以下是一个示例代码,用于标记沿着剖面线的曲率拐点:
import numpy as np
import matplotlib.pyplot as plt
def calculate_curvature(points):
# 计算曲率
x = points[:, 0]
y = points[:, 1]
dx_dt = np.gradient(x)
dy_dt = np.gradient(y)
d2x_dt2 = np.gradient(dx_dt)
d2y_dt2 = np.gradient(dy_dt)
curvature = np.abs(d2x_dt2 * dy_dt - dx_dt * d2y_dt2) / (dx_dt**2 + dy_dt**2)**1.5
return curvature
def find_inflection_points(points, threshold):
# 找到拐点
curvature = calculate_curvature(points)
inflection_points = []
for i in range(1, len(points)-1):
if curvature[i] > threshold and curvature[i-1] < curvature[i] and curvature[i+1] < curvature[i]:
inflection_points.append(points[i])
return np.array(inflection_points)
# 生成示例剖面线上的点
x = np.linspace(0, 10, 100)
y = np.sin(x)
points = np.column_stack((x, y))
# 标记拐点
threshold = 0.1
inflection_points = find_inflection_points(points, threshold)
# 绘制剖面线和标记的拐点
plt.plot(x, y)
plt.scatter(inflection_points[:, 0], inflection_points[:, 1], color='red')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
在上述代码中,首先定义了一个calculate_curvature
函数,用于计算给定点集的曲率。然后,定义了一个find_inflection_points
函数,用于找到曲率大于给定阈值且满足拐点条件的点。最后,生成示例剖面线上的点,并调用find_inflection_points
函数找到拐点,并将拐点标记为红色。最终,绘制出剖面线和标记的拐点。
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