判断多边形是否相交只需把多边形拆成一条条的线段，然后看线段是否相交即可
其中需要注意的是正方形顶点的求法，最好不使用三角函数去求。看我代码中的方法。
然后就比较好搞了
#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <map>
#include <sstream>
#include <queue>
#include <vector>
#define MAXN 100005
#define MAXM 211111
#define eps 1e-8
#define INF 50000001
using namespace std;
inline int dblcmp(double d)
{if(fabs(d) < eps) return 0;return d > eps ? 1 : -1;
}
struct point
{double x, y;point(){}point(double _x, double _y): x(_x), y(_y) {}void input(){scanf("%lf%lf", &x, &y);}bool operator ==(point a)const{return dblcmp(a.x - x) == 0 && dblcmp(a.y - y) == 0;}point sub(point p){return point(x - p.x, y - p.y);}double dot(point p){return x * p.x + y * p.y;}double det(point p){return x * p.y - y * p.x;}double distance(point p){return hypot(x - p.x, y - p.y);}
}p[33];
struct line
{point a, b;line(){}line(point _a, point _b){ a = _a; b = _b;}void input(){a.input();b.input();}int segcrossseg(line v){int d1 = dblcmp(b.sub(a).det(v.a.sub(a)));int d2 = dblcmp(b.sub(a).det(v.b.sub(a)));int d3 = dblcmp(v.b.sub(v.a).det(a.sub(v.a)));int d4 = dblcmp(v.b.sub(v.a).det(b.sub(v.a)));if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2)return 2;return (d1 == 0 && dblcmp(v.a.sub(a).dot(v.a.sub(b))) <= 0||d2 == 0 && dblcmp(v.b.sub(a).dot(v.b.sub(b))) <= 0||d3 == 0 && dblcmp(a.sub(v.a).dot(a.sub(v.b))) <= 0||d4 == 0 && dblcmp(b.sub(v.a).dot(b.sub(v.b))) <= 0);}int linecrossseg(line v)//v is seg{int d1 = dblcmp(b.sub(a).det(v.a.sub(a)));int d2 = dblcmp(b.sub(a).det(v.b.sub(a)));if ((d1 ^ d2) == -2) return 2;return (d1 == 0 || d2 == 0);}point crosspoint(line v){double a1 = v.b.sub(v.a).det(a.sub(v.a));double a2 = v.b.sub(v.a).det(b.sub(v.a));return point((a.x * a2 - b.x * a1) / (a2 - a1), (a.y * a2 - b.y * a1) / (a2 - a1));}};
struct node
{string name;vector<line>seg;
};
char sa[55], sb[55];
vector<node>g;
vector<string>ans[55];
bool cmp(node x, node y)
{return x.name < y.name;
}
bool ok(int k1, int k2)
{int sz1 = g[k1].seg.size();int sz2 = g[k2].seg.size();for(int i = 0; i < sz1; i++)for(int j = 0; j < sz2; j++)if(g[k1].seg[i].segcrossseg(g[k2].seg[j])) return true;return false;
}
void solve()
{for(int i = 0; i < 50; i++) ans[i].clear();sort(g.begin(), g.end(), cmp);int sz = g.size();for(int i = 0; i < sz; i++){for(int j = 0; j < sz; j++){if(i == j) continue;if(ok(i, j)) ans[i].push_back(g[j].name);}}for(int i = 0; i < sz; i++){if(ans[i].size() == 0) printf("%s has no intersections\n", g[i].name.c_str());else{if(ans[i].size() == 1){printf("%s intersects with %s\n", g[i].name.c_str(), ans[i][0].c_str());}else if(ans[i].size() == 2){printf("%s intersects with %s and %s\n", g[i].name.c_str(), ans[i][0].c_str(), ans[i][1].c_str());}else{printf("%s intersects with ", g[i].name.c_str());for(int j = 0; j < ans[i].size() - 1; j++) printf("%s, ", ans[i][j].c_str());printf("and %s\n", ans[i][ans[i].size() - 1].c_str());}}}g.clear();printf("\n");
}
int main()
{double xa, ya, xb, yb;while(scanf("%s", sa) != EOF){if(strcmp(sa, "-") == 0){solve();continue;}if(strcmp(sa, ".") == 0) break;node tmp;tmp.name = sa;scanf("%s", sb);if(sb[0] == 's'){point a, c;scanf(" (%lf,%lf)", &a.x, &a.y);scanf(" (%lf,%lf)", &c.x, &c.y);point b, d;double x, y, mx, my;mx = (a.x + c.x)/2.0, my = (a.y + c.y) / 2.0;x = a.x - mx; y = a.y - my;b.x = -y + mx; b.y = x + my;x = c.x - mx; y = c.y - my;d.x = - y + mx; d.y = x + my;tmp.seg.push_back(line(a, b));tmp.seg.push_back(line(b, c));tmp.seg.push_back(line(a, d));tmp.seg.push_back(line(c, d));}else if(sb[0] == 'l'){point a, b;scanf(" (%lf,%lf)", &a.x, &a.y);scanf(" (%lf,%lf)", &b.x, &b.y);tmp.seg.push_back(line(a, b));}else if(sb[0] == 't'){point a, b, c;scanf(" (%lf,%lf)", &a.x, &a.y);scanf(" (%lf,%lf)", &b.x, &b.y);scanf(" (%lf,%lf)", &c.x, &c.y);tmp.seg.push_back(line(a, b));tmp.seg.push_back(line(a, c));tmp.seg.push_back(line(b, c));}else if(sb[0] == 'r'){point a, b, c, d;scanf(" (%lf,%lf)", &a.x, &a.y);scanf(" (%lf,%lf)", &b.x, &b.y);scanf(" (%lf,%lf)", &c.x, &c.y);double dx = b.x - a.x;d.x = c.x - dx;double dy = b.y - a.y;d.y = c.y - dy;tmp.seg.push_back(line(a, b));tmp.seg.push_back(line(b, c));tmp.seg.push_back(line(a, d));tmp.seg.push_back(line(c, d));}else{int t;scanf("%d", &t);for(int i = 0; i < t; i++) scanf(" (%lf,%lf)", &p[i].x, &p[i].y);for(int i = 0; i < t; i++) tmp.seg.push_back(line(p[i], p[(i + 1) % t]));}g.push_back(tmp);}return 0;
}