I have the code below. If you run that program a scatter plot is created. The plot is very messy. I want every point to represent one car. I only want to see the point of the current position of each car in the animation. I am not very good at matplotlib, but how would I do that?
from matplotlib import pyplot as plt
import random
import math
from matplotlib import animation
import numpy as np
roadLength = 100
numFrames = 200
numCars = 60
velocities = []
positions = []
theta = []
r = []
color = []
probability = 0.5
vmax = 1
flowr = []
fig = plt.figure()
ax = fig.add_subplot(111, projection='polar')
ax.axis('off')
for i in range(numCars):
positions.append(i * 2)
theta.append(0)
r.append(1)
color.append(i)
velocities.append(0)
def pos(k):
rand = random.uniform(0,1)
if velocities[k] < vmax:
velocities[k] += 1
if k < numCars-1 and (positions[k+1] - positions[k]) <= velocities[k]:
velocities[k] = positions[k+1] - positions[k] - 1
if k == numCars-1 and (roadLength - (positions[k] - positions[0])) <= velocities[k]:
velocities[k] = roadLength - (positions[k] - positions[0]) - 1
if rand < probability and velocities[k] > 0:
velocities[k] = velocities[k] - 1
positions[k] = positions[k] + velocities[k]
return positions[k]
def animate(frameNr):
for i in range(numCars):
theta[i] = pos(i) * 2 * math.pi / roadLength
flowr.append(velocities[i])
ax.scatter(theta, r, c=color)
return ax.scatter(theta, r, c=color),
def simulate():
anim = animation.FuncAnimation(fig, animate,
frames=numFrames, interval=10, blit=True, repeat=False)
plt.show()
simulate()
Thanks in advance!
Edit:
I fixed so that it became a point plot I am now storing velocity, position and lane in an object for a later problem. My question is:
How do I make the points have different colors?
from matplotlib import pyplot as plt
import random
import math
from matplotlib import animation
import numpy as np
from operator import attrgetter
roadLength = 100
numFrames = 200
nlanes = 1
numCars = 20
posss =[]
theta = []
r = []
color = []
probability = 0.5
vmax = 1
flowr = []
cars=[]
class Car:
def __init__(self, position, velocity, lane):
self.position = position
self.velocity = velocity
self.lane = lane
def pos(car,k):
rand = random.uniform(0,1)
if car[k].velocity < vmax:
car[k].velocity += 1
if k < numCars-1 and (car[k+1].position - car[k].position) <= car[k].velocity:
car[k].velocity = car[k+1].position - car[k].position - 1
if k == numCars-1 and (roadLength - (car[k].position - car[0].position)) <= car[k].velocity:
car[k].velocity = roadLength - (car[k].position - car[0].position) - 1
if rand < probability and car[k].velocity > 0:
car[k].velocity = car[k].velocity - 1
car[k].position = car[k].position + car[k].velocity
return car[k].position
for i in range(numCars):
cars.append(Car(i, 0, 1))
theta.append(0)
r.append(1)
color.append(i)
posss.append(i)
fig = plt.figure()
ax = fig.add_subplot(111)
point, = ax.plot(posss, r, 'o')
ax.set_xlim(-10, 1.2*numFrames)
ax.set_ylim(-2, nlanes + 3)
def animate(frameNr):
sort_cars = sorted(cars, key=attrgetter("position"))
for i in range(numCars):
pos(sort_cars,i)
for k in range(numCars):
theta[k]=cars[k].position
point.set_data(theta, r)
return point,
def simulate():
anim = animation.FuncAnimation(fig, animate,
frames=numFrames, interval=10, blit=True, repeat=False)
plt.show()
simulate()
plot() returns a Line2D object, in which all points have the same color.
If you want your points to have different colors, you should use scatter(). The logic is exactly the same, except you use set_offsets(<2D array>) instead of set_data().
See this question for more details
Related
I need to simulate a penalty where the ball shoots in every direction. For this I use solve_ivp and I terminate the integration when the ball crosses the backline. When this happens I want to use the values found when the integration stops to see if the ball at that point is within the dimensions of the goal (and count it as a goal). However, solution.y does not give the required precision that I want. The desired values are within solution.y_events, however, I can't seem to be able to get receive them. I also can't find information about this online. My code:
import numpy as np
from scipy import integrate
from scipy import constants
import matplotlib.pyplot as plt
#### Constants
# Number of simulations
number_of_penalty_shots = 10
# Angle of the shots
theta = np.random.uniform(0, 2.0*np.pi, number_of_penalty_shots)
phi = np.random.uniform(0, np.pi, number_of_penalty_shots)
# Velocity of the ball
v_magnitude = 80
### Starting Position Ball (defined as the penalty stip)
pos_x = 0.0
pos_y = 0.0
pos_z = 0.0
in_position = np.array([pos_x, pos_y, pos_z]) # Inital position in m
def homo_magnetic_field(t, vector):
vx = vector[3] # dx/dt = vx
vy = vector[4] # dy/dt = vy
vz = vector[5] # dz/dt = vz
# ax = -0.05*vector[3] # dvx/dt = ax
# ay = -0.05*vector[4] # dvy/dy = ay
# az = -0.05*vector[5] - constants.g #dvz/dt = az
ax = 0
ay = 0
az = 0
dvectordt = (vx,vy,vz,ax,ay,az)
return(dvectordt)
def goal(t, vector):
return vector[1] - 11
def own_goal(t,vector):
return vector[1] + 100
def ground(t,vector):
return vector[2]
goal.terminal=True
own_goal.terminal=True
def is_it_goal(vector):
if vector.status == 1:
if (vector.y[1][len(vector.y[1])-1] > 0) and (-3.36 < vector.y[0][len(vector.y[1])-1] < 3.36) and (vector.y[2][len(vector.y[1])-1] < 2.44):
print("GOAAAAAAAAAAAAL!")
elif (vector.y[1][len(vector.y[1])-1] < 0) and (-3.36 < vector.y[0][len(vector.y[1])-1] < 3.36) and (vector.y[2][len(vector.y[1])-1] < 2.44):
print("Own goal?! Why?")
else: print("Awwwwh")
else: print("Not even close, lol")
# Integrating
time_range = (0.0, 10**2)
for i in range(number_of_penalty_shots):
v_x = v_magnitude*np.sin(phi[i])*np.cos(theta[i])
v_y = v_magnitude*np.sin(phi[i])*np.sin(theta[i])
v_z = v_magnitude*np.cos(phi[i])
in_velocity = np.array([v_x, v_y, v_z])
initial_point = np.array([in_position, in_velocity])
start_point = initial_point.reshape(6,)
solution = integrate.solve_ivp(homo_magnetic_field , time_range, start_point,events=(goal, own_goal))
is_it_goal(solution)
Here I want to change vector.y[1][len(vector.y[1])-1] into something like vector.y_events...
Trying to plot persuit curves with spiraling in lines and a shrinking, rotating polygon with corners at each of the current points
problem = can't get both line of sight lines and main lines to simultaneously plot
The figure flicks back and forth between the shrinking polygon(described by SightLine) and the main persuit curves (MainLines)
When individually animated one at a time, the polygon and pursuit curves plot fine but I just can't get them to work together on the same figure.
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
%matplotlib notebook
plt.style.use('dark_background')
NumOfPoints = 6
deltaT = 0.005
duration = 50
steps = int(duration / deltaT)
speed = 0.2
num = 0
CurrentXPoints = []
CurrentYPoints = []
DeltaX = np.zeros(NumOfPoints)
DeltaY = np.zeros(NumOfPoints)
MagnitudeDelta = np.zeros(NumOfPoints)
VelocityX = np.zeros(NumOfPoints)
VelocityY = np.zeros(NumOfPoints)
#Creates Initial Points by equally spacing the points around a polygon inscribed around circle
for i in range(0,NumOfPoints):
x = np.cos(((i/NumOfPoints)*2)*np.pi)
y = np.sin(((i/NumOfPoints)*2)*np.pi)
CurrentXPoints.append(x)
CurrentYPoints.append(y)
AllXPoints = np.array([CurrentXPoints])
AllYPoints = np.array([CurrentYPoints])
#Fills out both AllXPoints and AllYPoints with all points in duration
for i in range(int(steps)):
for j in range(0,NumOfPoints-1): #Calculates deltaX and deltaY at this timestep
DeltaX[j] = CurrentXPoints[j+1] - CurrentXPoints[j]
DeltaY[j] = CurrentYPoints[j+1] - CurrentYPoints[j]
DeltaX[NumOfPoints-1] = CurrentXPoints[0] - CurrentXPoints[NumOfPoints-1]
DeltaY[NumOfPoints-1] = CurrentYPoints[0] - CurrentYPoints[NumOfPoints-1]
for j in range(0,NumOfPoints): # calculats new X and Y Points
MagnitudeDelta[j] = ((DeltaX[j])**2 + (DeltaY[j])**2)**(1/2)
VelocityX[j] = speed * (DeltaX[j]/MagnitudeDelta[j])
VelocityY[j] = speed * (DeltaY[j]/MagnitudeDelta[j])
CurrentXPoints[j] += deltaT * VelocityX[j]
CurrentYPoints[j] += deltaT * VelocityY[j]
CurrentXPointsArr = np.array(CurrentXPoints)
CurrentYPointsArr = np.array(CurrentYPoints)
AllXPoints = np.vstack((AllXPoints,CurrentXPointsArr))
AllYPoints = np.vstack((AllYPoints,CurrentYPointsArr))
fig = plt.figure(figsize=(5,5))
ax = plt.axes()
ax.set_xlim(-2,2)
ax.set_ylim(-2,2)
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
MainLines = []
SightLines= []
AllLines = MainLines + SightLines
for i in range(NumOfPoints):
line, = ax.plot([AllXPoints[j][i] for j in range(steps)], [AllYPoints[j][i] for j in range(steps)])
MainLines.append(line)
SightLines.append(line)
def UpdateMain(num, AllXPoints, AllYPoints, MainLines):
for line in MainLines:
position = MainLines.index(line)
line.set_data([AllXPoints[i][position] for i in range(num)], [AllYPoints[i][position] for i in range(num)])
def UpdateSight(num, AllXPoints, AllYPoints, SightLines):
for line in SightLines:
position = SightLines.index(line)
if position < (NumOfPoints-1):
line.set_data([AllXPoints[num][position],AllXPoints[num][position+1]],
[AllYPoints[num][position],AllYPoints[num][position+1]])
else:
line.set_data([AllXPoints[num][position],AllXPoints[num][0]],
[AllYPoints[num][position],AllYPoints[num][0]])
ani1 = animation.FuncAnimation(fig, UpdateMain,steps, fargs=[AllXPoints, AllYPoints, MainLines],
interval=1, blit=True)
ani2 = animation.FuncAnimation(fig, UpdateSight,steps, fargs=[AllXPoints, AllYPoints, SightLines],
interval=1, blit=True)
plt.show()
First, you should use only one FuncAnimation that updates all the artists.
The main problem of your code are the lines
for i in range(NumOfPoints):
line, = ax.plot([AllXPoints[j][i] for j in range(steps)], [AllYPoints[j][i] for j in range(steps)])
MainLines.append(line)
SightLines.append(line)
where you are creating one artist (line) and assign it to two different lists. If you create 2 different lines for each list, then the output is as expected.
Full working code:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
%matplotlib notebook
plt.style.use('dark_background')
NumOfPoints = 6
deltaT = 0.005
duration = 50
steps = int(duration / deltaT)
speed = 0.2
num = 0
CurrentXPoints = []
CurrentYPoints = []
DeltaX = np.zeros(NumOfPoints)
DeltaY = np.zeros(NumOfPoints)
MagnitudeDelta = np.zeros(NumOfPoints)
VelocityX = np.zeros(NumOfPoints)
VelocityY = np.zeros(NumOfPoints)
def update(num, AllXPoints, AllYPoints, MainLines, SightLines):
out = []
out.append(UpdateMain(num, AllXPoints, AllYPoints, MainLines))
out.append(UpdateSight(num, AllXPoints, AllYPoints, SightLines))
return out
def UpdateMain(num, AllXPoints, AllYPoints, MainLines):
for line in MainLines:
position = MainLines.index(line)
line.set_data([AllXPoints[i][position] for i in range(num)], [AllYPoints[i][position] for i in range(num)])
return MainLines
def UpdateSight(num, AllXPoints, AllYPoints, SightLines):
for line in SightLines:
position = SightLines.index(line)
if position < (NumOfPoints-1):
line.set_data([AllXPoints[num][position],AllXPoints[num][position+1]],
[AllYPoints[num][position],AllYPoints[num][position+1]])
else:
line.set_data([AllXPoints[num][position],AllXPoints[num][0]],
[AllYPoints[num][position],AllYPoints[num][0]])
return SightLines
#Creates Initial Points by equally spacing the points around a polygon inscribed around circle
for i in range(0,NumOfPoints):
x = np.cos(((i/NumOfPoints)*2)*np.pi)
y = np.sin(((i/NumOfPoints)*2)*np.pi)
CurrentXPoints.append(x)
CurrentYPoints.append(y)
AllXPoints = np.array([CurrentXPoints])
AllYPoints = np.array([CurrentYPoints])
#Fills out both AllXPoints and AllYPoints with all points in duration
for i in range(int(steps)):
for j in range(0,NumOfPoints-1): #Calculates deltaX and deltaY at this timestep
DeltaX[j] = CurrentXPoints[j+1] - CurrentXPoints[j]
DeltaY[j] = CurrentYPoints[j+1] - CurrentYPoints[j]
DeltaX[NumOfPoints-1] = CurrentXPoints[0] - CurrentXPoints[NumOfPoints-1]
DeltaY[NumOfPoints-1] = CurrentYPoints[0] - CurrentYPoints[NumOfPoints-1]
for j in range(0,NumOfPoints): # calculats new X and Y Points
MagnitudeDelta[j] = ((DeltaX[j])**2 + (DeltaY[j])**2)**(1/2)
VelocityX[j] = speed * (DeltaX[j]/MagnitudeDelta[j])
VelocityY[j] = speed * (DeltaY[j]/MagnitudeDelta[j])
CurrentXPoints[j] += deltaT * VelocityX[j]
CurrentYPoints[j] += deltaT * VelocityY[j]
CurrentXPointsArr = np.array(CurrentXPoints)
CurrentYPointsArr = np.array(CurrentYPoints)
AllXPoints = np.vstack((AllXPoints,CurrentXPointsArr))
AllYPoints = np.vstack((AllYPoints,CurrentYPointsArr))
fig = plt.figure(figsize=(5,5))
ax = plt.axes()
ax.set_xlim(-2,2)
ax.set_ylim(-2,2)
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
MainLines = []
SightLines= []
AllLines = MainLines + SightLines
for i in range(NumOfPoints):
line1, = ax.plot([AllXPoints[j][i] for j in range(steps)], [AllYPoints[j][i] for j in range(steps)])
line2, = ax.plot([AllXPoints[j][i] for j in range(steps)], [AllYPoints[j][i] for j in range(steps)])
MainLines.append(line1)
SightLines.append(line2)
ani = animation.FuncAnimation(fig, update, steps, fargs=[AllXPoints, AllYPoints, MainLines, SightLines], interval=1, blit=True)
plt.show()
I want to make a 3d line plot animation with a point at the last point plotted, like a trajectory for a particule. In a case without blitting, I did it with a scatter plot and a line plot3d, updating both plots in the update function. I tried doing it in the same way, with blitting, but it throws the following error
TypeError: 'Path3DCollection' object is not iterable
My code is the following
import matplotlib.pyplot as m
import matplotlib.animation as animation
from mpl_toolkits.mplot3d import Axes3D
def ranstep(start,step,stop):
numberlist = int((stop - start)/step + 1)
lista = [0]*numberlist
i = 0
while i <= numberlist:
if i == 0:
lista[i] = start
i = i + 1
if i != 0 and i < numberlist - 1:
lista[i] = lista[i - 1] + step
i = i + 1
if i != 0 and i == numberlist - 1:
lista[i] = stop
break
return(lista)
k1 = 10.0
k2 = 28.0
k3 = 8.0/3.0
czeroA = 1
czeroB = 0
czeroC = 0
step = 0.001
tfinal = 100
time = list(ranstep(0,step,tfinal))
cA = [0]*len(time)
cB = [0]*len(time)
cC = [0]*len(time)
i = 0
while i <= len(time) - 1:
if i == 0:
cA[i] = czeroA
cB[i] = czeroB
cC[i] = czeroC
i = i + 1
else:
cA[i] = cA[i - 1] + k1*(cB[i - 1] - cA[i - 1])*step
cB[i] = cB[i - 1] + (cA[i - 1]*(k2 - cC[i - 1]) - cB[i-1])*step
cC[i] = cC[i - 1] + (cA[i - 1]*cB[i-1] - k3*cC[i-1])*step
i = i + 1
fig, ax = m.subplots()
ax = fig.add_subplot(111, projection='3d')
line, = ax.plot3D([], [], [], c = 'blue', lw = 1)
line, = ax.scatter([],[],[], c = 'red', s = 30)
def init():
ax.set_xlim([-20,20])
ax.set_ylim([-20,20])
ax.set_zlim([0,50])
ax.set_xlabel('$x(t)$')
ax.set_ylabel('$y(t)$')
ax.set_zlabel('$z(t)$')
return line,
def update(frame):
line.set_data(cA[0:frame*50],cB[0:frame*50])
line.set_3d_properties(cC[0:frame*50])
line.set_data(cA[frame*500,frame*500 + 1],cB[frame*500,frame*500 + 1])
line.set_3d_properties(cC[frame*500,frame*500 + 1])
return line,
ani = animation.FuncAnimation(fig, update,interval=5, frames = len(time),init_func=init, blit=True)
m.show()
I have been studying the 1D wave equations and making the animation of the equation. But there are some problems when using the anim.save of animation to save the video file. I have already installed ffmpeg on my computer (a Windows machine) and set the environment variables. But it keeps telling me this:
UserWarning: MovieWriter ffmpeg unavailable
...
RuntimeError: Error creating movie, return code: 4 Try running with --verbose-debug
Here is my code:
from numpy import zeros,linspace,sin,pi
import matplotlib.pyplot as mpl
from matplotlib import animation
mpl.rcParams['animation.ffmpeg_path'] = 'C:\\ffmpeg\\bin\\ffmpeg.exe'
def I(x):
return sin(2*x*pi/L)
def f(x,t):
return sin(0.5*x*t)
def solver0(I,f,c,L,n,dt,t):
# f is a function of x and t, I is a function of x
x = linspace(0,L,n+1)
dx = L/float(n)
if dt <= 0:
dt = dx/float(c)
C2 = (c*dt/dx)**2
dt2 = dt*dt
up = zeros(n+1)
u = up.copy()
um = up.copy()
for i in range(0,n):
u[i] = I(x[i])
for i in range(1,n-1):
um[i] = u[i]+0.5*C2*(u[i-1] - 2*u[i] + u[i+1]) + dt2*f(x[i],t)
um[0] = 0
um[n] = 0
while t <= tstop:
t_old = t
t += dt
#update all inner points:
for i in range(1,n-1):
up[i] = -um[i] + 2*u[i] + C2*(u[i-1] - 2*u[i] + u[i+1]) + dt2*f(x[i],t_old)
#insert boundary conditions:
up[0] = 0
up[n] = 0
#update data structures for next step
um = u.copy()
u = up.copy()
return u
c = 1.0
L = 10
n = 100
dt = 0
tstop = 40
fig = mpl.figure()
ax = mpl.axes(xlim=(0,10),ylim=(-1.0,1.0))
line, = ax.plot([],[],lw=2)
def init():
line.set_data([],[])
return line,
def animate(t):
x = linspace(0,L,n+1)
y = solver0(I, f, c, L, n, dt, t)
line.set_data(x,y)
return line,
anim = animation.FuncAnimation(fig, animate, init_func=init,
frames=200, interval=20, blit=True)
anim.save('seawave_1d_ani.mp4',writer='ffmpeg',fps=30)
mpl.show()
I believe the problem is in the part of the animation instead of the three functions above. Please help me find what mistake I have made.
I finally worked it out.It seemed that I missed two important lines.
mpl.rcParams['animation.ffmpeg_path'] = 'C:\\ffmpeg\\bin\\ffmpeg.exe' This line is correct.Both '\\' and '/' work in Windows,as far as I've tried.
I add mywriter = animation.FFMpegWriter()at the bottom and modify anim.save('seawave_1d_ani.mp4',writer='ffmpeg',fps=30) by anim.save('seawave_1d_ani.mp4',writer=mywriter,fps=30).It worked at last,thanks to Using FFmpeg and IPython.
Also grateful to those friends who helped me with this problem.
This class plots a curve. However, the inputs are currently set in main(). I'd like to set them as user-driven from mouse interaction. Some of this is possible and in the Matplotlib docs (see referenced sites below) but it's still not really setting it up to be a 'click and plot'. So, ideally the user would click a button to set the P and then whatever point (on the curve, has to be on the curve) they clicked next would be the new P. Same with Q. I'm sure this is a very simple question for anyone who's used Matplotlib but I'm teaching myself it right now, but it would probably take an entry-level dev just a few minutes to do something that I'm getting nowhere with.
Code:
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.axes_grid.axislines import SubplotZero
from math import sqrt
class ECC123(object):
def __init__(self,a,b,px,qx,qy):
self.a = a
self.b = b
self.pxlam = px
self.qxlam = qx
self.invertQy = qy
self.fig = plt.figure(1)
self.ax = SubplotZero(self.fig, 111)
def drawAxis(self):
#fig = plt.figure(1)
#ax = SubplotZero(fig, 111)
self.fig.add_subplot(self.ax)
for direction in ["xzero", "yzero"]:
self.ax.axis[direction].set_axisline_style("->")
self.ax.axis[direction].set_visible(True)
def plotGraph(self):
self.drawAxis()
y, x = np.ogrid[-10:10:100j, -10:10:100j] # range grid [from : to : how_many_points]
xlist = x.ravel(); ylist = y.ravel()
plt.contour(xlist, ylist, self.elliptic_curve(x,y), [0])
pylam = self.ecclambda(self.pxlam,self.a,self.b) # calculate P from pxlam
qylam = self.ecclambda(self.qxlam,self.a,self.b) # calculate Q from qxlam
if self.invertQy == 1: qylam = -qylam # optional, inverts qy to negative on the plot
plt.plot([self.pxlam,self.qxlam], [pylam,qylam], color = "c", linewidth=1)
plt.plot([self.pxlam], [pylam], "mo"); plt.plot([self.qxlam], [qylam], "mo")
plt.text(self.pxlam-0.25,pylam+0.5, '$P$'); plt.text(self.qxlam-0.25,self.qxlam+0.5, '$Q$')
s = (pylam - qylam)/(self.pxlam - self.qxlam) # calculate s slope
xr = s**2 - self.pxlam - self.qxlam # x-value of R
yr = pylam + s*(xr - self.pxlam) # y-value of -R; -y is R (inverted across x-axis)
plt.plot([xr],[yr],"mo")
plt.plot([xr],[-yr],"co")
plt.plot([self.qxlam,xr], [qylam,yr], color = "c", linewidth=1)
plt.plot([xr,xr], [yr,-yr], "x--")
plt.text(xr+0.25,yr, '$-R$'); plt.text(xr+0.25,-yr, '$R$')
plt.grid(True)
plt.show()
I've been going over the docs in Matplotlib, the scipy cookbook, and related questions here on SO and still not seeing exactly how to do this:
http://matplotlib.org/users/event_handling.html
http://matplotlib.org/1.3.1/api/widgets_api.html#matplotlib.widgets.Button.on_clicked
Cursors for data selection in matplotlib
How can I create a frontend for matplotlib?
http://wiki.scipy.org/Cookbook/Matplotlib
So far, I'm getting little red x's all over when I click and they don't even fall within the curve.
I modified your code a little, so that you can set location of P & Q by left & right click, I didn't accomplish all the graph data updates, the rest is left for you:
from mpl_toolkits.axes_grid.axislines import SubplotZero
import numpy as np
import matplotlib.pyplot as plt
from math import sqrt
class ECC(object):
"""
class to implement elliptic curve and find P+Q=R on the plot
"""
def __init__(self,a,b,px,qx,qy):
"""
initialize input variables
"""
self.a = a
self.b = b
self.pxlam = px
self.qxlam = qx
self.invertQy = qy
self.fig = plt.figure(1)
self.ax = SubplotZero(self.fig, 111)
def drawAxis(self):
"""
draw main x,y axis
"""
#fig = plt.figure(1)
#ax = SubplotZero(fig, 111)
self.fig.add_subplot(self.ax)
for direction in ["xzero", "yzero"]:
self.ax.axis[direction].set_axisline_style("->")
self.ax.axis[direction].set_visible(True)
def ecclambda(self,xl,a,b):
"""
returns points elliptic curve for P and Q
y**2 = x**3 + a*x + b
"""
return sqrt(xl**3 + a*xl + b)
def elliptic_curve(self,x,y):
"""
takes in x,y as set of points, returns the elliptic curve
y**2 = x**3 + a*x + b
"""
return pow(y, 2) - pow(x, 3) - x * self.a - self.b
def onclick(self, event):
x = event.xdata
if event.button == 1:
self.pxlam = x
if event.button == 3:
self.qxlam = x
self.update()
def update(self):
pylam = self.ecclambda(self.pxlam,self.a,self.b) # calculate P from pxlam
qylam = self.ecclambda(self.qxlam,self.a,self.b) # calculate Q from qxlam
self.p.set_data([self.pxlam], [pylam])
self.q.set_data([self.qxlam], [qylam])
self.pt.set_x(self.pxlam-0.25)
self.pt.set_y(pylam+0.5)
self.qt.set_x(self.qxlam-0.25)
self.qt.set_y(qylam+0.5)
plt.gcf().canvas.draw()
def plotGraph(self):
"""
main plotting of elliptic curve and points/line for P+Q=R
P+Q=R --->>> -R is plotted (xr,yr), R is plotted (xr, -yr)
conditional with invertQy allows inversion of Q across x-axis; set option in main()
"""
self.drawAxis()
y, x = np.ogrid[-10:10:100j, -10:10:100j] # range grid [from : to : how_many_points]
xlist = x.ravel(); ylist = y.ravel()
plt.contour(xlist, ylist, self.elliptic_curve(x,y), [0])
pylam = self.ecclambda(self.pxlam,self.a,self.b) # calculate P from pxlam
qylam = self.ecclambda(self.qxlam,self.a,self.b) # calculate Q from qxlam
if self.invertQy == 1: qylam = -qylam # optional, inverts qy to negative on the plot
plt.plot([self.pxlam,self.qxlam], [pylam,qylam], color = "c", linewidth=1)
self.p = plt.plot([self.pxlam], [pylam], "mo")[0]
self.q = plt.plot([self.qxlam], [qylam], "mo")[0]
self.pt = plt.text(self.pxlam-0.25,pylam+0.5, '$P$')
self.qt = plt.text(self.qxlam-0.25,self.qxlam+0.5, '$Q$')
s = (pylam - qylam)/(self.pxlam - self.qxlam) # calculate s slope
xr = s**2 - self.pxlam - self.qxlam # x-value of R
yr = pylam + s*(xr - self.pxlam) # y-value of -R; -y is R (inverted across x-axis)
plt.plot([xr],[yr],"mo")
plt.plot([xr],[-yr],"co")
plt.plot([self.qxlam,xr], [qylam,yr], color = "c", linewidth=1)
plt.plot([xr,xr], [yr,-yr], "x--")
plt.text(xr+0.25,yr, '$-R$'); plt.text(xr+0.25,-yr, '$R$')
plt.text(-9,6,' P: (%s ,%s) \n Q: (%s ,%s) \n R: (%s ,%s) \n a: %s \n b: %s '
%(self.pxlam,pylam,self.qxlam,qylam,xr,-yr,self.a,self.b),
fontsize=10, color = 'blue',bbox=dict(facecolor='tan', alpha=0.5))
plt.title(r"Elliptic Curve Implementation $y^{2} = x^{3} + a*x + b$", fontsize = 16, color = 'b')
self.fig.canvas.mpl_connect('button_press_event', self.onclick)
#[xi,yi] = plt.ginput(0)
##print "ginput ",xi,yi
plt.grid(True)
plt.show()
def main():
a = -2; b = 1; px = -1.55; qx = -0.1
invertQy = 0 # set to 1 if q should be inverted to negative along its y axis
ec = ECC(a,b,px,qx,invertQy)
ec.plotGraph()
if __name__ == '__main__':
main()