HDU 4667 Building Fence 计算几何 凸包+圆

1.三角形的所有端点

2.过所有三角形的端点对所有圆做切线，得到所有切点。

3.做任意两圆的外公切线，得到所有切点。

对上述所有点求凸包，标记每个点是三角形上的点还是某个圆上的点。

求完凸包后，因为所有点都是按逆时针（或顺时针）排好序的，如果相邻两点在同一圆上，那么求这段圆弧的距离，否则求这段直线的距离。最后得到所有周长。

 

#include <cstdio>

#include <cstdlib>

#include <cstring>

#include <cmath>

#include <algorithm>



using namespace std;



const double eps = 1e-9;

const double PI = acos(-1.0);

const int MAXN = 60;



struct Point

{

    double x, y;

    int id;         //点标号，标记是否在同一个圆上

    Point() { }

    Point( double x, double y ):x(x), y(y) { }

    Point( double x, double y, int id ):x(x), y(y), id(id) { }

    void readPoint()

    {

        scanf( "%lf%lf", &x, &y );

        return;

    }

};



struct Circle

{

    Point c;   //圆心坐标

    double r;  //半径

    Circle() {}

    Circle( Point c, double r ): c(c), r(r) {}

    Point getPoint( double theta )   //根据极角返回圆上一点的坐标

    {

        return Point( c.x + cos(theta)*r, c.y + sin(theta)*r );

    }

    void readCircle()

    {

        scanf("%lf%lf%lf", &c.x, &c.y, &r );

        return;

    }

};



typedef Point Vector;



Vector operator+( Vector A, Vector B )       //向量加

{

    return Vector( A.x + B.x, A.y + B.y );

}



Vector operator-( Vector A, Vector B )       //向量减

{

    return Vector( A.x - B.x, A.y - B.y );

}



Vector operator*( Vector A, double p )      //向量数乘

{

    return Vector( A.x * p, A.y * p );

}



Vector operator/( Vector A, double p )      //向量数除

{

    return Vector( A.x / p, A.y / p );

}



int dcmp( double x )    //控制精度

{

    if ( fabs(x) < eps ) return 0;

    else return x < 0 ? -1 : 1;

}



bool operator<( const Point& A, const Point& B )   //两点比较

{

    return dcmp( A.x - B.x) < 0 || ( dcmp(A.x - B.x ) == 0 && dcmp( A.y - B.y ) < 0 );

}



bool operator>( const Point& A, const Point& B )   //两点比较

{

    return dcmp( A.x - B.x) > 0 || ( dcmp(A.x - B.x ) == 0 && dcmp( A.y - B.y ) > 0 );

}



bool operator==( const Point& a, const Point& b )   //两点相等

{

    return dcmp( a.x - b.x ) == 0 && dcmp( a.y - b.y ) == 0;

}



double Cross( Vector A, Vector B )   //向量叉积

{

    return A.x * B.y - A.y * B.x;

}



double PointDis( Point a, Point b ) //两点距离的平方

{

    return (a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y);

}



//求凸包，graham算法，O(nlogn)，返回凸包点的个数

int graham( Point *p, int n, Point *ch )

{

    if ( n <= 2 ) return 0;

    int top = 0;

    sort( p, p + n );



    ch[ top ] = p[0];

    ch[ ++top ] = p[1];

    ch[ ++top ] = p[2];



    top = 1;



    for ( int i = 2; i < n; ++i )

    {

        while ( top && dcmp( Cross( ch[top] - ch[top - 1], p[i] - ch[top - 1] ) ) <= 0 ) --top;

        ch[++top] = p[i];

    }

    int len = top;

    ch[++top] = p[n - 2];

    for ( int i = n - 3; i >= 0; --i )

    {

        while ( top > len && dcmp( Cross( ch[top] - ch[top - 1], p[i] - ch[top - 1] ) ) <= 0 ) --top;

        ch[++top] = p[i];

    }

    return top;

}



//过定点做圆的切线,得到切点，返回切点个数

//tps保存切点坐标

int getTangentPoints( Point p, Circle C, Point *tps )

{

    int cnt = 0;



    double dis = sqrt( PointDis( p, C.c ) );

    int aa = dcmp( dis - C.r );

    if ( aa < 0 ) return 0;  //点在圆内

    else if ( aa == 0 ) //点在圆上，该点就是切点

    {

        tps[cnt] = p;

        ++cnt;

        return cnt;

    }



    //点在圆外，有两个切点

    double base = atan2( p.y - C.c.y, p.x - C.c.x );

    double ang = acos( C.r / dis );

    //printf( "base = %f ang=%f\n", base, ang );

    //printf( "base-ang=%f  base+ang=%f \n", base - ang, base + ang );



    tps[cnt] = C.getPoint( base - ang ), ++cnt;

    tps[cnt] = C.getPoint( base + ang ), ++cnt;



    return cnt;

}



//求两圆外公切线切点，返回切线个数

//p是圆c2在圆c1上的切点

int makeCircle( Circle c1, Circle c2, Point *p )

{

    int cnt = 0;

    double d = sqrt( PointDis(c1.c, c2.c) ), dr = c1.r - c2.r;

    double b = acos(dr / d);

    double a = atan2( c2.c.y - c1.c.y, c2.c.x - c1.c.x );

    double a1 = a - b, a2 = a + b;

    p[cnt++] = Point(cos(a1) * c1.r, sin(a1) * c1.r) + c1.c;

    p[cnt++] = Point(cos(a2) * c1.r, sin(a2) * c1.r) + c1.c;

    return cnt;

}



double DisOnCircle( Point a, Point b, Circle c )  //求圆上一段弧长

{

    Point o = c.c;

    double A = sqrt( PointDis( o, a ) );

    double B = sqrt( PointDis( o, b ) );

    double C = sqrt( PointDis( a, b ) );

    double alpha = acos( ( A*A + B*B - C*C ) / ( 2.0*A*B ) );

    if ( dcmp( Cross( o-a, o-b ) ) < 0 ) return alpha * c.r;

    else return ( 2.0*PI - alpha ) * c.r;

}



/**********************以上模板**********************/



int cntC, cntT;  //圆的个数，三角形的个数

Circle yuan[MAXN];   //所有圆

Point PP[300100];    //所有点

Point tubao[300100]; //凸包

int totPP;           //点总数



void showP( Point *p, int nn )

{

    printf( "allP = %d\n", nn );

    for ( int i = 0; i < nn; ++i )

        printf("%f %f\n", p[i].x, p[i].y );

    puts("-------------------------");

    return;

}



int main()

{

    //freopen( "10022.in", "r", stdin );

    //freopen( "s.out", "w", stdout );

    while ( scanf( "%d%d", &cntC, &cntT ) == 2 )

    {

        totPP = 0;

        for ( int i = 0; i < cntC; ++i )

            yuan[i].readCircle();

        for ( int i = 0; i < cntT; ++i )

        {

            for ( int j = 0; j < 3; ++j )

            {

                PP[totPP].readPoint();

                PP[totPP].id = -(totPP+2);

                ++totPP;

            }

        }



        if ( cntC == 1 && cntT == 0 )

        {

            printf("%.6f\n", 2.0 * PI * yuan[0].r );

            continue;

        }



        int pretot = totPP;

        //求两圆的外切点

        for ( int i = 0; i < cntC; ++i )

            for ( int j = i + 1; j < cntC; ++j )

            {

                Point PonA[4], PonB[4];

                makeCircle( yuan[i], yuan[j], PonA );

                int ans = makeCircle( yuan[j], yuan[i], PonB );

                for ( int k = 0; k < ans; ++k )

                {

                    PonA[k].id = i;

                    PonB[k].id = j;

                    PP[totPP++] = PonA[k];

                    PP[totPP++] = PonB[k];

                }

            }



        //求所有点与所有圆的切点

        for ( int i = 0; i < pretot; ++i )

        {

            for ( int j = 0; j < cntC; ++j )

            {

                Point qiedian[4];

                int ans = getTangentPoints( PP[i], yuan[j], qiedian );

                for ( int k = 0; k < ans; ++k )

                {

                    qiedian[k].id = j;

                    PP[totPP++] = qiedian[k];

                }

            }

        }



        //showP( PP, totPP );

        int cntBao = graham( PP, totPP, tubao );

        //puts("*********");

        //showP( tubao, cntBao );

        double girth = 0.0;

        tubao[cntBao] = tubao[0];



        for ( int i = 1; i <= cntBao; ++i )

        {

            if ( tubao[i].id == tubao[i - 1].id )  //如果两点在同一个圆上

                girth += DisOnCircle( tubao[i], tubao[i - 1], yuan[ tubao[i].id ] );

            else

                girth += sqrt( PointDis( tubao[i], tubao[i - 1] ) );



        }



        printf( "%.5lf\n", girth );

    }

    return 0;

}