301294.png
5. My question
Can someone point out some drawbacks or error of this method?
Is there some algorithms more aligned with my target?
Thanks a lot!

There are many for-loop in your code, it's not the numpy way.
Make some sample data first:
import numpy as np
import pandas as pd
from scipy.spatial import KDTree
import pylab as pl
xc1, xc2, yc1, yc2 = 113.49805889531724, 115.5030664238035, 37.39995194888143, 38.789235929357105
N = 1000
GSIZE = 20
x, y = np.random.multivariate_normal([(xc1 + xc2)*0.5, (yc1 + yc2)*0.5], [[0.1, 0.02], [0.02, 0.1]], size=N).T
value = np.ones(N)
df_points = pd.DataFrame({"x":x, "y":y, "v":value})
For equal space grids you can use hist2d():
pl.hist2d(df_points.x, df_points.y, weights=df_points.v, bins=20, cmap="viridis");
Here is the output:
Here is the code to use KdTree:
X, Y = np.mgrid[x.min():x.max():GSIZE*1j, y.min():y.max():GSIZE*1j]
grid = np.c_[X.ravel(), Y.ravel()]
points = np.c_[df_points.x, df_points.y]
tree = KDTree(grid)
dist, indices = tree.query(points)
grid_values = df_points.groupby(indices).v.sum()
df_grid = pd.DataFrame(grid, columns=["x", "y"])
df_grid["v"] = grid_values
fig, ax = pl.subplots(figsize=(10, 8))
ax.plot(df_points.x, df_points.y, "kx", alpha=0.2)
mapper = ax.scatter(df_grid.x, df_grid.y, c=df_grid.v,
cmap="viridis",
linewidths=0,
s=100, marker="o")
pl.colorbar(mapper, ax=ax);
the output is: