计算几何初步模板

点结构

struct Point {
    double x;
    double y;
    Point(double a = 0, double b = 0) : x(a), y(b) {}
};

 

1、浮点数过滤

int dbcmp(double x) {
    if(x > eps)    return 1;
    else if(x < -eps)    return -1;
    return 0;
}

2、线段求交点（简化一下可以用来判线段相交（规范相交））

 

double det(double x1, double y1, double x2, double y2) {    //求叉积
    return x1*y2 - x2*y1;
}

double cross(Point a, Point b, Point c) {    //向量ab，和向量ac
    return det(b.x - a.x, b.y - a.y, c.x - a.x, c.y - a.y);
}

double dotdet(double x1, double y1, double x2, double y2) {    //点积
    return x1*x2 + y1*y2;
}

double dot(Point a, Point b, Point c) {
    return dotdet(b.x - a.x, b.y - a.y, c.x - a.x, c.y - a.y);
}

int betweenCmp(Point a, Point b, Point c) {    //判断a是不是在bc范围内
    return dbcmp(dot(a, b, c));
}

bool segcross(Point a, Point b, Point c, Point d) {
    double s1, s2;
    int d1, d2, d3, d4;
    d1 = dbcmp(s1 = cross(a, b, c));
    d2 = dbcmp(s2 = cross(a, b, d));
    d3 = dbcmp(cross(c, d, a));
    d4 = dbcmp(cross(c, d, b));
    if((d1^d2) == -2 && (d3^d4) == -2) {    //规范相交
        return true;
    }
    //非规范相交
    if((d1 == 0 && betweenCmp(c, a, b) <= 0) ||
       (d2 == 0 && betweenCmp(d, a, b) <= 0) ||
       (d3 == 0 && betweenCmp(a, c, d) <= 0) ||
       (d4 == 0 && betweenCmp(b, c, d) <= 0))
        return true;
    return false;
}

 

 

  

3、叉积求多边形面积

double area(Point p[],int n) { //这里是相对于原点(0, 0)，也可以在多边形上找一个点作为向量的起点
    double s = 0;
    int i;
    p[n].x = p[0].x;
    p[n].y = p[0].y;
    for(i = 0; i < n; ++i)
        s += det(p[i].x, p[i].y, p[i+1].x, p[i+1].y);
    return fabs(s / 2.0);
}

4、Graham-Scan法求凸包（黑书上的优化算法）

void graham(int dir) {
    int i; t = 0;
    for(i = 0; i < n; ++i) {
        if(vis[i])    continue;
        while(t > 1 && dir*cross(p[st[t-1]], p[st[t]], p[i]) < 0)    --t;
        st[++t] = i;
    }
    for(i = 2; i < t; ++i)    vis[st[i]] = true;
}

//main

for(i = 0; i < n; ++i) {
    scanf("%lf%lf", &p[i].x, &p[i].y);
}
sort(p, p + n, cmp);    //按y排序，如果相等，再按x排序
memset(vis, 0, sizeof(vis));
graham(1);
for(i = 1; i <= t; ++i)    f[i] = st[i]; m = t;
graham(-1);
for(i = 1; i < t; ++i)    f[m + i] = st[t - i]; m += t-1;

 

ps：暂时就这些，以后还会补充。