C# 求坐标点绕Z轴旋转α角度后的坐标方法

在C#中，你可以使用三维向量数学来计算一个坐标点绕Z轴旋转的角度。假设我们有一个Point3D结构体表示三维坐标点，其包含X、Y和Z三个元素。绕Z轴旋转的数学公式可以使用 Rodrigues' rotation formula 实现。这里是一个简单的示例：

using System;

public struct Point3D
{
    public double X;
    public double Y;
    public double Z;
}

public static class RotationHelper
{
    // 计算绕Z轴旋转的辅助函数
    private static Point3D CrossProduct(Point3D a, Point3D b)
    {
        return new Point3D(a.Y * b.Z - a.Z * b.Y,
                          a.Z * b.X - a.X * b.Z,
                          a.X * b.Y - a.Y * b.X);
    }

    public static Point3D RotateAroundZAxis(Point3D point, double angleInRadians)
    {
        double cosa = Math.Cos(angleInRadians);
        double sina = Math.Sin(angleInRadians);

        Point3D rotatedX = new Point3D(point.Y * sina, -point.X * sina, 0);
        Point3D rotatedY = new Point3D(cosa * point.Y + sina * point.Z, cosa * (-point.X) + sina * point.W, -cosa * point.Z + sina * point.Y);

        return new Point3D(point.X + rotatedX.X, point.Y + rotatedY.Y, point.Z + rotatedY.Z);
    }
}

要使用这个方法，你可以创建一个`Point3D`实例，然后传入想要旋转的角度（单位为弧度）：

Point3D originalPoint = new Point3D(1, 2, 3);
double rotationAngleInDegrees = 45; // 转换为弧度
rotationAngleInRadians = Math.PI / 180 * rotationAngleInDegrees;

Point3D rotatedPoint = RotationHelper.RotateAroundZAxis(originalPoint, rotationAngleInRadians);