trilinear的python代码

以下是一个使用 NumPy 实现 trilinear 插值的 Python 代码示例：

import numpy as np

def trilinear_interp(xyz, uvw, data):
    """
    Trilinear interpolation of a 3D volume.

    xyz: 3D point to be interpolated, in (x, y, z) format
    uvw: normalized coordinates within the volume, in (u, v, w) format
    data: 3D volume data
    """
    # Get the integer coordinates of the 8 corner points
    i, j, k = np.floor(xyz).astype(int)
    
    # Get the fractional distances between the point and the corners
    di, dj, dk = xyz - np.floor(xyz)
    
    # Calculate the weights for each corner point
    w000 = (1 - di) * (1 - dj) * (1 - dk)
    w001 = (1 - di) * (1 - dj) * dk
    w010 = (1 - di) * dj * (1 - dk)
    w011 = (1 - di) * dj * dk
    w100 = di * (1 - dj) * (1 - dk)
    w101 = di * (1 - dj) * dk
    w110 = di * dj * (1 - dk)
    w111 = di * dj * dk
    
    # Interpolate along the x-axis at y = j, z = k
    c00 = w000 * data[i, j, k] + w100 * data[i+1, j, k]
    c01 = w001 * data[i, j, k+1] + w101 * data[i+1, j, k+1]
    c10 = w010 * data[i, j+1, k] + w110 * data[i+1, j+1, k]
    c11 = w011 * data[i, j+1, k+1] + w111 * data[i+1, j+1, k+1]
    c0 = (1 - dw) * c00 + dw * c01
    c1 = (1 - dw) * c10 + dw * c11
    
    # Interpolate along the y-axis at z = k
    c = (1 - dv) * c0 + dv * c1
    
    # Interpolate along the z-axis
    result = (1 - du) * c + du * data[i, j, k+1]
    
    return result

其中，`xyz` 是要进行插值的点的坐标，`uvw` 是该点在数据体中的归一化坐标，`data` 是一个三维的数据体。函数返回在该点处的插值结果。该函数假定数据体是规则的（即等间距采样），并且输入的归一化坐标是在数据体范围内的。