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these are polylines
ok so i wanted to make something that regularises and finds symmetry
so i made this script
import numpy as np
import matplotlib.pyplot as plt
import cv2
import csv

def read_csv(csv_path):
"""Reads a CSV file and organizes the points into paths."""
np_path_XYs = np.genfromtxt(csv_path, delimiter=',')
path_XYs = []
for i in np.unique(np_path_XYs[:, 0]):
npXYs = np_path_XYs[np_path_XYs[:, 0] == i][:, 1:]
XYs = []
for j in np.unique(npXYs[:, 0]):
XY = npXYs[npXYs[:, 0] == j][:, 1:]
XYs.append(XY)
path_XYs.append(XYs)
return path_XYs

def detect_shape(XY):
"""Detects the shape type from the provided points."""
contour = np.array(XY, dtype=np.int32).reshape((-1, 1, 2))
peri = cv2.arcLength(contour, True)
approx = cv2.approxPolyDP(contour, 0.04 * peri, True)
area = cv2.contourArea(contour)

if area < 100:
return " "

if is_straight_line(XY):
return "Straight Line"

if len(approx) == 4:
if is_square(contour):
return "Square"
else:
return "Rectangle"

elif len(approx) > 5:
if is_star(approx):
return "Star"

circularity = 4 * np.pi * area / (peri * peri)

if circularity > 0.95:
return "Circle"
elif 0.8 <= circularity < 0.95:
ellipse = cv2.fitEllipse(contour)
major_axis, minor_axis = max(ellipse[1]), min(ellipse[1])
if major_axis / minor_axis > 1.05:
return "Ellipse"
else:
return "Circle"
return " "
def is_square(contour, tolerance=0.05):
"""Checks if the contour forms a square."""
rect = cv2.minAreaRect(contour)
box = cv2.boxPoints(rect)
box = np.intp(box)

width = np.linalg.norm(box[0] - box[1])
height = np.linalg.norm(box[1] - box[2])
aspect_ratio = min(width, height) / max(width, height)

contour_area = cv2.contourArea(contour)
rect_area = width * height
area_ratio = contour_area / rect_area

is_square_shape = abs(1 - aspect_ratio) < tolerance
is_filled = area_ratio > (1 - tolerance)

return is_square_shape and is_filled
def is_star(approx):
"""Checks if the contour forms a star shape."""
num_vertices = len(approx)
if num_vertices > 8:
angles = []
for i in range(num_vertices):
p1 = approx[i][0]
p2 = approx[(i + 1) % num_vertices][0]
p3 = approx[(i + 2) % num_vertices][0]
angle = calculate_angle(p1, p2, p3)
angles.append(angle)

sharp_angles = [angle for angle in angles if angle < 60 or angle > 300]
if len(sharp_angles) >= 5:
return True
return False
def calculate_angle(p1, p2, p3):
"""Calculates the angle between three points."""
a = np.array(p1)
b = np.array(p2)
c = np.array(p3)
ab = b - a
cb = b - c
cosine_angle = np.dot(ab, cb) / (np.linalg.norm(ab) * np.linalg.norm(cb))
angle = np.degrees(np.arccos(cosine_angle))
return angle

def is_straight_line(XY, tolerance=0.05):
"""Checks if the points form a straight line."""
if len(XY) < 3:
return True

total_length = np.sum(np.sqrt(np.sum(np.diff(XY, axis=0)**2, axis=1)))
start_to_end = np.linalg.norm(XY[-1] - XY[0])
return (total_length - start_to_end) / total_length < tolerance
def regularize_circle(XY):
"""Regularizes the points to form a perfect circle."""
xc, yc, r = kasa_circle_fitting(XY)
t = np.linspace(0, 2 * np.pi, 100)
x_fit = xc + r * np.cos(t)
y_fit = yc + r * np.sin(t)
return np.vstack((x_fit, y_fit)).T

def kasa_circle_fitting(XY):
"""Fits a circle to the points using Kasa's method."""
x = XY[:, 0]
y = XY[:, 1]
A = np.array([x, y, np.ones_like(x)]).T
b = x2 + y2
c = np.linalg.lstsq(A, b, rcond=None)[0]
xc = c[0] / 2
yc = c[1] / 2
r = np.sqrt(c[2] + xc2 + yc2)
return xc, yc, r

def regularize_ellipse(XY):
"""Regularizes the points to form a perfect ellipse."""
x_min, y_min = np.min(XY, axis=0)
x_max, y_max = np.max(XY, axis=0)
center = [(x_min + x_max) / 2, (y_min + y_max) / 2]
width = x_max - x_min
height = y_max - y_min
t = np.linspace(0, 2 * np.pi, 200)
x = center[0] + width/2 * np.cos(t)
y = center[1] + height/2 * np.sin(t)

return np.column_stack((x, y))
def regularize_rectangle(XY):
"""Regularizes the points to form a perfect rectangle."""
x_min, y_min = np.min(XY, axis=0)
x_max, y_max = np.max(XY, axis=0)

regularized = np.array([
[x_min, y_min],
[x_max, y_min],
[x_max, y_max],
[x_min, y_max],
[x_min, y_min]
])

return regularized
def regularize_square(XY):
"""Regularizes the points to form a perfect square."""
x_min, y_min = np.min(XY, axis=0)
x_max, y_max = np.max(XY, axis=0)

side_length = min(x_max - x_min, y_max - y_min)

reg_XY = np.array([
[x_min, y_min],
[x_min + side_length, y_min],
[x_min + side_length, y_min + side_length],
[x_min, y_min + side_length],
[x_min, y_min]
])

return reg_XY
def regularize_star(XY, num_points=5):
"""Regularizes the points to form a perfect star."""
centroid = np.mean(XY, axis=0)

radii = np.linalg.norm(XY - centroid, axis=1)
outer_radius = np.max(radii)
inner_radius = np.min(radii)

angles = np.linspace(0, 2np.pi, 2num_points, endpoint=False)

star_points = []
for i, angle in enumerate(angles):
r = outer_radius if i % 2 == 0 else inner_radius
x = centroid[0] + r * np.cos(angle)
y = centroid[1] + r * np.sin(angle)
star_points.append([x, y])

star_points.append(star_points[0])

return np.array(star_points)
def regularize_straight_line(XY):
"""Regularizes the points to form a perfect straight line."""
return np.array([XY[0], XY[-1]])

def detect_and_regularize_shape(XY):
"""Detects the shape and returns the regularized points."""
if is_straight_line(XY):
return "Straight Line", regularize_straight_line(XY)

shape = detect_shape(XY)
if shape == "Circle":
regularized_XY = regularize_circle(XY)
elif shape == "Ellipse":
regularized_XY = regularize_ellipse(XY)
elif shape == "Rectangle":
regularized_XY = regularize_rectangle(XY)
elif shape == "Square":
regularized_XY = regularize_square(XY)
elif shape == "Star":
regularized_XY = regularize_star(XY)
else:
regularized_XY = XY
return shape, regularized_XY
def calculate_symmetry_lines(XY, shape_type):
"""Calculates symmetry lines for the given shape."""
if shape_type in ["Circle", "Ellipse", "Square", "Rectangle"]:
centroid = np.mean(XY, axis=0)
if shape_type == "Circle" or shape_type == "Square":
return [
([centroid[0], np.min(XY[:, 1])], [centroid[0], np.max(XY[:, 1])]), # Vertical
([np.min(XY[:, 0]), centroid[1]], [np.max(XY[:, 0]), centroid[1]]) # Horizontal
]
elif shape_type == "Ellipse" or shape_type == "Rectangle":
return [
([np.min(XY[:, 0]), centroid[1]], [np.max(XY[:, 0]), centroid[1]]) # Horizontal
]
elif shape_type == "Star":
centroid = np.mean(XY, axis=0)
angles = np.linspace(0, 2*np.pi, 5, endpoint=False)
lines = []
for angle in angles:
x = centroid[0] + np.cos(angle) * 1000
y = centroid[1] + np.sin(angle) * 1000
lines.append(([centroid[0], centroid[1]], [x, y]))
return lines
return []

def plot_shapes(path_XYs, regularized_XYs):
"""Plots original and regularized shapes with symmetry lines, and prints information about detected shapes."""
fig, ax = plt.subplots(1, 2, tight_layout=True, figsize=(16, 8))
colors = ['r', 'g', 'b', 'c', 'm', 'y', 'k']

for a in ax:
a.set_aspect('equal')

Print shapes detected and regularized in bold
print("\033[1mShapes Detected and Regularized:\033[0m")

for i, (orig_XYs, reg_XYs) in enumerate(zip(path_XYs, regularized_XYs)):
color = colors[i % len(colors)]
for XY, reg_XY in zip(orig_XYs, reg_XYs):
shape_type, _ = detect_and_regularize_shape(XY)


# Print the name of the detected shape
print(f"- {shape_type}")

ax[0].plot(XY[:, 0], XY[:, 1], c=color, linewidth=2)
ax[1].plot(reg_XY[:, 0], reg_XY[:, 1], c=color, linewidth=2)

# Draw symmetry lines and count them
draw_symmetry_lines(ax[1], shape_type, reg_XY, 'k')
ax[0].set_title('Original Shapes')
ax[1].set_title('Regularized Shapes with Symmetry Lines')

plt.show()
def draw_symmetry_lines(ax, shape, reg_XY, color):
def plot_line(ax, start, end, color):
ax.plot([start[0], end[0]], [start[1], end[1]], color=color, linestyle='--', linewidth=1)

if shape == "Ellipse":
x_min, y_min = np.min(reg_XY, axis=0)
x_max, y_max = np.max(reg_XY, axis=0)
center_x, center_y = (x_min + x_max) / 2, (y_min + y_max) / 2
plot_line(ax, [x_min, center_y], [x_max, center_y], color)
plot_line(ax, [center_x, y_min], [center_x, y_max], color)

Print number of symmetry lines
print(f" - {shape} has 2 lines of symmetry.")
elif shape == "Rectangle":
x_min, y_min = np.min(reg_XY, axis=0)
x_max, y_max = np.max(reg_XY, axis=0)
plot_line(ax, [(x_min + x_max)/2, y_min], [(x_min + x_max)/2, y_max], color)
plot_line(ax, [x_min, (y_min + y_max)/2], [x_max, (y_min + y_max)/2], color)

Print number of symmetry lines
print(f" - {shape} has 2 lines of symmetry.")
elif shape == "Star":
num_points = len(reg_XY) // 2
for i in range(num_points):
start_point = reg_XY[i]
end_point = reg_XY[(i + num_points) % len(reg_XY)]
plot_line(ax, start_point, end_point, color)

Print number of symmetry lines
print(f" - {shape} has {num_points} lines of symmetry.")
else:
print(f" - No specific symmetry lines defined for {shape}.")
def polylines2csv(paths_XYs, csv_path):
"""Writes the regularized shapes to a CSV file."""
with open(csv_path, 'w', newline='') as f:
writer = csv.writer(f)
for path_XYs in paths_XYs:
for i, XY in enumerate(path_XYs):
for point in XY:
writer.writerow([i] + point.tolist())

def main():
input_csv = "problems/isolated.csv"
output_csv = "regularized_shapes.csv"
path_XYs = read_csv(input_csv)
regularized_XYs = []

for path in path_XYs:
reg_XYs = []
for XY in path:
_, reg_XY = detect_and_regularize_shape(XY)
reg_XYs.append(reg_XY)
regularized_XYs.append(reg_XYs)

plot_shapes(path_XYs, regularized_XYs)
polylines2csv(regularized_XYs, output_csv)
if name == "main":
main()
but like in this dataset int he followinf, multiple segements form a shape too but this script only regularises as per segements alone
so how can i regulare the shapes formed by multiple segements
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what to do?
give complete script