Visualize point P that works with Python

What i did

I drew a point P that works with Python and output it as a gif.

example

Let's visualize the problem of moving point P as follows.

There is a rectangular ABCD with AB = 4cm, BC = 6cm, and the point P starts from A and progresses from A to B to C to D at 1cm per second. Let the area of △ APD after $ x $ seconds from departure be $ y $ cm ^{2 </ sup>.}

Source https://math.005net.com/yoten/doten.php (However, 2 cm per second is 1 cm per second.)

drawing

environment

• Anaconda3 + jupyter notebook
• Python 3.6
• matplotlib 3.1.1
• numpy 1.16.5

1. Make an empty figure

First, prepare for drawing the figure.

import matplotlib.pyplot as plt

fig = plt.figure()
ax1 = fig.add_subplot(111)

plt.show()

2. Display a rectangle

Make a rectangle 4 cm long and 6 cm wide. Here, there are various ways to choose where to put the coordinate origin $ O $. This time, select the center of gravity of the rectangle (2 cm in length and 3 cm in width) as the origin $ O $, and determine the coordinates of points A, B, C, and D. This will make the code easier if you later want the label to appear on the outside of the rectangle.

• Use matplotlib.patches to draw the shape. Also, I want to treat the coordinates of the point as a vector, so I also enter numpy.

• Use set_xlim, set_ylim to make the x-axis and y-axis ranges slightly larger than the rectangle so that the rectangle fits in the frame.

• Define the coordinates of points A, B, C, D with the np.array type.

• Make a rectangle with pat.Polygon and add it to ʻax1`.

import numpy as np #add to
import matplotlib.pyplot as plt
import matplotlib.patches as pat #add to

fig = plt.figure()

ax1 = fig.add_subplot(111)

ax1.set_xlim(-4,4)
ax1.set_ylim(-3,3)

A=np.array([-3,2])
B=np.array([-3,-2])
C=np.array([3,-2])
D=np.array([3,2])

p = pat.Polygon(xy = [A,B,C,D],
                edgecolor='black',
                facecolor='white',
                linewidth=1.6)

ax1.add_patch(p)

plt.show()

3. Display the length of the side and the name of the vertex

Draw the length of the side text can draw characters by specifying the x coordinate in the first argument, the y coordinate in the second argument, and the name in the third argument.

#Display the length of the side
ax1.text(-3.5,0.0,"4cm",horizontalalignment='center',verticalalignment='center')
ax1.text(0.0,-2.5,"6cm",horizontalalignment='center',verticalalignment='center')

Fine-tune the placement to your liking.

Next, the name of the point is displayed on the outside of the rectangle. You may decide the display position by hand as well as the length of the side.

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as pat

fig = plt.figure()
ax1 = fig.add_subplot(111)

ax1.set_xlim(-4,4)
ax1.set_ylim(-3,3)

A=np.array([-3,2])
B=np.array([-3,-2])
C=np.array([3,-2])
D=np.array([3,2])

pol = pat.Polygon(xy = [A,B,C,D],
                edgecolor='black',
                facecolor='white',
                linewidth=1.6)

ax1.add_patch(pol)

#Display the length of the side
ax1.text(-3.5,0.0,"4cm",horizontalalignment='center',verticalalignment='center')
ax1.text(0.0,-2.5,"6cm",horizontalalignment='center',verticalalignment='center')

#Display the name of the vertex
scale=1.1
ax1.text(A[0]*scale,A[1]*scale,"A",fontsize=15,horizontalalignment='center',verticalalignment='center')
ax1.text(B[0]*scale,B[1]*scale,"B",fontsize=15,horizontalalignment='center',verticalalignment='center')
ax1.text(C[0]*scale,C[1]*scale,"C",fontsize=15,horizontalalignment='center',verticalalignment='center')
ax1.text(D[0]*scale,D[1]*scale,"D",fontsize=15,horizontalalignment='center',verticalalignment='center')

plt.show()

4. Display point P

The leading role is finally here. Define the coordinates of point P and display the point with ʻax1.plot () `. The way to display the name of point P is the same as that of points A, B, C and D.

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as pat

fig = plt.figure()

ax1 = fig.add_subplot(111)

ax1.set_xlim(-4,4)
ax1.set_ylim(-3,3)

A=np.array([-3,2])
B=np.array([-3,-2])
C=np.array([3,-2])
D=np.array([3,2])

pol = pat.Polygon(xy = [A,B,C,D],
                edgecolor='black',
                facecolor='white',
                linewidth=1.6)

ax1.add_patch(pol)

ax1.text(-3.5,0.0,"4cm",horizontalalignment='center',verticalalignment='center')
ax1.text(0.0,-2.5,"6cm",horizontalalignment='center',verticalalignment='center')

scale=1.1
ax1.text(A[0]*scale,A[1]*scale,"A",fontsize=15,horizontalalignment='center',verticalalignment='center')
ax1.text(B[0]*scale,B[1]*scale,"B",fontsize=15,horizontalalignment='center',verticalalignment='center')
ax1.text(C[0]*scale,C[1]*scale,"C",fontsize=15,horizontalalignment='center',verticalalignment='center')
ax1.text(D[0]*scale,D[1]*scale,"D",fontsize=15,horizontalalignment='center',verticalalignment='center')

P=np.array([-3.0,1.0])

#Display the moving point P
scale_P=1.2
ax1.plot(P[0],P[1],marker='o',color='black')
ax1.text(P[0]*scale_P,P[1]*scale_P,"P",fontsize=15,horizontalalignment='center',verticalalignment='center')

plt.show()

5. Display △ APD

Create a triangular APD and add it to the diagram as you did when you created the rectangular ABCD, then erase the x-axis and y-axis.

%matplotlib nbagg
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as pat

fig = plt.figure()

ax1 = fig.add_subplot(111)

ax1.set_xlim(-4,4)
ax1.set_ylim(-3,3)

A=np.array([-3,2])
B=np.array([-3,-2])
C=np.array([3,-2])
D=np.array([3,2])

pol = pat.Polygon(xy = [A,B,C,D],
                edgecolor='black',
                facecolor='white',
                linewidth=1.6)

ax1.add_patch(pol)

ax1.text(-3.5,0.0,"4cm",horizontalalignment='center',verticalalignment='center')
ax1.text(0.0,-2.5,"6cm",horizontalalignment='center',verticalalignment='center')

scale=1.1
ax1.text(A[0]*scale,A[1]*scale,"A",fontsize=15,horizontalalignment='center',verticalalignment='center')
ax1.text(B[0]*scale,B[1]*scale,"B",fontsize=15,horizontalalignment='center',verticalalignment='center')
ax1.text(C[0]*scale,C[1]*scale,"C",fontsize=15,horizontalalignment='center',verticalalignment='center')
ax1.text(D[0]*scale,D[1]*scale,"D",fontsize=15,horizontalalignment='center',verticalalignment='center')

P=np.array([-3.0,1.0])

scale_P=1.2
ax1.plot(P[0],P[1],marker='o',color='black')
ax1.text(P[0]*scale_P,P[1]*scale_P,"P",fontsize=15,horizontalalignment='center',verticalalignment='center')

#△ Added APD
S = pat.Polygon(xy = [A,P,D],
                    edgecolor='black',
                    facecolor='lightgray',
                    linewidth=1.6)

ax1.add_patch(S)

#Erase the frame
plt.axis('off')

plt.show()

6. Move

Move the moving point P and output it as a gif animation. The coordinates of the moving point P after $ x $ seconds are updated every time, and the animation is created by drawing frame by frame.

• In advance, ʻinitialize ()` summarizes operations that do not change over time, such as drawing a rectangle ABCD.
• moveP (x) classifies where the moving point P is on the line segments AB, BC, and CD from the elapsed time, and returns the coordinates of the moving point P.
• The speed (velocity) of the moving point P is 1 cm per second, and the drawing interval (time step) is 0.1 seconds.
• Use PillowWriter and FuncAnimation to create animations. ʻAnimate (i)summarizes all the operations to be performed in one drawing update, and creates an animation by taking the argument ofFuncAnimation`.
• You can output a video with ʻanim.save () `.

%matplotlib nbagg #Required to animate on jupyter notebook
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as pat
from matplotlib.animation import PillowWriter,FuncAnimation #Added for video creation

fig = plt.figure()
ax1 = fig.add_subplot(111)

A=np.array([-3,2])
B=np.array([-3,-2])
C=np.array([3,-2])
D=np.array([3,2])

scale=1.1
scaleP=1.2

p = pat.Polygon(xy = [A,B,C,D],
                edgecolor='black',
                facecolor='white',
                linewidth=1.6)

def initialize():
    ax1.set_xlim(-4,4)
    ax1.set_ylim(-3,3)
    ax1.add_patch(p)


    ax1.text(A[0]*scale,A[1]*scale,"A",fontsize=15,horizontalalignment='center',verticalalignment='center')
    ax1.text(B[0]*scale,B[1]*scale,"B",fontsize=15,horizontalalignment='center',verticalalignment='center')
    ax1.text(C[0]*scale,C[1]*scale,"C",fontsize=15,horizontalalignment='center',verticalalignment='center')
    ax1.text(D[0]*scale,D[1]*scale,"D",fontsize=15,horizontalalignment='center',verticalalignment='center')

    ax1.text(-3.5,0.0,"4cm",horizontalalignment='center',verticalalignment='center')
    ax1.text(0.0,-2.5,"6cm",horizontalalignment='center',verticalalignment='center')

   
def moveP(x):
    if 0<= x <4:
        return A+np.array([0,-1])*x*velocity
    elif 4<=x <10:
        return B+np.array([1,0])*(x-4)*velocity
    elif 10<= x <14:
        return C+np.array([0,1])*(x-10)*velocity
    else:
        return D
        
velocity=1.0
timestep=0.1

def animate(t):
    plt.cla()
    initialize()
    
    x=timestep*t
    P=moveP(x)
    
    ax1.plot(P[0],P[1],marker='o',color='black')
    ax1.text(P[0]*scaleP,P[1]*scaleP,"P",fontsize=15,horizontalalignment='center',verticalalignment='center')
    
    S = pat.Polygon(xy = [A,P,D],
                    edgecolor='black',
                    facecolor='lightgray',
                    linewidth=1.6)

    ax1.add_patch(S)
    
    plt.axis('off')
    plt.title('x=' + '{:.1f}'.format(x)+'sec')
    
anim = FuncAnimation(fig,animate,frames=140,repeat=True,interval=timestep*1000)
#anim.save("ugokutenP.gif", writer='pillow',fps=10)
plt.show()