segments robust intersection code

segment_intersection.cpp

#include <stdio.h>

struct Point2f {
    float x, y;
    Point2f(float _x, float _y): x(_x), y(_y) {}
    Point2f(): x(0), y(0) {}
};

Point2f operator -(Point2f p1, Point2f p2) {
    return Point2f(p1.x - p2.x, p1.y - p2.y); 
}
Point2f operator *(float alpha, Point2f p2) {
    return Point2f(alpha*p2.x, alpha*p2.y); 
}
Point2f operator +(Point2f p1, Point2f p2) {
    return Point2f(p1.x + p2.x, p1.y + p2.y); 
}

bool intersection(Point2f start1, Point2f end1, Point2f start2, Point2f end2, Point2f *out_intersection)
{
    Point2f dir1 = end1 - start1;
    Point2f dir2 = end2 - start2;

    //считаем уравнения прямых проходящих через отрезки
    float a1 = -dir1.y;
    float b1 = +dir1.x;
    float d1 = -(a1*start1.x + b1*start1.y);

    float a2 = -dir2.y;
    float b2 = +dir2.x;
    float d2 = -(a2*start2.x + b2*start2.y);

    //подставляем концы отрезков, для выяснения в каких полуплоскотях они
    float seg1_line2_start = a2*start1.x + b2*start1.y + d2;
    float seg1_line2_end = a2*end1.x + b2*end1.y + d2;

    float seg2_line1_start = a1*start2.x + b1*start2.y + d1;
    float seg2_line1_end = a1*end2.x + b1*end2.y + d1;
    

    //если концы одного отрезка имеют один знак, значит он в одной полуплоскости и пересечения нет.
    if (seg1_line2_start * seg1_line2_end >= 0 || seg2_line1_start * seg2_line1_end >= 0) 
        return false;

    float u = seg1_line2_start / (seg1_line2_start - seg1_line2_end);
    *out_intersection =  start1 + u*dir1;

    return true;
}

int main() {
    Point2f A1(0, 0);
    Point2f A2(15, 12.146760941);
    
    Point2f B1(5.4513401985, -4.4144082069);
    Point2f B2(7771.4594727, 6293.2041016);
    
    Point2f result;
    
    if (intersection(A1, A2, B1, B2, &result)) {
        printf("%g %g\n", result.x, result.y);
    }
}