I want to draw ellipse on top of my scatter plot like this 
I can do it with matplotlib but I don’t know how to do it with plotly since the shapes/draw in plotly is only have circle object with given parameter x0,y0,x1,y1 I can’t use that to draw my ellipse
what I actually need is a method like this matplotlib method https://matplotlib.org/api/_as_gen/matplotlib.patches.Ellipse.html
since the parameter is x coordinate, y coordinate, width(diameter), and height(diameter)
This is a plotly.py question. Please change its category from Plotly.js to Plotly.py.
Here is a function that draws the ellipse as a line:
import numpy as np
from numpy import pi, sin, cos
import plotly.graph_objects as go
def ellipse(x_center=0, y_center=0, ax1 = [1, 0], ax2 = [0,1], a=1, b =1, N=100):
# x_center, y_center the coordinates of ellipse center
# ax1 ax2 two orthonormal vectors representing the ellipse axis directions
# a, b the ellipse parameters
if np.linalg.norm(ax1) != 1 or np.linalg.norm(ax2) != 1:
raise ValueError('ax1, ax2 must be unit vectors')
if abs(np.dot(ax1, ax2)) > 1e-06:
raise ValueError('ax1, ax2 must be orthogonal vectors')
t = np.linspace(0, 2*pi, N)
#ellipse parameterization with respect to a system of axes of directions a1, a2
xs = a * cos(t)
ys = b * sin(t)
#rotation matrix
R = np.array([ax1, ax2]).T
# coordinate of the ellipse points with respect to the system of axes [1, 0], [0,1] with origin (0,0)
xp, yp = np.dot(R, [xs, ys])
x = xp + x_center
y = yp + y_center
return x, y
#EXAMPLE
fig = go.Figure()
x_center=1
y_center=0.75
x, y = ellipse_arc(x_center=x_center, y_center=y_center,
ax1 =[cos(pi/6), sin(pi/6)], ax2=[-sin(pi/6),cos(pi/6)],
a=3, b =2)
fig.add_scatter(
x=x,
y=y,
mode = 'lines')
fig.update_layout(width =600, height=525)
@empet Thank you for the great function. I am using your function to draw an ellipsoid around several lines. Its work fine with vertical and horizontal lines when using it as:
ellipse(x_center=x_center, y_center=y_center, ax1 =[cos(pi/2), sin(pi/2)], ax2=[-sin(pi/2),cos(pi/2)], a=a8, b =b8)
However, when using it with titled lines, the ellipsoids shifted slightly and appeared not perfectly aligned with the lines. Please see the image attached for more clarification. So my question is can we consider the rotation of the lines so the ellipse fit with the lines by using the Xs and Ys of the lines? And even without having the rotation angle of the lines? Or how we can calculate it and incorporated it
Any help to fix this problem will be much appreciated. Many thanks for considering my request.
Ramy
Could you, please, provide your data for the dots you plotted inside ellipses? To give an answer I need to know what role and coordinates have the blue (dots) in your plot.
Your ax1 has the direction of positive yaxis, while ax2 of the negative xaxis. I suspect that there is a conflict between the dot coordinates given with respect to the reference frame consisting in positive xaxis and positive yaxis, and the reverted axes for ellipses.
The initial function is lacking a test on the detrminat of R. This is the updated function:
import numpy as np
from numpy import pi, sin, cos
import plotly.graph_objects as go
def ellipse(x_center=0, y_center=0, ax1 = [1, 0], ax2 = [0,1], a=1, b =1, N=100):
# x_center, y_center the coordinates of ellipse center
# ax1 ax2 two orthonormal vectors representing the ellipse axis directions
# a, b the ellipse parameters
if np.linalg.norm(ax1) != 1 or np.linalg.norm(ax2) != 1:
raise ValueError('ax1, ax2 must be unit vectors')
if abs(np.dot(ax1, ax2)) > 1e-06:
raise ValueError('ax1, ax2 must be orthogonal vectors')
#rotation matrix
R = np.array([ax1, ax2]).T
if np.linalg.det(R) <0:
raise ValueError("the det(R) must be positive to get a positively oriented ellipse reference frame")
t = np.linspace(0, 2*pi, N)
#ellipse parameterization with respect to a system of axes of directions a1, a2
xs = a * cos(t)
ys = b * sin(t)
# coordinate of the ellipse points with respect to the system of axes [1, 0], [0,1] with origin (0,0)
xp, yp = np.dot(R, [xs, ys])
x = xp + x_center
y = yp + y_center
return x, y
Your det(R) is positive as required, but as I said, I suspect a conflict between the coordinate system associated to dots, respectively to the ellipse.
I really appreciated it! @empet Thank you so much for your quick reply and discussion. Yes, I am using geological data to model uncertainty in the subsurface interpretations, so the Y-axis represent the depth and parts of the Y-axis that are above the earth surface is positive and going down to the subsurface the Y-axis became negative. However, all the x-axis are positive. All the data are from the same coordinate system and exported together, so the X & Y values should be correct. Yeah, maybe the conflict is between the data coordinates and the frame generated, although I can’t figure out how I overcome this! Please have a look at my data points:
| x | z | Name |
|---|---|---|
| 127.732 | -24.5685 | Tunnel_Well |
| 127.7654 | -25.2623 | Tunnel_Well |
| 127.7978 | -25.935 | Tunnel_Well |
| 127.8282 | -26.5662 | Tunnel_Well |
| 127.8556 | -27.1367 | Tunnel_Well |
| 127.8793 | -27.6291 | Tunnel_Well |
| 127.8986 | -28.0286 | Tunnel_Well |
| 127.9127 | -28.3229 | Tunnel_Well |
| 127.9214 | -28.5032 | Tunnel_Well |
| 127.9243 | -28.5639 | Tunnel_Well |
| 127.9214 | -28.5032 | Tunnel_Well |
| 127.9127 | -28.3229 | Tunnel_Well |
| 127.8986 | -28.0286 | Tunnel_Well |
| 127.8793 | -27.6291 | Tunnel_Well |
| 127.8556 | -27.1367 | Tunnel_Well |
| 127.8282 | -26.5662 | Tunnel_Well |
| 127.7978 | -25.935 | Tunnel_Well |
| 127.7654 | -25.2623 | Tunnel_Well |
| 127.732 | -24.5685 | Tunnel_Well |
| 127.6986 | -23.8747 | Tunnel_Well |
| 127.6662 | -23.202 | Tunnel_Well |
| 127.6358 | -22.5708 | Tunnel_Well |
| 127.6083 | -22.0003 | Tunnel_Well |
| 127.5846 | -21.5078 | Tunnel_Well |
| 127.5654 | -21.1084 | Tunnel_Well |
| 127.5512 | -20.8141 | Tunnel_Well |
| 127.5425 | -20.6338 | Tunnel_Well |
| 127.5396 | -20.5731 | Tunnel_Well |
| 127.5425 | -20.6338 | Tunnel_Well |
| 127.5512 | -20.8141 | Tunnel_Well |
| 127.5654 | -21.1084 | Tunnel_Well |
| 127.5846 | -21.5078 | Tunnel_Well |
| 127.6083 | -22.0003 | Tunnel_Well |
| 127.6358 | -22.5708 | Tunnel_Well |
| 127.6662 | -23.202 | Tunnel_Well |
| 127.6986 | -23.8747 | Tunnel_Well |
| 238.2299 | -19.2482 | Tunnel_Well |
| 238.2633 | -19.942 | Tunnel_Well |
| 238.2956 | -20.6147 | Tunnel_Well |
| 238.326 | -21.2459 | Tunnel_Well |
| 238.3535 | -21.8164 | Tunnel_Well |
| 238.3772 | -22.3088 | Tunnel_Well |
| 238.3965 | -22.7083 | Tunnel_Well |
| 238.4106 | -23.0026 | Tunnel_Well |
| 238.4193 | -23.1829 | Tunnel_Well |
| 238.4222 | -23.2436 | Tunnel_Well |
| 238.4193 | -23.1829 | Tunnel_Well |
| 238.4106 | -23.0026 | Tunnel_Well |
| 238.3965 | -22.7083 | Tunnel_Well |
| 238.3772 | -22.3088 | Tunnel_Well |
| 238.3535 | -21.8164 | Tunnel_Well |
| 238.326 | -21.2459 | Tunnel_Well |
| 238.2956 | -20.6147 | Tunnel_Well |
| 238.2633 | -19.942 | Tunnel_Well |
| 238.2299 | -19.2482 | Tunnel_Well |
| 238.1964 | -18.5544 | Tunnel_Well |
| 238.1641 | -17.8817 | Tunnel_Well |
| 238.1337 | -17.2505 | Tunnel_Well |
| 238.1062 | -16.68 | Tunnel_Well |
| 238.0825 | -16.1876 | Tunnel_Well |
| 238.0633 | -15.7881 | Tunnel_Well |
| 238.0491 | -15.4938 | Tunnel_Well |
| 238.0404 | -15.3135 | Tunnel_Well |
| 238.0375 | -15.2528 | Tunnel_Well |
| 238.0404 | -15.3135 | Tunnel_Well |
| 238.0491 | -15.4938 | Tunnel_Well |
| 238.0633 | -15.7881 | Tunnel_Well |
| 238.0825 | -16.1876 | Tunnel_Well |
| 238.1062 | -16.68 | Tunnel_Well |
| 238.1337 | -17.2505 | Tunnel_Well |
| 238.1641 | -17.8817 | Tunnel_Well |
| 238.1964 | -18.5544 | Tunnel_Well |
| 348.7277 | -13.9279 | Tunnel_Well |
| 348.7611 | -14.6217 | Tunnel_Well |
| 348.7935 | -15.2944 | Tunnel_Well |
| 348.8239 | -15.9256 | Tunnel_Well |
| 348.8514 | -16.4961 | Tunnel_Well |
| 348.8751 | -16.9886 | Tunnel_Well |
| 348.8943 | -17.388 | Tunnel_Well |
| 348.9085 | -17.6824 | Tunnel_Well |
| 348.9172 | -17.8626 | Tunnel_Well |
| 348.9201 | -17.9233 | Tunnel_Well |
| 348.9172 | -17.8626 | Tunnel_Well |
| 348.9085 | -17.6824 | Tunnel_Well |
| 348.8943 | -17.388 | Tunnel_Well |
| 348.8751 | -16.9886 | Tunnel_Well |
| 348.8514 | -16.4961 | Tunnel_Well |
| 348.8239 | -15.9256 | Tunnel_Well |
| 348.7935 | -15.2944 | Tunnel_Well |
| 348.7611 | -14.6217 | Tunnel_Well |
| 348.7277 | -13.9279 | Tunnel_Well |
| 348.6943 | -13.2342 | Tunnel_Well |
| 348.6619 | -12.5614 | Tunnel_Well |
| 348.6316 | -11.9303 | Tunnel_Well |
| 348.6041 | -11.3598 | Tunnel_Well |
| 348.5804 | -10.8673 | Tunnel_Well |
| 348.5611 | -10.4678 | Tunnel_Well |
| 348.547 | -10.1735 | Tunnel_Well |
| 348.5383 | -9.9933 | Tunnel_Well |
| 348.5354 | -9.9326 | Tunnel_Well |
| 348.5383 | -9.9933 | Tunnel_Well |
| 348.547 | -10.1735 | Tunnel_Well |
| 348.5611 | -10.4678 | Tunnel_Well |
| 348.5804 | -10.8673 | Tunnel_Well |
| 348.6041 | -11.3598 | Tunnel_Well |
| 348.6316 | -11.9303 | Tunnel_Well |
| 348.6619 | -12.5614 | Tunnel_Well |
| 348.6943 | -13.2342 | Tunnel_Well |
| 459.2256 | -8.6077 | Tunnel_Well |
| 459.259 | -9.3015 | Tunnel_Well |
| 459.2914 | -9.9742 | Tunnel_Well |
| 459.3218 | -10.6054 | Tunnel_Well |
| 459.3493 | -11.1758 | Tunnel_Well |
| 459.373 | -11.6683 | Tunnel_Well |
| 459.3922 | -12.0678 | Tunnel_Well |
| 459.4064 | -12.3621 | Tunnel_Well |
| 459.4151 | -12.5423 | Tunnel_Well |
| 459.418 | -12.603 | Tunnel_Well |
| 459.4151 | -12.5423 | Tunnel_Well |
| 459.4064 | -12.3621 | Tunnel_Well |
| 459.3922 | -12.0678 | Tunnel_Well |
| 459.373 | -11.6683 | Tunnel_Well |
| 459.3493 | -11.1758 | Tunnel_Well |
| 459.3218 | -10.6054 | Tunnel_Well |
| 459.2914 | -9.9742 | Tunnel_Well |
| 459.259 | -9.3015 | Tunnel_Well |
| 459.2256 | -8.6077 | Tunnel_Well |
| 459.1922 | -7.9139 | Tunnel_Well |
| 459.1598 | -7.2412 | Tunnel_Well |
| 459.1294 | -6.61 | Tunnel_Well |
| 459.102 | -6.0395 | Tunnel_Well |
| 459.0783 | -5.547 | Tunnel_Well |
| 459.059 | -5.1476 | Tunnel_Well |
| 459.0449 | -4.8533 | Tunnel_Well |
| 459.0362 | -4.673 | Tunnel_Well |
| 459.0333 | -4.6123 | Tunnel_Well |
| 459.0362 | -4.673 | Tunnel_Well |
| 459.0449 | -4.8533 | Tunnel_Well |
| 459.059 | -5.1476 | Tunnel_Well |
| 459.0783 | -5.547 | Tunnel_Well |
| 459.102 | -6.0395 | Tunnel_Well |
| 459.1294 | -6.61 | Tunnel_Well |
| 459.1598 | -7.2412 | Tunnel_Well |
| 459.1922 | -7.9139 | Tunnel_Well |
| 569.7235 | -3.2874 | Tunnel_Well |
| 569.7569 | -3.9812 | Tunnel_Well |
| 569.7893 | -4.6539 | Tunnel_Well |
| 569.8197 | -5.2851 | Tunnel_Well |
| 569.8472 | -5.8556 | Tunnel_Well |
| 569.8709 | -6.348 | Tunnel_Well |
| 569.8901 | -6.7475 | Tunnel_Well |
| 569.9043 | -7.0418 | Tunnel_Well |
| 569.913 | -7.2221 | Tunnel_Well |
| 569.9159 | -7.2828 | Tunnel_Well |
| 569.913 | -7.2221 | Tunnel_Well |
| 569.9043 | -7.0418 | Tunnel_Well |
| 569.8901 | -6.7475 | Tunnel_Well |
| 569.8709 | -6.348 | Tunnel_Well |
| 569.8472 | -5.8556 | Tunnel_Well |
| 569.8197 | -5.2851 | Tunnel_Well |
| 569.7893 | -4.6539 | Tunnel_Well |
| 569.7569 | -3.9812 | Tunnel_Well |
| 569.7235 | -3.2874 | Tunnel_Well |
| 569.6901 | -2.5936 | Tunnel_Well |
| 569.6577 | -1.9209 | Tunnel_Well |
| 569.6273 | -1.2897 | Tunnel_Well |
| 569.5999 | -0.7192 | Tunnel_Well |
| 569.5762 | -0.2268 | Tunnel_Well |
| 569.5569 | 0.1727 | Tunnel_Well |
| 569.5427 | 0.467 | Tunnel_Well |
| 569.5341 | 0.6473 | Tunnel_Well |
| 569.5311 | 0.708 | Tunnel_Well |
| 569.5341 | 0.6473 | Tunnel_Well |
| 569.5427 | 0.467 | Tunnel_Well |
| 569.5569 | 0.1727 | Tunnel_Well |
| 569.5762 | -0.2268 | Tunnel_Well |
| 569.5999 | -0.7192 | Tunnel_Well |
| 569.6273 | -1.2897 | Tunnel_Well |
| 569.6577 | -1.9209 | Tunnel_Well |
| 569.6901 | -2.5936 | Tunnel_Well |
| 680.2214 | 2.0329 | Tunnel_Well |
| 680.2548 | 1.3391 | Tunnel_Well |
| 680.2872 | 0.6664 | Tunnel_Well |
| 680.3176 | 0.0352 | Tunnel_Well |
| 680.3451 | -0.5353 | Tunnel_Well |
| 680.3688 | -1.0278 | Tunnel_Well |
| 680.388 | -1.4272 | Tunnel_Well |
| 680.4022 | -1.7216 | Tunnel_Well |
| 680.4108 | -1.9018 | Tunnel_Well |
| 680.4138 | -1.9625 | Tunnel_Well |
| 680.4108 | -1.9018 | Tunnel_Well |
| 680.4022 | -1.7216 | Tunnel_Well |
| 680.388 | -1.4272 | Tunnel_Well |
| 680.3688 | -1.0278 | Tunnel_Well |
| 680.3451 | -0.5353 | Tunnel_Well |
| 680.3176 | 0.0352 | Tunnel_Well |
| 680.2872 | 0.6664 | Tunnel_Well |
| 680.2548 | 1.3391 | Tunnel_Well |
| 680.2214 | 2.0329 | Tunnel_Well |
| 680.188 | 2.7267 | Tunnel_Well |
| 680.1556 | 3.3994 | Tunnel_Well |
| 680.1252 | 4.0305 | Tunnel_Well |
| 680.0977 | 4.601 | Tunnel_Well |
| 680.074 | 5.0935 | Tunnel_Well |
| 680.0548 | 5.493 | Tunnel_Well |
| 680.0406 | 5.7873 | Tunnel_Well |
| 680.032 | 5.9675 | Tunnel_Well |
| 680.029 | 6.0282 | Tunnel_Well |
| 680.032 | 5.9675 | Tunnel_Well |
| 680.0406 | 5.7873 | Tunnel_Well |
| 680.0548 | 5.493 | Tunnel_Well |
| 680.074 | 5.0935 | Tunnel_Well |
| 680.0977 | 4.601 | Tunnel_Well |
| 680.1252 | 4.0305 | Tunnel_Well |
| 680.1556 | 3.3994 | Tunnel_Well |
| 680.188 | 2.7267 | Tunnel_Well |
Many thanks
Please post x_center, y_center, and a8, b8, to reproduce exactly your code and data.
@empet Sure:
x_center(h1)=403.97665, y_center(k1)=-11.26785, a1=24.374465, b1=390.936924.
For more lines:
| x | z | Name |
|---|---|---|
| 452.1491 | -8.9484 | Tunnel_Well |
| 451.4558 | -8.9903 | Tunnel_Well |
| 450.7835 | -9.0309 | Tunnel_Well |
| 450.1527 | -9.069 | Tunnel_Well |
| 449.5826 | -9.1035 | Tunnel_Well |
| 449.0905 | -9.1332 | Tunnel_Well |
| 448.6913 | -9.1573 | Tunnel_Well |
| 448.3972 | -9.1751 | Tunnel_Well |
| 448.217 | -9.186 | Tunnel_Well |
| 448.1564 | -9.1897 | Tunnel_Well |
| 448.217 | -9.186 | Tunnel_Well |
| 448.3972 | -9.1751 | Tunnel_Well |
| 448.6913 | -9.1573 | Tunnel_Well |
| 449.0905 | -9.1332 | Tunnel_Well |
| 449.5826 | -9.1035 | Tunnel_Well |
| 450.1527 | -9.069 | Tunnel_Well |
| 450.7835 | -9.0309 | Tunnel_Well |
| 451.4558 | -8.9903 | Tunnel_Well |
| 452.1491 | -8.9484 | Tunnel_Well |
| 452.8424 | -8.9065 | Tunnel_Well |
| 453.5147 | -8.8659 | Tunnel_Well |
| 454.1455 | -8.8278 | Tunnel_Well |
| 454.7156 | -8.7933 | Tunnel_Well |
| 455.2077 | -8.7636 | Tunnel_Well |
| 455.6069 | -8.7395 | Tunnel_Well |
| 455.901 | -8.7217 | Tunnel_Well |
| 456.0812 | -8.7108 | Tunnel_Well |
| 456.1418 | -8.7071 | Tunnel_Well |
| 456.0812 | -8.7108 | Tunnel_Well |
| 455.901 | -8.7217 | Tunnel_Well |
| 455.6069 | -8.7395 | Tunnel_Well |
| 455.2077 | -8.7636 | Tunnel_Well |
| 454.7156 | -8.7933 | Tunnel_Well |
| 454.1455 | -8.8278 | Tunnel_Well |
| 453.5147 | -8.8659 | Tunnel_Well |
| 452.8424 | -8.9065 | Tunnel_Well |
| 455.193 | -59.3234 | Tunnel_Well |
| 454.4997 | -59.3653 | Tunnel_Well |
| 453.8274 | -59.4059 | Tunnel_Well |
| 453.1967 | -59.444 | Tunnel_Well |
| 452.6266 | -59.4785 | Tunnel_Well |
| 452.1344 | -59.5082 | Tunnel_Well |
| 451.7352 | -59.5324 | Tunnel_Well |
| 451.4411 | -59.5501 | Tunnel_Well |
| 451.261 | -59.561 | Tunnel_Well |
| 451.2003 | -59.5647 | Tunnel_Well |
| 451.261 | -59.561 | Tunnel_Well |
| 451.4411 | -59.5501 | Tunnel_Well |
| 451.7352 | -59.5324 | Tunnel_Well |
| 452.1344 | -59.5082 | Tunnel_Well |
| 452.6266 | -59.4785 | Tunnel_Well |
| 453.1967 | -59.444 | Tunnel_Well |
| 453.8274 | -59.4059 | Tunnel_Well |
| 454.4997 | -59.3653 | Tunnel_Well |
| 455.193 | -59.3234 | Tunnel_Well |
| 455.8864 | -59.2815 | Tunnel_Well |
| 456.5586 | -59.2409 | Tunnel_Well |
| 457.1894 | -59.2028 | Tunnel_Well |
| 457.7595 | -59.1683 | Tunnel_Well |
| 458.2516 | -59.1386 | Tunnel_Well |
| 458.6508 | -59.1145 | Tunnel_Well |
| 458.945 | -59.0967 | Tunnel_Well |
| 459.1251 | -59.0858 | Tunnel_Well |
| 459.1858 | -59.0822 | Tunnel_Well |
| 459.1251 | -59.0858 | Tunnel_Well |
| 458.945 | -59.0967 | Tunnel_Well |
| 458.6508 | -59.1145 | Tunnel_Well |
| 458.2516 | -59.1386 | Tunnel_Well |
| 457.7595 | -59.1683 | Tunnel_Well |
| 457.1894 | -59.2028 | Tunnel_Well |
| 456.5586 | -59.2409 | Tunnel_Well |
| 455.8864 | -59.2815 | Tunnel_Well |
And the X_center and y_center, a and b:
h3=453.67105, k3=-34.1359, a3=35.956521, b3=7.713191
@RamySaleem
I took only a few data, because it takes time to copy, paste and format data (insering comma after each value, adding [ ], for each row, etc).
I didn’t hit any row in the copied data that didn’t line up.
vals = np.array([[455.901, -8.7217],
[456.081, -8.7108],
[456.141, -8.7071],
[456.0812, -8.7108],
[455.6069, -8.7395],
[455.2077, -8.7636],
[454.7156, -8.7933],
[454.1455,-8.8278],
[453.5147,-8.8659],
[452.8424,-8.9065],
[449.5826,-9.1035],
[449.0905,-9.1332],
[448.6913,-9.1573],
[448.3972,-9.1751],
[448.217,-9.186],
[448.1564,-9.1897],
[448.217,-9.186]])
fig = go.Figure()
x_center=453.67105
y_center=-34.1359
a3=35.956521
b3=7.713191
x, y = ellipse(x_center=x_center, y_center=y_center,
ax1 =[cos(pi/2), sin(pi/2)], ax2=[-sin(pi/2),cos(pi/2)],
a=a3, b =b3)
fig.add_scatter(
x=x,
y=y,
mode = 'lines')
fig.add_scatter(x= vals[:, 0], y=vals[:, 1], mode="markers", marker_size=6)
fig.update_layout(width =600, height=525)
Yeah, with small data in the midlle it looks fine but if we select data from the start and end we will see that the generated elipside unfit. I have posted to you few raws show the problem, please have a look:
([[127.9214, -28.5032],
[127.9127, -28.3229],
[127.8986,-28.0286],
[127.8793, -27.6291],
[127.8556, -27.1367],
[127.8282, -26.5662],
[680.0548, 5.493],
[680.074, 5.0935],
[680.0977, 4.601],
[680.1252, 4.0305],
[680.1556, 3.3994],
[680.188, 2.7267]])
The orange ellipsoid shows it’s not perfectly covering the data points. I also realised that if we plot just one ellipsoid is not clearly showing the problem. Check the orange ellipsoid on the first image not showing clearly the rotation problem because of the vertical exaggeration but it’s still there?
Are you sure that all data coordinates are inside some ellipse? I cannot reproduce your plot, because I have only dthe center and axes for a single ellipse.
Your problem isn’t the Plotly trace definition, but your data.
Yes they are inside the same ellipse, and I belevie my data is correct. I think we need to consider the roation angle of the ellipsod! This is the code I use to generat the plot:
Create figure
fig = go.Figure()
fig.add_trace(go.Scatter(x=x11, y=z11, name="line-1", mode="markers", marker_color='gray'))
well-1
x_center=404.0081
y_center=-11.505099999999999
x1, y1 = ellipse_new(x_center=x_center, y_center=y_center, ax1 =[cos(pi/2), sin(pi/2)], ax2=[-sin(pi/2),cos(pi/2)], a=24.038943, b =390.577360)
fig.add_scatter( x=x1, y=y1, mode = 'lines')
fig.update_layout(showlegend=True)
fig.show()
I just add this to make the plot longer in the y-axis and make the probelm clearer
fig.add_scatter( x=x8, y=y8, mode = 'lines')
The ellipse_new is your new function and x11, and z
I have also plotted the same data on matplotlib using the following function:
def confidence_ellipse(x, y, ax, n_std=3.0, facecolor='none', **kwargs): if x.size != y.size: raise ValueError("x and y must be the same size") cov = np.cov(x, y) pearson = cov[0, 1]/np.sqrt(cov[0, 0] * cov[1, 1]) ell_radius_x = np.sqrt(1 + pearson) ell_radius_y = np.sqrt(1 - pearson) ellipse = Ellipse((0, 0), width=ell_radius_x * 2, height=ell_radius_y * 2, facecolor=facecolor, **kwargs) scale_x = np.sqrt(cov[0, 0]) * n_std mean_x = np.mean(x) scale_y = np.sqrt(cov[1, 1]) * n_std mean_y = np.mean(y) transf = transforms.Affine2D() \ .rotate_deg(45) \ .scale(scale_x, scale_y) \ .translate(mean_x, mean_y) ellipse.set_transform(transf + ax.transData) return ax.add_patch(ellipse)
The code as follow:
fig, ax_kwargs = plt.subplots(figsize=(16, 16)) ax_kwargs.axvline(c='grey', lw=1) ax_kwargs.axhline(c='grey', lw=1)
x, y = x11, z11 xmin=min(x) ymin=min(y) xmax=max(x) ymax=max(y) h = (xmin + xmax)/2 k = (ymin + ymax)/2 mu = h, k
confidence_ellipse(x, y, ax_kwargs, alpha=0.5, facecolor='pink', edgecolor='purple', zorder=0)
`ax_kwargs.scatter(x, y, s=0.5)
ax_kwargs.scatter(mu[0], mu[1], c=‘red’, s=3)
ax_kwargs.set_title(‘Uncertainty Modelling’)
fig.subplots_adjust(hspace=0.25) plt.show()
Please see the resulting image.
I really want to use Plotly since its interactivity, and I can easily get the ellipsoid coordinates by your function to apply further analysis!
Hi!
i’m really interested in this topic too, thank’s both for maintain alive this thread.
I was trying to plot a covariance ellipse in a plotly polar plot with no luck yet.
I just find an article that could help (code is at the bottom) on this question:
://www.visiondummy.com/2014/04/draw-error-ellipse-representing-covariance-matrix/
Hi Laikus, thanks for the interst! Yeah, I think it is important to draw the ellipsoid with the correct rotational angle to the data points! In the example, you can get the max and min of your point then get the rectangle height and wedith. Then get the x-centre and y-centre, a and b to draw your ellipsoid. I believe empet function will plot your ellipsoid perfectly since the rotational angle is not that important as in my case, You can use:
def get_centre_a_b(source_df):
x_source = source_df['x']
z_source = source_df['z']
xmin=min(x_source)
ymin=min(z_source)
xmax=max(x_source)
ymax=max(z_source)
h = (xmin + xmax)/2
k = (ymin + ymax)/2
rh = ymax - ymin
a=rh/math.sqrt(2)
rw = xmax - xmin
b=rw/math.sqrt(2)
return h, k, a, b, rh, rw
Then apply empt function mentioned above.
@empet I have also put my data in a g-drive to make it easy to re-produce my plots.
https://drive.google.com/drive/folders/1JGKdnfqu9aZy8YFtL_2kL-NnJ-fJHcMM?usp=sharing
One of the solutions I found is to include the rotational angel when we creating the ellipsoids.
When we call the function, and we define the rotational angle as follow:
Example-1:
Notice that we define pi/1.93, which will result in the rotational angel in my model. This will be user define and verified visually by the user.
# well-4
x_center = h4
y_center = k4
angel_4 = pi/1.93
x, y = ellipse(x_center=x_center, y_center=y_center, ax1 =[cos(angel_4), sin(angel_4)], ax2=[-sin(angel_4),cos(angel_4)], a=a4, b =b4)
fig.add_scatter(x=x, y=y, mode = 'lines', name='Zone-1 - well-4', fill='toself', opacity=0.5)
Example-2:
Notice that we define pi/1.935 to rotate the ellipse.
# well-5
x_center = h5
y_center = k5
angel_5 = pi/1.935
x, y = ellipse(x_center=x_center, y_center=y_center, ax1 =[cos(angel_5), sin(angel_5)], ax2=[-sin(angel_5),cos(angel_5)], a=a5-20, b =b5-140)
fig.add_scatter(x=x, y=y, mode = 'lines', name='Zone-1 - well-5', fill='toself', opacity=0.5)
Example-3
Notice that we define pi/1.921 to rotate the ellipse.
# well-6
x_center=h6
y_center=k6
angel_6 = pi/1.921
x, y = ellipse(x_center=x_center, y_center=y_center, ax1 =[cos(angel_6), sin(angel_6)], ax2=[-sin(angel_6),cos(angel_6)], a=a6-25, b =b6-140)
fig.add_scatter(x=x, y=y, mode = 'lines', name='Zone-1 - well-6', fill='toself', opacity=0.8)
Please see the attached figure as an example.