図形情報を扱うのに大事なことは、全部高校で教わった ref: https://qiita.com/yuba/items/2f35d1e5e162f44fc1b3

file0.c

typedef struct{
    double x;
    double y;
} vector2D;

vector2D nearest(vector2D A, vector2D B, vector2D P) {
    vector2D a, b;
    double r;

    a.x = B.x - A.x;
    a.y = B.y - A.y;
    b.x = P.x - A.x;
    b.y = P.y - A.y;

    // 内積 ÷ |a|^2
    r = (a.x * b.x + a.y * b.y) / (a.x * a.x + a.y * a.y);

    if(r <= 0){
        return A;
    }else if(r >= 1){
        return B;
    }else{
        vector2D result;
        result.x = A.x + r * a.x;
        result.y = A.y + r * a.y;
        return result;
    }
}