Plotly: How to find and annotate the intersection point between two lines?

Question

I am trying to find and annotate the intersection point of two-line using Plotly. I know we can use (plt.plot(*intersection.xy,'ko')) to get the intersection point in Mathplotlib, but how can do it in plotly or if it can be done.

import numpy as np
import pandas as pd
import plotly.express as px

test = pd.merge(ps,uts,on = 'Time')
print(test)

time = test['Time']
omfr = test['Orifice Mass Flow Rate']
qab = test['Qab']

fig = px.line(test, x=time, y=[omfr,qab])
fig.update_layout( title='Pipe stress and UTS (MPa)',xaxis_title="Time (s)",yaxis_title="Pipe stress and UTS (MPa)",
                  hovermode='x')

Output of the code:

Intersection point:

Answer 1

Annotating and showing the intersection is easy. Finding it is the hard part, and my suggestion in that regard builds directly on the contributions in the post How do I compute the intersection point of two lines. I'll include a few lines on the details in my suggestion when I find the time. For now, the complete code snippet at the end of my answer will produce the following figure using this dataset:

Data

   x  y1  y2
0  1   1  11.00
1  2   8  14.59
2  3  27  21.21
3  4  64  31.11

Plot

Edit - Annotation

If you'd like to change the text annotation, just change

text="intersect"

... to something like:

text = 'lines intersect at x = ' + str(round(x[0], 2)) + ' and y = ' + str(round(y[0], 2))

Result:

Complete code

import pandas as pd
import plotly.graph_objects as go
import numpy as np
# import dash


# sample dataframe
df = pd.DataFrame()
df['x'] = np.arange(4) +1
df['y1'] = df['x']**3
df['y2'] = [10+val**2.2 for val in df['x']]

# intersection stuff
def _rect_inter_inner(x1,x2):
    n1=x1.shape[0]-1
    n2=x2.shape[0]-1
    X1=np.c_[x1[:-1],x1[1:]]
    X2=np.c_[x2[:-1],x2[1:]]
    S1=np.tile(X1.min(axis=1),(n2,1)).T
    S2=np.tile(X2.max(axis=1),(n1,1))
    S3=np.tile(X1.max(axis=1),(n2,1)).T
    S4=np.tile(X2.min(axis=1),(n1,1))
    return S1,S2,S3,S4

def _rectangle_intersection_(x1,y1,x2,y2):
    S1,S2,S3,S4=_rect_inter_inner(x1,x2)
    S5,S6,S7,S8=_rect_inter_inner(y1,y2)

    C1=np.less_equal(S1,S2)
    C2=np.greater_equal(S3,S4)
    C3=np.less_equal(S5,S6)
    C4=np.greater_equal(S7,S8)

    ii,jj=np.nonzero(C1 & C2 & C3 & C4)
    return ii,jj

def intersection(x1,y1,x2,y2):

    ii,jj=_rectangle_intersection_(x1,y1,x2,y2)
    n=len(ii)

    dxy1=np.diff(np.c_[x1,y1],axis=0)
    dxy2=np.diff(np.c_[x2,y2],axis=0)

    T=np.zeros((4,n))
    AA=np.zeros((4,4,n))
    AA[0:2,2,:]=-1
    AA[2:4,3,:]=-1
    AA[0::2,0,:]=dxy1[ii,:].T
    AA[1::2,1,:]=dxy2[jj,:].T

    BB=np.zeros((4,n))
    BB[0,:]=-x1[ii].ravel()
    BB[1,:]=-x2[jj].ravel()
    BB[2,:]=-y1[ii].ravel()
    BB[3,:]=-y2[jj].ravel()

    for i in range(n):
        try:
            T[:,i]=np.linalg.solve(AA[:,:,i],BB[:,i])
        except:
            T[:,i]=np.NaN


    in_range= (T[0,:] >=0) & (T[1,:] >=0) & (T[0,:] <=1) & (T[1,:] <=1)

    xy0=T[2:,in_range]
    xy0=xy0.T
    return xy0[:,0],xy0[:,1]

# plotly figure
x,y=intersection(np.array(df['x'].values.astype('float')),np.array(df['y1'].values.astype('float')),
                 np.array(df['x'].values.astype('float')),np.array(df['y2'].values.astype('float')))

fig = go.Figure(data=go.Scatter(x=df['x'], y=df['y1'], mode = 'lines'))
fig.add_traces(go.Scatter(x=df['x'], y=df['y2'], mode = 'lines'))
fig.add_traces(go.Scatter(x=x, y=y,
                          mode = 'markers',
                          marker=dict(line=dict(color='black', width = 2),
                                      symbol = 'diamond',
                                      size = 14,
                                      color = 'rgba(255, 255, 0, 0.6)'),
                         name = 'intersect'),
              )
fig.add_annotation(x=x[0], y=y[0],
                    # text="intersect",
                    text = 'lines intersect at x = ' + str(round(x[0], 2)) + ' and y = ' + str(round(y[0], 2)),
                    font=dict(family="sans serif",
                                  size=18,
                                  color="black"),
                    ax=0,
                    ay=-100,
                    showarrow=True,
                    arrowhead=1)

fig.show()