投影外的二维插值

import numpy as np

# 已知数据点
x = [1, 2, 3, 4]
y = [5, 9, 3, 7]
z = [6, 2, 8, 4]

# 要插值的点
x_interp = 5
y_interp = 2

# 线性外推
x_min = min(x)
x_max = max(x)
y_min = min(y)
y_max = max(y)

if x_interp < x_min or x_interp > x_max or y_interp < y_min or y_interp > y_max:
    # 超出数据范围，进行外推
    x_nearest = min(x, key=lambda xi: abs(xi - x_interp))
    y_nearest = min(y, key=lambda yi: abs(yi - y_interp))

    index_nearest = x.index(x_nearest)
    x_next = x[index_nearest + 1]
    y_next = y[index_nearest + 1]

    # 计算斜率
    slope = (z[index_nearest + 1] - z[index_nearest]) / (x_next - x_nearest)

    # 使用斜率进行外推
    z_interp = z[index_nearest] + slope * (x_interp - x_nearest)
else:
    # 在数据范围内，进行插值
    z_interp = np.interp(x_interp, x, z)

print(f"插值结果：{z_interp}")