空间点绕直线旋转 c++

在 C++ 中，可以使用数学库来实现空间点绕直线旋转。以下是一个示例代码：

#include <iostream>
#include <cmath>

struct Point3D {
    double x;
    double y;
    double z;
};

// 计算点围绕直线旋转后的新坐标
Point3D rotatePoint(const Point3D& point, const Point3D& axisPoint, const Point3D& axisDirection, double angle) {
    // 计算旋转矩阵
    double cosTheta = cos(angle);
    double sinTheta = sin(angle);

    // 平移点使得旋转轴过原点
    Point3D translatedPoint;
    translatedPoint.x = point.x - axisPoint.x;
    translatedPoint.y = point.y - axisPoint.y;
    translatedPoint.z = point.z - axisPoint.z;

    // 进行旋转变换
    Point3D rotatedPoint;
    rotatedPoint.x = (cosTheta + (1 - cosTheta) * axisDirection.x * axisDirection.x) * translatedPoint.x +
                     ((1 - cosTheta) * axisDirection.x * axisDirection.y - sinTheta * axisDirection.z) * translatedPoint.y +
                     ((1 - cosTheta) * axisDirection.x * axisDirection.z + sinTheta * axisDirection.y) * translatedPoint.z;

    rotatedPoint.y = ((1 - cosTheta) * axisDirection.x * axisDirection.y + sinTheta * axisDirection.z) * translatedPoint.x +
                     (cosTheta + (1 - cosTheta) * axisDirection.y * axisDirection.y) * translatedPoint.y +
                     ((1 - cosTheta) * axisDirection.y * axisDirection.z - sinTheta * axisDirection.x) * translatedPoint.z;

    rotatedPoint.z = ((1 - cosTheta) * axisDirection.x * axisDirection.z - sinTheta * axisDirection.y) * translatedPoint.x +
                     ((1 - cosTheta) * axisDirection.y * axisDirection.z + sinTheta * axisDirection.x) * translatedPoint.y +
                     (cosTheta + (1 - cosTheta) * axisDirection.z * axisDirection.z) * translatedPoint.z;

    // 平移点回到原来的位置
    rotatedPoint.x += axisPoint.x;
    rotatedPoint.y += axisPoint.y;
    rotatedPoint.z += axisPoint.z;

    return rotatedPoint;
}

int main() {
    Point3D point {1.0, 2.0, 3.0}; // 待旋转的点
    Point3D axisPoint {0.0, 0.0, 0.0}; // 直线上的一点
    Point3D axisDirection {1.0, 0.0, 0.0}; // 直线的方向向量
    double angle = M_PI / 2; // 旋转角度，这里以弧度表示（90度）

    Point3D rotatedPoint = rotatePoint(point, axisPoint, axisDirection, angle);

    std::cout << "Rotated Point: (" << rotatedPoint.x << ", " << rotatedPoint.y << ", " << rotatedPoint.z << ")" << std::endl;

    return 0;
}

上述代码中，`Point3D` 结构体表示一个三维点，`rotatePoint` 函数接受待旋转的点、直线上的一点、直线的方向向量和旋转角度作为参数，返回旋转后的点坐标。在 `main` 函数中，我们定义了一个待旋转的点、直线上的一点、直线的方向向量和旋转角度，然后调用 `rotatePoint` 函数进行计算，并打印出旋转后的点坐标。

请注意，上述示例代码仅演示了基本的空间点绕直线旋转的原理，实际应用中可能需要根据具体需求进行适当的修改和优化。