pls

Created on: June 4, 2025

Answered using O3 by Chat01

Question

Screenshot 2025-06-04 12.25.54 PM.png

pls

Python

python
from PIL import Image
import matplotlib.pyplot as plt

img = Image.open('/mnt/data/Screenshot 2025-06-04 12.25.54 PM.png')
plt.imshow(img)
plt.axis('off')

(-0.5, 603.5, 484.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(img.crop((200,100,650,650)))
plt.axis('off')

(-0.5, 449.5, 549.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(img.crop((230,126,420,315)))
plt.axis('off')

(-0.5, 189.5, 188.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(img.crop((240,150,380,280)))
plt.axis('off')

(-0.5, 139.5, 129.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(img.crop((250,160,330,240)))
plt.axis('off')

(-0.5, 79.5, 79.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(img.crop((260,170,310,220)))
plt.axis('off')

(-0.5, 49.5, 49.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(img.crop((210,100,430,320)))
plt.axis('off')

(-0.5, 219.5, 219.5, -0.5)

Python

python
plt.figure(figsize=(3,3))
plt.imshow(img.crop((210,100,260,320)))
plt.axis('off')

(-0.5, 49.5, 219.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(img.crop((210,240,430,280)))
plt.axis('off')

(-0.5, 219.5, 39.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(img.crop((210,100,430,320)))
plt.axis('off')
plt.show()

Python

python
plt.figure(figsize=(3,3))
plt.imshow(img.crop((250,160,390,305)))
plt.axis('off')

(-0.5, 139.5, 144.5, -0.5)

Python

python
plt.figure(figsize=(3,3))
plt.imshow(img.crop((350,100,500,250)))
plt.axis('off')

(-0.5, 149.5, 149.5, -0.5)

Python

python
plt.figure(figsize=(3,3))
plt.imshow(img.crop((320,60,420,190)))
plt.axis('off')

(-0.5, 99.5, 129.5, -0.5)

Python

python
plt.figure(figsize=(6,6))
plt.imshow(img.crop((180,80,480,380)))
plt.axis('off')

(-0.5, 299.5, 299.5, -0.5)

Python

python
plt.figure(figsize=(6,2))
plt.imshow(img.crop((180,190,480,260)))
plt.axis('off')

(-0.5, 299.5, 69.5, -0.5)

Python

python
plt.figure(figsize=(3,4))
plt.imshow(img.crop((220,80,280,300)))
plt.axis('off')

(-0.5, 59.5, 219.5, -0.5)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(img.crop((260,135,370,210)))
plt.axis('off')

(-0.5, 109.5, 74.5, -0.5)

Python

python
plt.figure(figsize=(6,6))
plt.imshow(img.crop((220,110,370,260)))
plt.axis('off')

(-0.5, 149.5, 149.5, -0.5)

Python

python
plt.figure(figsize=(3,3))
plt.imshow(img.crop((250,150,290,190)))
plt.axis('off')

(-0.5, 39.5, 39.5, -0.5)

Python

python
plt.figure(figsize=(3,3))
plt.imshow(img.crop((285,150,315,190)))
plt.axis('off')

(-0.5, 29.5, 39.5, -0.5)

Python

python
import numpy as np
import cv2
import matplotlib.pyplot as plt

# load grayscale version
gray = cv2.cvtColor(np.array(img), cv2.COLOR_BGR2GRAY)
# find vertical gray axis maybe darker grey line without black.
# Let's find column with many dark pixels horizontally across mix.
# compute vertical sum of low intensities under threshold
h, w = gray.shape
threshold = 100
col_sums = np.sum(gray < threshold, axis=0)
# display peaks
# find index of maximum
x_axis = np.argmax(col_sums)
x_axis

30

Python

python
plt.figure(figsize=(4,4))
plt.imshow(img)
plt.axvline(x=30,color='red')
plt.axis('off')

(-0.5, 603.5, 484.5, -0.5)

Python

python
graph = img.crop((180,80,480,380))
grayg = cv2.cvtColor(np.array(graph), cv2.COLOR_BGR2GRAY)
h2,w2 = grayg.shape
col_s = np.sum(grayg < threshold, axis=0)
row_s = np.sum(grayg < threshold, axis=1)
# find vertical axis, choose col with high sum
x_axis_col = np.argmax(col_s)
y_axis_row = np.argmax(row_s)
x_axis_col, y_axis_row

(116, 119)

Python

python
plt.figure(figsize=(4,4))
plt.imshow(graph)
plt.axvline(x=x_axis_col,color='red')
plt.axhline(y=y_axis_row,color='blue')
plt.axis('off')

(-0.5, 299.5, 299.5, -0.5)

Python

python
# detect black pixels
# threshold: black pixel intensity < 50 maybe
mask = grayg < 50
# find coordinates of mask
coords = np.column_stack(np.where(mask))
# choose coords where x <= x_axis_col perhaps for left side
left_coords = coords[coords[:,1] < x_axis_col - 5]  # avoid axis
# may also filter above y axis row maybe y<=y_axis_row? Actually P is above y-axis and above origin maybe around y slightly above axis row
# Actually P is above x-axis maybe above row y_axis_row?
# Let's filter rows less than maybe y_axis_row but greater than y_axis_row - some margin?
p_candidates = left_coords[left_coords[:,0] <= y_axis_row + 10]  # within maybe 10 px above axis row
# Actually P dot is above x-axis maybe 1-3 squares above axis, which may be around 2*grid spacing ~ maybe 40 pixels above y_axis_row?
# Let's search candidates where row < y_axis_row
p_candidates = left_coords[left_coords[:,0] < y_axis_row - 10]
# compute mean row/col of cluster
py, px = np.mean(p_candidates, axis=0)
py, px

(93.45161290322581, 103.58064516129032)

Thought

I've detected the approximate crosspoint of the axes at (x=116, y=119) in the graph crop. Now, I'm focusing on finding the coordinates of point P by detecting black pixel clusters near the left-middle part of the graph. Based on this, I found the actual coordinates of point P as (x=104, y=93). Now I need to compute the pixel deltas from the axes' crosspoint. After that, I’ll estimate the grid spacing and figure out the distance between the grid lines, considering possible errors along the way.

Thought for 4m 54s

Answer

El punto P parte de (-1, 2).
Al girarlo 90° en sentido horario alrededor del origen, sus coordenadas se transforman según (x, y) → (y, −x), de modo que

$P' = (\,2,\;1\,)$ .

Por lo tanto, la coordenada $y$ de $P'$ es 1.

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