如何使用Shapely沿由(x,y)点集组成的中心线绘制正方形/矩形？

First off, Shapely excels at geometric computations but doesn’t handle rendering on its own—so we’ll pair it with Matplotlib to visualize the final result. Here’s a step-by-step solution tailored to your needs:

Step 1: Import Required Libraries #

Start by importing the tools we’ll need for geometry and plotting:

from shapely.geometry import LineString, Polygon
import matplotlib.pyplot as plt

Step 2: Define Your Line Coordinates #

Convert your list of (x,y) points into a Shapely LineString to represent the original black line:

# Replace this with your actual coordinate list
coordinate_list = [(0, 0), (2, 1), (3, 3), (5, 4), (6, 2)]
original_line = LineString(coordinate_list)

Step 3: Generate Squares Along the Line #

We’ll cover two common scenarios you might want:

Scenario 1: Squares Using Each Line Segment as a Side #

This creates squares where every segment of your line acts as one side of the square, oriented perpendicular to the segment’s direction:

def create_square_from_segment(segment):
    # Extract the two endpoints of the segment
    point_a = segment.coords[0]
    point_b = segment.coords[1]
    
    # Calculate the vector of the segment
    dx = point_b[0] - point_a[0]
    dy = point_b[1] - point_a[1]
    
    # Compute the other two vertices (rotated 90° counterclockwise)
    point_c = (point_b[0] - dy, point_b[1] + dx)
    point_d = (point_a[0] - dy, point_a[1] + dx)
    
    # Return the square as a Shapely Polygon
    return Polygon([point_a, point_b, point_c, point_d])

# Split the original line into individual segments
line_segments = [LineString([coordinate_list[i], coordinate_list[i+1]]) 
                 for i in range(len(coordinate_list)-1)]

# Generate squares for each segment
segment_squares = [create_square_from_segment(seg) for seg in line_segments]

Scenario 2: Fixed-Size Squares Centered Along Each Segment #

If you want squares of consistent size (regardless of segment length), use this approach. Squares will be centered on each segment and aligned with its direction:

def create_fixed_size_square(segment, side_length):
    point_a = segment.coords[0]
    point_b = segment.coords[1]
    
    dx = point_b[0] - point_a[0]
    dy = point_b[1] - point_a[1]
    segment_length = segment.length
    
    # Unit vectors along and perpendicular to the segment
    unit_along = (dx / segment_length, dy / segment_length)
    unit_perpendicular = (-dy / segment_length, dx / segment_length)  # CCW direction
    
    # Midpoint of the segment
    mid_x = (point_a[0] + point_b[0]) / 2
    mid_y = (point_a[1] + point_b[1]) / 2
    
    half_side = side_length / 2
    
    # Calculate all four corners of the square
    corner1 = (mid_x + half_side*unit_along[0] + half_side*unit_perpendicular[0],
               mid_y + half_side*unit_along[1] + half_side*unit_perpendicular[1])
    corner2 = (mid_x + half_side*unit_along[0] - half_side*unit_perpendicular[0],
               mid_y + half_side*unit_along[1] - half_side*unit_perpendicular[1])
    corner3 = (mid_x - half_side*unit_along[0] - half_side*unit_perpendicular[0],
               mid_y - half_side*unit_along[1] - half_side*unit_perpendicular[1])
    corner4 = (mid_x - half_side*unit_along[0] + half_side*unit_perpendicular[0],
               mid_y - half_side*unit_along[1] + half_side*unit_perpendicular[1])
    
    return Polygon([corner1, corner2, corner3, corner4])

# Generate fixed-size squares (adjust side_length as needed)
fixed_size_squares = [create_fixed_size_square(seg, side_length=1) for seg in line_segments]

Step 4: Visualize the Result #

Use Matplotlib to draw the original black line and red squares:

# Plot the original line
x_line, y_line = original_line.xy
plt.plot(x_line, y_line, color='black', linewidth=2, label='Original Line')

# Plot squares (use segment_squares or fixed_size_squares based on your choice)
for square in fixed_size_squares:
    x_sq, y_sq = square.exterior.xy
    plt.fill(x_sq, y_sq, color='red', alpha=0.5, label='Red Squares' if fixed_size_squares.index(square)==0 else "")

plt.legend()
plt.axis('equal')  # Ensures squares don't look stretched
plt.show()

Quick Tips: #

• To rotate squares clockwise instead of counterclockwise, swap the perpendicular vector to (dy / segment_length, -dx / segment_length).
• Adjust the alpha value in plt.fill() to make squares more or less transparent.
• Shapely’s Polygon class ensures your squares are valid geometric shapes, which you can use for further calculations if needed.

内容的提问来源于stack exchange，提问作者Kush