POJ 3449 Geometric Shapes --计算几何，线段相交

题意： 给一些多边形或线段，输出与每一个多边形或线段的有哪一些多边形或线段。

解法： 想法不难，直接暴力将所有的图形处理成线段，然后暴力枚举，相交就加入其vector就行了。主要是代码有点麻烦，一步一步来吧。

还有收集了一个线段旋转的函数。

给定正方形对角求其他两点用到了线段旋转。

Vector Rotate(Point P,Vector A,double rad){     //以P为基准点把向量A旋转rad
    return Vector(P.x+A.x*cos(rad)-A.y*sin(rad),P.y+A.x*sin(rad)+A.y*cos(rad));
}

从POJ Discuss上面搞了一点数据下来：

【input】

Z line (,) (,)
A square (,) (,)
R polygon  (,) (-,-) (,-) (,) (-,-)
V line (,) (-,)
P line (-,-) (-,)
S rectangle (,-) (,-) (,-)
B triangle (-,) (,) (,)
T line (-,) (-,)
L triangle (-,) (-,) (,)
M rectangle (-,) (,-) (,-)
N line (-,) (-,)
O square (,-) (,)
C line (-,) (,)
Q square (-,-) (-,)
-
D line (-,-) (-,)
K line (,) (-,)
H square (-,-) (-,)
C rectangle (-,-) (,) (-,-)
M line (,) (-,)
W rectangle (,) (-,-) (,)
T square (,-) (,)
Z rectangle (,-) (,-) (,-)
E line (,) (-,-)
A rectangle (-,-) (-,) (-,)
F rectangle (,-) (,-) (,-)
G line (,) (,)
I triangle (,-) (,) (-,)
Q line (-,) (,)
N line (,-) (-,)
-
Q polygon  (,) (-,) (,) (,) (,-) (-,-) (-,)
A rectangle (-,-) (-,-) (-,)
K triangle (-,) (,-) (-,-)
J square (,) (,-)
X square (-,-) (,)
S line (,-) (,)
E rectangle (-,-) (-,-) (-,)
O triangle (-,-) (,-) (,)
F rectangle (,-) (,-) (,-)
-
W square (,-) (,)
X polygon  (,) (-,-) (,)
T square (-,-) (-,)
K square (,-) (,)
E rectangle (,) (,) (,)
Y square (-,-) (-,)
V polygon  (-,) (,) (,) (,) (,) (,-) (-,-) (-,) (-,-) (,)
Z polygon  (-,) (-,) (-,) (,-) (,) (,) (,-) (,)
B polygon  (,-) (,) (,) (,) (,) (,) (-,) (-,-) (,-) (-,) (-,)
A rectangle (-,-) (,) (-,-)
U rectangle (,-) (-,-) (,)
H triangle (-,) (,-) (,)
C square (-,) (,)
D rectangle (,) (,-) (,)
F square (-,) (,-)
G rectangle (-,) (,-) (,-)
Q triangle (-,) (-,) (,-)
S square (-,-) (,)
R line (,-) (,-)
I square (,) (,-)
J line (,) (,)
L triangle (-,-) (,) (,-)
M rectangle (-,-) (,-) (,-)
-
Q polygon  (-,) (,) (-,) (-,) (-,-) (,-) (,-) (,) (,) (,) (,) (-,)
X line (-,) (,)
K square (,-) (,-)
Y polygon  (,-) (,) (-,-) (,)
Z polygon  (,-) (,-) (,-) (,-) (,-) (-,-) (-,-) (,) (-,-) (,-) (,) (,-) (,)
C polygon  (,) (-,) (,) (-,-) (,-) (,-) (,) (,) (,)
F polygon  (,) (,) (-,) (,) (,) (-,) (,)
A square (,-) (,)
U polygon  (,) (,) (,) (-,) (,) (,) (-,) (-,) (,) (-,) (-,-)
G rectangle (,) (-,) (,)
D polygon  (,-) (-,) (,) (,) (,) (,-) (,) (,-) (,)
-
P polygon  (-,) (,) (,) (,) (,-) (-,-) (-,-) (-,-) (,-) (-,-) (,)
O triangle (,) (,) (,)
G rectangle (,) (-,-) (,)
M square (-,-) (-,)
K line (-,) (-,-)
E triangle (,) (,-) (,)
X square (,-) (,)
-
E square (-,-) (-,)
X polygon  (,-) (-,-) (-,-) (,-) (-,)
O rectangle (-,) (-,) (,-)
M square (,-) (-,-)
I polygon  (,) (,-) (,-) (,) (,) (-,) (,) (-,) (-,) (-,) (,) (-,-)
C square (-,-) (-,)
D line (,-) (-,)
N polygon  (,) (,) (,) (,) (-,) (,-) (-,-) (-,-) (-,-) (-,) (,) (,)
P line (,-) (-,-)
Y triangle (,-) (,) (-,-)
-
U polygon  (,) (,) (,) (,-) (,-) (-,) (-,-) (-,) (-,) (,) (-,)
O square (-,) (,-)
B triangle (,-) (-,-) (,)
H line (,-) (-,)
E rectangle (-,-) (,-) (,-)
Q rectangle (-,-) (-,-) (,-)
P rectangle (-,-) (-,-) (-,)
-
O square (,-) (-,)
I square (-,) (,-)
X polygon  (,-) (-,) (-,-) (-,-)
U square (-,) (,)
Z triangle (-,-) (,) (-,)
Y rectangle (,-) (,-) (,-)
-
G triangle (,-) (,) (,-)
C square (,) (-,)
O rectangle (,-) (,-) (,-)
J rectangle (-,-) (-,) (-,)
K polygon  (-,) (,-) (,-) (,-) (,) (,) (,) (,-) (,-) (,-) (-,-)
H square (-,-) (,)
Z triangle (,) (-,) (,-)
D rectangle (,-) (-,) (-,)
R rectangle (-,) (,) (-,-)
W triangle (,) (,) (,-)
A triangle (,-) (,-) (,)
U square (-,-) (-,-)
L square (,) (,-)
T square (,) (,-)
X rectangle (,-) (,) (-,-)
M triangle (,) (,) (,)
B line (,) (,)
F rectangle (,) (,-) (,-)
I polygon  (-,-) (-,-) (-,-) (,-) (,) (,)
N triangle (,) (,) (,)
Y square (,) (-,-)
P polygon  (,) (-,) (-,-) (,-) (-,-) (,) (-,) (,)
Q square (,) (,-)
E square (,-) (,)
S square (,) (-,-)
V triangle (-,) (,) (,)
-
.

【output】
A intersects with Z
B intersects with L, N, O, P, Q, R, T, and V
C intersects with N, O, P, Q, and R
L intersects with B, P, Q, R, T, and Z
M intersects with O, R, and S
N intersects with B and C
O intersects with B, C, M, P, Q, R, S, and V
P intersects with B, C, L, O, Q, R, and V
Q intersects with B, C, L, O, P, R, and V
R intersects with B, C, L, M, O, P, Q, and V
S intersects with M and O
T intersects with B and L
V intersects with B, O, P, Q, R, and Z
Z intersects with A, L, and V

A intersects with C, D, E, T, and W
C intersects with A, H, I, and T
D intersects with A and E
E intersects with A, D, G, H, I, K, M, N, Q, and T
F intersects with H, I, T, and Z
G intersects with E, K, and Q
H intersects with C, E, F, I, K, N, Q, T, W, and Z
I intersects with C, E, F, H, K, N, T, W, and Z
K intersects with E, G, H, I, N, T, and W
M intersects with E, N, and Q
N intersects with E, H, I, K, M, Q, T, and W
Q intersects with E, G, H, M, and N
T intersects with A, C, E, F, H, I, K, N, W, and Z
W intersects with A, H, I, K, N, and T
Z intersects with F, H, I, and T

A intersects with K, O, and X
E intersects with O and X
F has no intersections
J intersects with K, O, Q, and X
K intersects with A, J, O, Q, and X
O intersects with A, E, J, K, Q, and X
Q intersects with J, K, O, S, and X
S intersects with Q
X intersects with A, E, J, K, O, and Q

A intersects with B, F, G, L, M, Q, S, V, W, Y, and Z
B intersects with A, C, D, F, G, H, I, J, K, L, M, Q, S, T, U, V, W, X, Y, and Z
C intersects with B, D, E, F, H, I, J, L, S, T, U, V, W, X, and Z
D intersects with B, C, E, F, G, H, I, J, L, S, U, W, X, and Z
E intersects with C, D, F, I, L, U, and X
F intersects with A, B, C, D, E, G, H, L, M, Q, U, V, W, X, Y, and Z
G intersects with A, B, D, F, H, L, M, U, V, X, and Z
H intersects with B, C, D, F, G, I, J, L, M, S, T, U, V, W, X, and Z
I intersects with B, C, D, E, H, J, K, L, S, U, V, W, X, and Z
J intersects with B, C, D, H, I, U, V, W, X, and Z
K intersects with B, I, V, W, and Z
L intersects with A, B, C, D, E, F, G, H, I, M, Q, U, V, W, X, Y, and Z
M intersects with A, B, F, G, H, L, Q, S, U, V, W, and X
Q intersects with A, B, F, L, M, S, T, U, V, W, X, and Y
R intersects with V
S intersects with A, B, C, D, H, I, M, Q, T, U, V, W, X, Y, and Z
T intersects with B, C, H, Q, S, V, W, Y, and Z
U intersects with B, C, D, E, F, G, H, I, J, L, M, Q, S, V, W, X, and Z
V intersects with A, B, C, F, G, H, I, J, K, L, M, Q, R, S, T, U, W, X, Y, and Z
W intersects with A, B, C, D, F, H, I, J, K, L, M, Q, S, T, U, V, X, Y, and Z
X intersects with B, C, D, E, F, G, H, I, J, L, M, Q, S, U, V, W, and Z
Y intersects with A, B, F, L, Q, S, T, V, W, and Z
Z intersects with A, B, C, D, F, G, H, I, J, K, L, S, T, U, V, W, X, and Y

A intersects with C, D, F, G, K, Q, U, Y, and Z
C intersects with A, D, F, G, K, Q, U, X, Y, and Z
D intersects with A, C, F, G, K, Q, U, X, Y, and Z
F intersects with A, C, D, G, Q, U, X, Y, and Z
G intersects with A, C, D, F, Q, U, X, Y, and Z
K intersects with A, C, D, Q, Y, and Z
Q intersects with A, C, D, F, G, K, U, X, Y, and Z
U intersects with A, C, D, F, G, Q, X, Y, and Z
X intersects with C, D, F, G, Q, U, Y, and Z
Y intersects with A, C, D, F, G, K, Q, U, X, and Z
Z intersects with A, C, D, F, G, K, Q, U, X, and Y

E intersects with O, P, and X
G intersects with M, P, and X
K intersects with M and P
M intersects with G, K, P, and X
O intersects with E, P, and X
P intersects with E, G, K, M, O, and X
X intersects with E, G, M, O, and P

C intersects with E, I, M, N, X, and Y
D intersects with I, N, X, and Y
E intersects with C, I, M, N, O, X, and Y
I intersects with C, D, E, M, N, O, X, and Y
M intersects with C, E, I, N, O, X, and Y
N intersects with C, D, E, I, M, P, X, and Y
O intersects with E, I, M, X, and Y
P intersects with N
X intersects with C, D, E, I, M, N, O, and Y
Y intersects with C, D, E, I, M, N, O, and X

B intersects with E, H, O, P, Q, and U
E intersects with B, H, O, P, Q, and U
H intersects with B, E, O, P, Q, and U
O intersects with B, E, H, P, Q, and U
P intersects with B, E, H, O, Q, and U
Q intersects with B, E, H, O, P, and U
U intersects with B, E, H, O, P, and Q

I intersects with O, X, and Z
O intersects with I, X, and Z
U has no intersections
X intersects with I, O, and Z
Y has no intersections
Z intersects with I, O, and X

A intersects with C, E, H, I, K, L, N, P, Q, S, T, and W
B intersects with H, K, N, P, T, V, W, and Z
C intersects with A, E, F, G, H, I, J, K, L, M, N, P, Q, R, S, V, W, X, Y, and Z
D intersects with I, J, K, L, P, R, T, X, and Z
E intersects with A, C, F, H, I, K, L, N, P, Q, S, T, W, and Z
F intersects with C, E, G, H, I, K, L, O, P, Q, S, T, X, Y, and Z
G intersects with C, F, H, I, K, L, N, P, Q, S, T, V, Y, and Z
H intersects with A, B, C, E, F, G, I, K, L, N, P, Q, R, S, T, U, W, Y, and Z
I intersects with A, C, D, E, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, Y, and Z
J intersects with C, D, I, K, L, P, R, T, and X
K intersects with A, B, C, D, E, F, G, H, I, J, L, M, N, O, P, Q, R, S, T, W, X, Y, and Z
L intersects with A, C, D, E, F, G, H, I, J, K, M, P, Q, R, S, T, V, W, X, Y, and Z
M intersects with C, I, K, L, N, S, T, V, and W
N intersects with A, B, C, E, G, H, I, K, M, P, Q, S, T, V, W, Y, and Z
O intersects with F, K, P, R, and T
P intersects with A, B, C, D, E, F, G, H, I, J, K, L, N, O, Q, R, S, T, U, V, W, X, Y, and Z
Q intersects with A, C, E, F, G, H, I, K, L, N, P, S, T, W, Y, and Z
R intersects with C, D, H, I, J, K, L, O, P, S, T, X, and Y
S intersects with A, C, E, F, G, H, I, K, L, M, N, P, Q, R, V, W, and Y
T intersects with A, B, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, V, W, X, Y, and Z
U intersects with H and P
V intersects with B, C, G, I, L, M, N, P, S, T, W, Y, and Z
W intersects with A, B, C, E, H, I, K, L, M, N, P, Q, S, T, and V
X intersects with C, D, F, J, K, L, P, R, T, and Z
Y intersects with C, F, G, H, I, K, L, N, P, Q, R, S, T, V, and Z
Z intersects with B, C, D, E, F, G, H, I, K, L, N, P, Q, T, V, X, and Y

---------------------------------------------------------------------

代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <vector>
#define pi acos(-1.0)
#define eps 1e-8
using namespace std;

struct Point{
    double x,y;
    Point(double x=, double y=):x(x),y(y) {}
    void input() { scanf("%lf%lf",&x,&y); }
};
typedef Point Vector;
struct Line{
    Point p;
    Vector v;
    double ang;
    Line(){}
    Line(Point p, Vector v):p(p),v(v) { ang = atan2(v.y,v.x); }
    Point point(double t) { return Point(p.x + t*v.x, p.y + t*v.y); }
    bool operator < (const Line &L)const { return ang < L.ang; }
};
int dcmp(double x) {
    if(x < -eps) return -;
    if(x > eps) return ;
    return ;
}
template <class T> T sqr(T x) { return x * x;}
Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }
Vector operator - (Vector A, Vector B) { return Vector(A.x - B.x, A.y - B.y); }
Vector operator * (Vector A, double p) { return Vector(A.x*p, A.y*p); }
Vector operator / (Vector A, double p) { return Vector(A.x/p, A.y/p); }
bool operator < (const Point& a, const Point& b) { return a.x < b.x || (a.x == b.x && a.y < b.y); }
bool operator >= (const Point& a, const Point& b) { return a.x >= b.x && a.y >= b.y; }
bool operator <= (const Point& a, const Point& b) { return a.x <= b.x && a.y <= b.y; }
bool operator == (const Point& a, const Point& b) { return dcmp(a.x-b.x) ==  && dcmp(a.y-b.y) == ; }
double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }
double Length(Vector A) { return sqrt(Dot(A, A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }
Vector VectorUnit(Vector x){ return x / Length(x);}
Vector Normal(Vector x) { return Point(-x.y, x.x) / Length(x);}
double angle(Vector v) { return atan2(v.y, v.x); }

bool SegmentIntersection(Point A,Point B,Point C,Point D) {
    return max(A.x,B.x) >= min(C.x,D.x) &&
           max(C.x,D.x) >= min(A.x,B.x) &&
           max(A.y,B.y) >= min(C.y,D.y) &&
           max(C.y,D.y) >= min(A.y,B.y) &&
           dcmp(Cross(C-A,B-A)*Cross(D-A,B-A)) <=  &&
           dcmp(Cross(A-C,D-C)*Cross(B-C,D-C)) <= ;
}
Vector Rotate(Point P,Vector A,double rad){     //以P为基准点把向量A旋转rad
    return Vector(P.x+A.x*cos(rad)-A.y*sin(rad),P.y+A.x*sin(rad)+A.y*cos(rad));
}

struct node {
    char id;
    int cnt;
    Line line[];
    vector<char> inter;
}poly[];
int cmp(node ka,node kb) { return ka.id < kb.id; }

int main()
{
    char ss[],shape[];
    int tot = ,i,j,e,k;
    while(scanf("%s",ss)!=EOF)
    {
        if(ss[] == '.') break;
        if(ss[] != '-') {
            poly[++tot].id = ss[];
            scanf("%s",shape);
            if(shape[] == 't') {                 //triangle
                poly[tot].cnt = ;
                Point P[];
                for(i=;i<;i++) scanf(" (%lf,%lf)",&P[i].x,&P[i].y);
                for(i=;i<;i++) poly[tot].line[i] = Line(P[i],P[(i+)%]-P[i]);
            }
            else if(shape[] == 's') {            //square
                poly[tot].cnt = ;
                Point A,B,C,D;
                scanf(" (%lf,%lf)",&A.x,&A.y);
                scanf(" (%lf,%lf)",&C.x,&C.y);
                B = Rotate(A,C-A,pi*0.25); B = A + (B-A)/sqrt(2.0);
                D = C + (A-B);
                poly[tot].line[] = Line(A,B-A), poly[tot].line[] = Line(B,C-B);
                poly[tot].line[] = Line(C,D-C), poly[tot].line[] = Line(D,A-D);
            }
            else if(shape[] == 'r') {             //rectangle
                poly[tot].cnt = ;
                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);
                D = A + (C-B);
                poly[tot].line[] = Line(A,B-A), poly[tot].line[] = Line(B,C-B);
                poly[tot].line[] = Line(C,D-C), poly[tot].line[] = Line(D,A-D);
            }
            else if(shape[] == 'l') {             //line
                poly[tot].cnt = ;
                Point A,B;
                scanf(" (%lf,%lf)",&A.x,&A.y);
                scanf(" (%lf,%lf)",&B.x,&B.y);
                poly[tot].line[] = Line(A,B-A);
            }
            else if(shape[] == 'p') {             //polygon
                scanf("%d",&poly[tot].cnt);
                Point P[];
                for(i=;i<poly[tot].cnt;i++) {
                    scanf(" (%lf,%lf)",&P[i].x,&P[i].y);
                    if(i >= ) poly[tot].line[i-] = Line(P[i-],P[i]-P[i-]);
                }
                poly[tot].line[i-] = Line(P[i-],P[]-P[i-]);
            }
        }
        else                                    //processing...
        {
            for(i=;i<=tot;i++)                 //处理第i个多边形
            {
                poly[i].inter.clear();
                for(e=;e<poly[i].cnt;e++)      //枚举每条边
                {
                    for(j=;j<=tot;j++)         //枚举别的多边形
                    {
                        if(i == j) continue;
                        for(k=;k<poly[j].cnt;k++)   //枚举别的多边形的每条边
                        {
                            Point A = poly[i].line[e].p, B = poly[i].line[e].p+poly[i].line[e].v;
                            Point C = poly[j].line[k].p, D = poly[j].line[k].p+poly[j].line[k].v;
                            if(SegmentIntersection(A,B,C,D))
                            {
                                poly[i].inter.push_back(poly[j].id);
                                break;
                            }
                        }
                    }
                }
                sort(poly[i].inter.begin(),poly[i].inter.end());
                poly[i].inter.erase(unique(poly[i].inter.begin(),poly[i].inter.end()),poly[i].inter.end());
            }
            sort(poly+,poly+tot+,cmp);
            for(i=;i<=tot;i++) {
                printf("%c",poly[i].id);
                int sz = poly[i].inter.size();
                if(sz == )
                    puts(" has no intersections");
                else {
                    printf(" intersects with ");
                    if(sz == )
                        printf("%c\n",poly[i].inter[]);
                    else if(sz == )
                        printf("%c and %c\n",poly[i].inter[],poly[i].inter[]);
                    else {
                        for(j=;j<sz-;j++) printf("%c, ",poly[i].inter[j]);
                        printf("and %c\n",poly[i].inter[j]);
                    }
                }
            }
            puts("");
            tot = ;
        }
    }
    return ;
}