ACOS两个向量之间的C ++角度

Question

I'm trying to get this code to work and it gives out angles but not the right ones though, they don't add up to 180° and I can't find the problem. I've implemented a Vector2 struct which resembles a two-dimensional Vector and I have been trying to define the ^ operator for it as the function to give the angles between the two vectors.

Thanks for the help in advance!

#include <iostream>
#include <cstdlib>
#include <cmath>

using namespace std;

struct Vector2 {
    double x, y;
};

ostream& operator<<(ostream& out, const Vector2& w){
    cout  << '[' << w.x << " , " << w.y << ']';
    return out;
}

double operator*(const Vector2& a, const Vector2& b){
    double w = a.x*b.x + a.y*b.y;
    return w;
}

double absc(const Vector2& d) {
    return sqrt(d*d);  
}

constexpr Vector2 operator+(const Vector2& a, const Vector2& b){
    Vector2 y{a.x+b.x, a.y+a.y};
    return y;
}

constexpr Vector2 operator-(const Vector2& a,const Vector2& b){
    Vector2 z{a.x-b.x, a.y-b.y};
    return z;
}

double operator^(const Vector2& a,const Vector2& b){
    double n = (absc(a))*(absc(b));
    double c = acos((a*b)/n);
    return c;
}

int main(){
    Vector2 a = {1.0, 1.0};
    Vector2 b = {4.0, 7.0};
    Vector2 c = {-2.0, 5.0};
    double d =c^b;
    double e = a^c;
    double f = a^b;
    auto grad = [](double rad) { return rad * (45./atan(1.0)); };

    cout<<"Angle Alpha: "<<grad(c^b)<<"rad "<<d<<"\n";
    cout<<"Angle Beta: "<<grad(a^c)<<"rad "<<e<<"\n";
    cout<<"Angle Gamma: "<<grad(a^b)<<"rad "<<f<<"\n";

    return EXIT_SUCCESS;
}

Answer 1

You are not comparing the right angles, try this instead (create the vectors from the points you have):

double d = (a-c)^(a-b);
double e = (b-a)^(b-c);
double f = (c-b)^(c-a);
auto grad = [](double rad) { return rad * (45./atan(1.0)); };

cout<<"Angle Alpha: "<<grad((a-c)^(a-b))<<"rad "<<d;
cout<<"\nAngle Beta: "<<grad((b-a)^(b-c))<<"rad "<<e;
cout<<"\nAngle Gamma: "<<grad((c-a)^(c-b))<<"rad "<<f;

And now you have 180° or pi.