2D上での矩形衝突検知を大小比較のみで行ってみた(C++サンプル付き) ref: https://qiita.com/Najaran/items/779286014607f0f23e54

2D_rect_collision_judge.cpp

#include    <iostream>

using namespace std;

typedef struct _pos {
    double x;   // X-axis
    double y;   // Y-axis
}pos;

int main() {
    pos a1, a2, b1, b2;

    cout << "RectA: ";
    cin >> a1.x >> a1.y >> a2.x >> a2.y;

    cout << "RectB: ";
    cin >> b1.x >> b1.y >> b2.x >> b2.y;

    if(a2.x < b1.x || b2.x < a1.x || a2.y < b1.y || b2.y < a1.y)
        cout << "no collision" << endl;  // 衝突していないと判定
    else
        cout << "collision" << endl;     // 衝突していると判定

    return 0;
}

file0.txt

\left(x_{a2}<x_{b1}\right)\vee\left(x_{b2}<x_{a1}\right)\vee\left(y_{a2}<y_{b1}\right)\vee\left(y_{b2}<y_{a1}\right)

file1.txt

(5<0)\vee(6<1)\vee(5<1)\vee(4<0)=F \vee F \vee F \vee F=F

file2.txt

\begin{eqnarray}
x成分&:&(x_{a1} < x_{a2} < x_{b1} < x_{b2}) &\vee& (x_{b1} < x_{b2} < x_{a1} < x_{a2})\\
y成分&:&(y_{a1} < y_{a2} < y_{b1} < y_{b2}) &\vee& (y_{b1} < y_{b2} < y_{a1} < y_{a2})
\end{eqnarray}

file3.txt

\begin{eqnarray}
(x_{a1} < x_{a2} < x_{b1} < x_{b2}) &\vee& (x_{b1} < x_{b2} < x_{a1} < x_{a2})\\
\ \ &\vee&(y_{a1} < y_{a2} < y_{b1} < y_{b2})\\
\ \ &\vee&(y_{b1} < y_{b2} < y_{a1} < y_{a2})
\end{eqnarray}

file4.txt

(x_{a1} < x_{a2}),\ \ (x_{b1} < x_{b2}),\ \  (y_{a1} < y_{a2}),\ \ (y_{b1} < y_{b2})

file5.txt

\left(x_{a2}<x_{b1}\right)\vee\left(x_{b2}<x_{a1}\right)\vee\left(y_{a2}<y_{b1}\right)\vee\left(y_{b2}<y_{a1}\right)