如何在Python中旋转矢量

import numpy as np

def rotate_2d_vector(vector, angle):
    """
    旋转二维矢量
    :param vector: 输入的二维矢量，例如 (x, y)
    :param angle: 旋转角度（弧度）
    :return: 旋转后的矢量
    """
    # 创建旋转矩阵
    rotation_matrix = np.array([
        [np.cos(angle), -np.sin(angle)],
        [np.sin(angle), np np.cos(angle)]
    ])
    
    # 将矢量转换为numpy数组
    vector = np.array(vector)
    
    # 应用旋转矩阵
    rotated_vector = np.dot(rotation_matrix, vector)
    
    return rotated_vector

# 示例使用
vector = (3, 4)
angle = np.radians(45)  # 将角度转换为弧度
rotated_vector = rotate_2d_vector(vector, angle)
print("旋转后的矢量:", rotated_vector)

import numpy as np

def rotate_3d_vector(vector, axis, angle):
    """
    旋转三维矢量
    :param vector: 输入的三维矢量，例如 (x, y, z)
    :param axis: 旋转轴，例如 (1, 0, 0) 表示绕x轴旋转
    :param angle: 旋转角度（弧度）
    :return: 旋转后的矢量
    """
    # 归一化旋转轴
    axis = np.array(axis)
    axis = axis / np.linalg.norm(axis)
    
    # 创建旋转矩阵
    a = np.cos(angle / 2.0)
    b, c, d = -axis * np.sin(angle / 2.0)
    aa, bb, cc, dd = a * a, b * b, c * c, d * d
    bc, ad, ac, ab, bd, cd = b * c, a * d, a * c, a * b, b * d, c * d
    
    rotation_matrix = np.array([
        [aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac)],
        [2 * (bc - ad), aa + cc - bb - dd, 2 * (cd + ab)],
        [2 * (bd + ac), 2 * (cd - ab), aa + dd - bb - cc]
    ])
    
    # 将矢量转换为numpy数组
    vector = np.array(vector)
    
    # 应用旋转矩阵
    rotated_vector = np.dot(rotation_matrix, vector)
    
    return rotated_vector

# 示例使用
vector = (1, 0, 0)
axis = (0, 1, 0)  # 绕y轴旋转
angle = np.radians(90)  # 将角度转换为弧度
rotated_vector = rotate_3d_vector(vector, axis, angle)
print("旋转后的矢量:", rotated_vector)