HDU3060 Area2 简单多边形面积并

不需要正规的三角剖分，用求多边形面积的思想，从一点出发连接多边形的边得到很多三
角形，三角形有向边方向决定有向面积有正有负，相加得到多边形面积的正值或负值。
把两个多边形都分成若干这样的三角形，求每对三角形的交，根据两三角形有向边顺逆时
针关系确定相交面积的正负号，最后两多边形面积和减去相交面积。

  1 #include<stdio.h>

  2 #include<string.h>

  3 #include<stdlib.h>

  4 #include<math.h>

  5 #include<algorithm>

  6 const int maxn = 555;

  7 const int maxisn = 10;

  8 const double eps = 1e-8;

  9 const double pi = acos(-1.0);

 10 int dcmp(double x)

 11 {

 12     if(x > eps) return 1;

 13     return x < -eps ? -1 : 0;

 14 }

 15 inline double min(double a, double b)

 16 {return a < b ? a : b;}

 17 inline double max(double a, double b)

 18 {return a > b ? a : b;}

 19 inline double Sqr(double x)

 20 {return x * x;}

 21 struct Point

 22 {

 23     double x, y;

 24     Point(){x = y = 0;}

 25     Point(double a, double b)

 26     {x = a, y = b;}

 27     inline Point operator-(const Point &b)const

 28     {return Point(x - b.x, y - b.y);}

 29     inline Point operator+(const Point &b)const

 30     {return Point(x + b.x, y + b.y);}

 31     inline double dot(const Point &b)const

 32     {return x * b.x + y * b.y;}

 33     inline double cross(const Point &b, const Point &c)const

 34     {return (b.x - x) * (c.y - y) - (c.x - x) * (b.y - y);}

 35 };

 36 Point LineCross(const Point &a, const Point &b, const Point &c, const Point &d)

 37 {

 38     double u = a.cross(b, c), v = b.cross(a, d);

 39     return Point((c.x * v + d.x * u) / (u + v), (c.y * v + d.y * u) / (u + v));

 40 }

 41 double PolygonArea(Point p[], int n)

 42 {

 43     if(n < 3) return 0.0;

 44     double s = p[0].y * (p[n - 1].x - p[1].x);

 45     p[n] = p[0];

 46     for(int i = 1; i < n; ++ i)

 47         s += p[i].y * (p[i - 1].x - p[i + 1].x);

 48     return fabs(s * 0.5);

 49 }

 50 double CPIA(Point a[], Point b[], int na, int nb)//ConvexPolygonIntersectArea

 51 {

 52     Point p[maxisn], tmp[maxisn];

 53     int i, j, tn, sflag, eflag;

 54     a[na] = a[0], b[nb] = b[0];

 55     memcpy(p, b, sizeof(Point) * (nb + 1));

 56     for(i = 0; i < na && nb > 2; ++ i)

 57     {

 58         sflag = dcmp(a[i].cross(a[i + 1], p[0]));

 59         for(j = tn = 0; j < nb; ++ j, sflag = eflag)

 60         {

 61             if(sflag >= 0) tmp[tn ++] = p[j];

 62             eflag = dcmp(a[i].cross(a[i + 1], p[j + 1]));

 63             if((sflag ^ eflag) == -2)

 64                 tmp[tn ++] = LineCross(a[i], a[i + 1], p[j], p[j + 1]);

 65         }

 66         memcpy(p, tmp, sizeof(Point) * tn);

 67         nb = tn, p[nb] = p[0];

 68     }

 69     if(nb < 3) return 0.0;

 70     return PolygonArea(p, nb);

 71 }

 72 double SPIA(Point a[], Point b[], int na, int nb)//SimplePolygonIntersectArea

 73 {

 74     int i, j;

 75     Point t1[4], t2[4];

 76     double res = 0, if_clock_t1, if_clock_t2;

 77     a[na] = t1[0] = a[0], b[nb] = t2[0] = b[0];

 78     for(i = 2; i < na; ++ i)

 79     {

 80         t1[1] = a[i - 1], t1[2] = a[i];

 81         if_clock_t1 = dcmp(t1[0].cross(t1[1], t1[2]));

 82         if(if_clock_t1 < 0) std::swap(t1[1], t1[2]);

 83         for(j = 2; j < nb; ++ j)

 84         {

 85             t2[1] = b[j - 1], t2[2] = b[j];

 86             if_clock_t2 = dcmp(t2[0].cross(t2[1], t2[2]));

 87             if(if_clock_t2 < 0) std::swap(t2[1], t2[2]);

 88             res += CPIA(t1, t2, 3, 3) * if_clock_t1 * if_clock_t2;

 89         }

 90     }

 91     return PolygonArea(a, na) + PolygonArea(b, nb) - res;

 92 }

 93 Point p1[maxn], p2[maxn];

 94 int n1, n2;

 95 int main()

 96 {

 97     int i;

 98     while(scanf("%d%d", &n1, &n2) != EOF)

 99     {

100         for(i = 0; i < n1; ++ i) scanf("%lf%lf", &p1[i].x, &p1[i].y);

101         for(i = 0; i < n2; ++ i) scanf("%lf%lf", &p2[i].x, &p2[i].y);

102         printf("%.2f\n", SPIA(p1, p2, n1, n2) + eps);

103     }

104     return 0;

105 }