POJ 3449 Geometric Shapes --计算几何，线段相交

【input】

Z line (1933,2413) (2607,388)
A square (2434,925) (2065,1534)
R polygon 5 (1251,2398) (-1319,-569) (1964,-1947) (1705,2845) (-994,-551)
V line (2689,2103) (-1350,457)
P line (-121,-709) (-937,1486)
S rectangle (377,-24) (441,-258) (1845,-642)
B triangle (-1820,1247) (566,964) (1564,1972)
T line (-670,2470) (-395,1531)
L triangle (-1466,969) (-239,1757) (2848,2404)
M rectangle (-242,202) (63,-413) (3753,-2243)
N line (-1507,42) (-1804,1740)
O square (304,-715) (534,1418)
C line (-1977,499) (1868,83)
Q square (-1804,-210) (-315,2600)
-
D line (-1336,-714) (-1702,308)
K line (2153,1486) (-138,893)
H square (-450,-1268) (-1739,2968)
C rectangle (-157,-301) (337,278) (-1400,-1204)
M line (1374,1711) (-1074,2984)
W rectangle (149,221) (-361,-191) (463,829)
T square (651,-980) (707,1451)
Z rectangle (35,-140) (429,-265) (679,-1053)
E line (2167,2402) (-1630,-807)
A rectangle (-243,-493) (-419,191) (-2471,719)
F rectangle (136,-109) (429,-59) (329,-645)
G line (1912,1384) (560,2522)
I triangle (803,-1493) (1250,428) (-1355,1769)
Q line (-686,1911) (2760,1923)
N line (967,-1234) (-77,2731)
-
Q polygon 7 (19,407) (-146,774) (74,1867) (2970,2297) (165,-1021) (-1567,-1801) (-1099,443)
A rectangle (-243,-183) (-312,-2) (-674,136)
K triangle (-695,1986) (905,-1405) (-211,-1490)
J square (530,1487) (118,-1696)
X square (-374,-790) (2502,1957)
S line (2859,-1561) (2557,2955)
E rectangle (-5,-305) (-147,-251) (-363,317)
O triangle (-625,-1042) (1377,-115) (37,1641)
F rectangle (259,-429) (289,-404) (139,-584)
-
W square (996,-1997) (2218,2787)
X polygon 3 (787,1020) (-969,-1508) (2270,2500)
T square (-1125,-187) (-1414,2113)
K square (2880,-1273) (2986,304)
E rectangle (205,368) (236,212) (1016,57)
Y square (-1996,-1348) (-1545,1840)
V polygon 10 (-543,1468) (1328,2443) (2619,806) (2353,1091) (2447,570) (2837,-1825) (-1857,-1586) (-331,625) (-1113,-1502) (197,574)
Z polygon 8 (-156,1249) (-133,1674) (-1392,1042) (2105,-957) (2912,1975) (1195,2697) (1082,-64) (1081,681)
B polygon 11 (2391,-1682) (2569,1841) (2316,804) (1625,92) (823,1035) (612,1308) (-1664,2716) (-1363,-460) (1971,-1782) (-1194,35) (-699,573)
A rectangle (-371,-235) (9,363) (-3579,-1917)
U rectangle (307,-40) (-159,-500) (2141,1830)
H triangle (-780,2320) (1012,-1816) (1980,1349)
C square (-759,1872) (2836,1399)
D rectangle (472,83) (78,-46) (723,1924)
F square (-384,229) (736,-577)
G rectangle (-77,317) (426,-100) (1260,-1106)
Q triangle (-778,579) (-1534,474) (196,-293)
S square (-1893,-690) (2521,431)
R line (1885,-1907) (2891,-1798)
I square (2291,2484) (2162,-1280)
J line (2999,1660) (721,1597)
L triangle (-824,-757) (769,1373) (950,-180)
M rectangle (-370,-221) (341,-125) (53,-2258)
-
Q polygon 12 (-242,643) (447,350) (-1396,1043) (-1264,126) (-473,-963) (2475,-1568) (1870,-1091) (1190,50) (669,2183) (1776,1305) (833,2334) (-676,1920)
X line (-383,836) (592,155)
K square (2799,-129) (1052,-245)
Y polygon 4 (2145,-823) (2708,2578) (-1952,-1383) (2120,98)
Z polygon 13 (2098,-1112) (2036,-1014) (1174,-1851) (640,-1658) (739,-725) (-700,-1844) (-629,-1083) (596,1095) (-94,-207) (94,-1100) (1594,1569) (1604,-528) (2158,149)
C polygon 9 (144,2825) (-1637,857) (502,292) (-463,-1422) (1411,-1399) (2525,-304) (2444,2672) (1494,2284) (1832,2775)
F polygon 7 (2935,828) (1354,2770) (-1218,94) (2482,1107) (841,855) (-17,908) (1532,1742)
A square (835,-944) (1100,2163)
U polygon 11 (1460,964) (1461,2840) (328,1658) (-70,876) (295,1377) (1366,2643) (-274,123) (-492,789) (833,2817) (-1407,395) (-1889,-733)
G rectangle (214,146) (-195,62) (225,2107)
D polygon 9 (754,-1107) (-1781,48) (569,1700) (1268,2019) (1862,724) (2589,-1323) (1157,1865) (1282,-178) (422,254)
-
P polygon 11 (-728,2666) (1962,2817) (1123,291) (235,1939) (1372,-477) (-1133,-689) (-1054,-1382) (-521,-1179) (522,-1582) (-1935,-1361) (318,845)
O triangle (2168,1629) (1926,1507) (1645,2840)
G rectangle (358,132) (-414,-167) (184,1377)
M square (-353,-803) (-509,2311)
K line (-1210,965) (-1016,-792)
E triangle (2878,1579) (2969,-1407) (748,2950)
X square (1596,-1289) (1278,2865)
-
E square (-98,-814) (-1374,527)
X polygon 5 (598,-184) (-1979,-302) (-234,-1108) (2306,-1638) (-397,1936)
O rectangle (-302,384) (-73,236) (667,-909)
M square (685,-1324) (-878,-347)
I polygon 12 (1328,150) (492,-1801) (1774,-101) (2613,1777) (545,1108) (-765,1653) (25,2299) (-1428,2967) (-1014,272) (-1412,28) (2149,1361) (-345,-1171)
C square (-699,-1701) (-1564,415)
D line (2565,-666) (-1685,1340)
N polygon 12 (2824,1092) (1730,392) (1820,1654) (853,1092) (-957,1834) (1520,-1461) (-600,-623) (-97,-960) (-1933,-1920) (-1841,2538) (2656,1754) (2737,1410)
P line (1752,-1990) (-1944,-1653)
Y triangle (2792,-1185) (1624,2964) (-1179,-523)
-
U polygon 11 (2042,1312) (480,913) (2225,633) (646,-843) (357,-278) (-988,1486) (-1622,-1297) (-1890,2941) (-1055,2398) (2353,2712) (-360,1116)
O square (-1014,323) (293,-1208)
B triangle (529,-411) (-1412,-1990) (2503,2813)
H line (322,-648) (-1776,1334)
E rectangle (-110,-199) (395,-165) (259,-2185)
Q rectangle (-161,-135) (-231,-411) (321,-271)
P rectangle (-5,-360) (-491,-476) (-143,982)
-
O square (2411,-1619) (-562,1085)
I square (-580,924) (1616,-190)
X polygon 4 (2110,-857) (-1269,1251) (-1848,-1245) (-315,-898)
U square (-135,1875) (412,2950)
Z triangle (-630,-762) (2043,2532) (-185,259)
Y rectangle (223,-223) (264,-244) (348,-408)
-
G triangle (2020,-1129) (156,2172) (978,-1807)
C square (2815,1491) (-1652,228)
O rectangle (155,-336) (47,-450) (275,-234)
J rectangle (-70,-341) (-116,208) (-1214,300)
K polygon 11 (-1731,557) (1333,-1555) (1420,-157) (77,-539) (98,932) (2645,998) (2884,2095) (2491,-958) (1492,-1027) (1294,-1742) (-1399,-556)
H square (-1742,-1851) (1394,780)
Z triangle (775,1442) (-521,460) (1887,-749)
D rectangle (212,-98) (-252,209) (-559,673)
R rectangle (-256,27) (148,69) (-104,-2355)
W triangle (1617,2635) (542,1875) (2785,-1064)
A triangle (2858,-1217) (2104,-663) (1243,991)
U square (-1692,-348) (-1698,-92)
L square (41,2517) (2946,-1079)
T square (1094,2127) (37,-288)
X rectangle (87,-248) (368,95) (-661,-748)
M triangle (2666,2416) (1974,2009) (1356,873)
B line (1175,578) (1074,2230)
F rectangle (28,392) (313,-104) (2297,-1244)
I polygon 6 (-1403,-1004) (-548,-1972) (-10,-651) (2168,-1142) (1268,2669) (902,2117)
N triangle (2586,116) (329,1299) (2801,1527)
Y square (511,1750) (-1539,-1789)
P polygon 8 (887,1982) (-1247,2002) (-1879,-1626) (2562,-145) (-346,-131) (2295,194) (-377,460) (2244,2935)
Q square (1719,975) (1858,-1099)
E square (2468,-1370) (2817,1254)
S square (1221,2873) (-1496,-1673)
V triangle (-1299,2790) (1833,1707) (1012,1128)
-
.



【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

#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=0, double y=0):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 -1;
    if(x > eps) return 1;
    return 0;
}
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) == 0 && dcmp(a.y-b.y) == 0; }
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)) <= 0 &&
           dcmp(Cross(A-C,D-C)*Cross(B-C,D-C)) <= 0;
}
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[23];
    vector<char> inter;
}poly[33];
int cmp(node ka,node kb) { return ka.id < kb.id; }

int main()
{
    char ss[4],shape[20];
    int tot = 0,i,j,e,k;
    while(scanf("%s",ss)!=EOF)
    {
        if(ss[0] == ‘.‘) break;
        if(ss[0] != ‘-‘) {
            poly[++tot].id = ss[0];
            scanf("%s",shape);
            if(shape[0] == ‘t‘) {                 //triangle
                poly[tot].cnt = 3;
                Point P[3];
                for(i=0;i<3;i++) scanf(" (%lf,%lf)",&P[i].x,&P[i].y);
                for(i=0;i<3;i++) poly[tot].line[i] = Line(P[i],P[(i+1)%3]-P[i]);
            }
            else if(shape[0] == ‘s‘) {            //square
                poly[tot].cnt = 4;
                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[0] = Line(A,B-A), poly[tot].line[1] = Line(B,C-B);
                poly[tot].line[2] = Line(C,D-C), poly[tot].line[3] = Line(D,A-D);
            }
            else if(shape[0] == ‘r‘) {             //rectangle
                poly[tot].cnt = 4;
                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[0] = Line(A,B-A), poly[tot].line[1] = Line(B,C-B);
                poly[tot].line[2] = Line(C,D-C), poly[tot].line[3] = Line(D,A-D);
            }
            else if(shape[0] == ‘l‘) {             //line
                poly[tot].cnt = 1;
                Point A,B;
                scanf(" (%lf,%lf)",&A.x,&A.y);
                scanf(" (%lf,%lf)",&B.x,&B.y);
                poly[tot].line[0] = Line(A,B-A);
            }
            else if(shape[0] == ‘p‘) {             //polygon
                scanf("%d",&poly[tot].cnt);
                Point P[22];
                for(i=0;i<poly[tot].cnt;i++) {
                    scanf(" (%lf,%lf)",&P[i].x,&P[i].y);
                    if(i >= 1) poly[tot].line[i-1] = Line(P[i-1],P[i]-P[i-1]);
                }
                poly[tot].line[i-1] = Line(P[i-1],P[0]-P[i-1]);
            }
        }
        else                                    //processing...
        {
            for(i=1;i<=tot;i++)                 //处理第i个多边形
            {
                poly[i].inter.clear();
                for(e=0;e<poly[i].cnt;e++)      //枚举每条边
                {
                    for(j=1;j<=tot;j++)         //枚举别的多边形
                    {
                        if(i == j) continue;
                        for(k=0;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+1,poly+tot+1,cmp);
            for(i=1;i<=tot;i++) {
                printf("%c",poly[i].id);
                int sz = poly[i].inter.size();
                if(sz == 0)
                    puts(" has no intersections");
                else {
                    printf(" intersects with ");
                    if(sz == 1)
                        printf("%c\n",poly[i].inter[0]);
                    else if(sz == 2)
                        printf("%c and %c\n",poly[i].inter[0],poly[i].inter[1]);
                    else {
                        for(j=0;j<sz-1;j++) printf("%c, ",poly[i].inter[j]);
                        printf("and %c\n",poly[i].inter[j]);
                    }
                }
            }
            puts("");
            tot = 0;
        }
    }
    return 0;
}