The angle between two vectors space requirements

Three-dimensional space vector cross product:

 

 

Vector dot product:

 

 Thus binding (0) and (1) can be obtained: 

　　　　　　　　　　　　　　　　　　i = al t al n 2 ( s i n ( i ) , c o s ( i ) ) = al t al n 2 ( ( A × Breakfast ) * n , A * Breakfast ) = al t al n 2 ( ( A × Breakfast ) . n o r m ( ) ,A∗B)      { 0<θ<180 }

 

#include <iostream>
#include <Eigen/Dense>

typedef Eigen::Vector3d Point;

double getDegAngle(Point p1, Point p2, Point p3) {
    Eigen::Vector3d v1 = p2 - p1;
    Eigen::Vector3d v2 = p3 - p1;
    //one method, radian_angle belong to 0~pi
    //double radian_angle = atan2(v1.cross(v2).transpose() * (v1.cross(v2) / v1.cross(v2).norm()), v1.transpose() * v2);
    //another method, radian_angle belong to 0~pi
    double radian_angle = atan2(v1.cross(v2).norm(), v1.transpose() * v2);
    if (v1.cross(v2).z() < 0) {
        radian_angle = 2 * M_PI - radian_angle;
    }
    return radian_angle * 180 / M_PI;
}

int main() {
    //Point p1(0, 0, 0), p2(1, 0, 0), p3(0, -1, 0);
    //Point p1(0, 0, 0), p2(1, 0, 0), p3(0, 1, 0);
    //Point p1(0, 0, 0), p2(1, 0, 0), p3(0.5, 0.5, 0);
    Point p1(0, 0, 0), p2(1, 0, 0), p3(0.5, -0.5, 0);
    std::cout << "The Degree Angle is: " << getDegAngle(p1, p2, p3) << "\n";
    return 0;
}