LA 4127 - The Sky is the Limit (离散化 扫描线 几何模板)

题目链接

非原创 原创地址：http://blog.csdn.net/jingqi814/article/details/26117241

题意：输入n座山的信息（山的横坐标，高度，山底宽度），计算他们的轮廓线，

即露出来的表面边长，有些山是重叠的不计。空白地带不计，每座山都是等腰三角形。

分析：大白书P414页。

求小山的总长度，用一些虚线将其离散化，分成一段一段的，特征点：山脚，山顶，交点。这样就能保

证相邻两个扫描点之间再无交点。然后一最上面的点就是分割点，维护上一个点lastp即可。

 #include<iostream>
 #include<cmath>
 #include<cstdio>
 #include<algorithm>
 #include<vector>
 const double eps=1e-;
 using namespace std;

 struct Point{    //定义点
     double x;
     double y;
     Point(double x=,double y=):x(x),y(y){}   //构造函数
     //void operator<<(Point &A) {cout<<A.x<<' '<<A.y<<endl;}
 };

 int dcmp(double x)  {return (x>eps)-(x<-eps); }   //判断精度

 typedef  Point  Vector;    //自定义别名

 Vector  operator +(Vector A,Vector B) { return Vector(A.x+B.x,A.y+B.y);} //向量+向量=向量，点+向量=点

 Vector  operator -(Vector A,Vector B) { return Vector(A.x-B.x,A.y-B.y); }  //点-点=向量

 Vector  operator *(Vector A,double p) { return Vector(A.x*p,A.y*p);  }   //向量*数=向量

 Vector  operator /(Vector A,double p) {return Vector(A.x/p,A.y/p);}    //向量/数=向量

 ostream &operator<<(ostream & out,Point & P) { out<<P.x<<' '<<P.y<<endl; return out;}  //输出点的 符号重载

 bool  operator< (const Point &A,const Point &B) { return A.x<B.x||(A.x==B.x&&A.y<B.y); }  //小于号 重载

 bool  operator== ( const Point &A,const Point &B) { return dcmp(A.x-B.x)==&&dcmp(A.y-B.y)==;}  //等于号 重载

 double  Dot(Vector A,Vector B) {return A.x*B.x+A.y*B.y;}  //点积

 double  Cross(Vector A,Vector B)  {return A.x*B.y-B.x*A.y; } //叉积

 double  Length(Vector A)  { return sqrt(Dot(A, A));}  //向量长度

 double  Angle(Vector A,Vector B) {return acos(Dot(A,B)/Length(A)/Length(B));}  //向量夹角

 double  Area2(Point A,Point B,Point C ) {return Cross(B-A, C-A);}  //三角形面积

 Vector Rotate(Vector A,double rad) { return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));} //向量旋转，rad为逆时针旋转的弧度
 Vector Normal(Vector A) {double L=Length(A);return Vector(-A.y/L,A.x/L);}  //计算向量的单位法线，需确保A不是零向量。

 Point GetLineIntersection(Point P,Vector v,Point Q,Vector w)  //两直线的交点。需确保直线 P+tv 和 Q+tw有唯一交点，cross(v,w)需非0。
 {                                                             //t是参数，v，w分别为两直线的向量。
     Vector u=P-Q;
     double t=Cross(w, u)/Cross(v,w);
     return P+v*t;
 }

 double DistanceToLine(Point P,Point A,Point B)  //点到直线的距离，p到ab的距离
 {
     Vector v1=P-A; Vector v2=B-A;
     return fabs(Cross(v1,v2))/Length(v2);
 }

 double DistanceToSegment(Point P,Point A,Point B)  //点到线段的距离，p到ab
 {
     if(A==B)  return Length(P-A);
     Vector v1=B-A;
     Vector v2=P-A;
     Vector v3=P-B;

     if(dcmp(Dot(v1,v2))==-)    return  Length(v2);
     else if(Dot(v1,v3)>)    return Length(v3);
     else return DistanceToLine(P, A, B);

 }

 Point GetLineProjection(Point P,Point A,Point B)  //点在直线的投影，p到ab
 {
     Vector v=B-A;
     Vector v1=P-A;
     double t=Dot(v,v1)/Dot(v,v);
     return  A+v*t;
 }

 bool  SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2)  //判断线段相交，交点不在端点上（如果交点在端点上可以借助下面的OnSegment来判断）
 {
     double c1=Cross(b1-a1, a2-a1);
     double c2=Cross(b2-a1, a2-a1);
     double c3=Cross(a1-b1, b2-b1);
     double c4=Cross(a2-b1, b2-b1);
     return dcmp(c1)*dcmp(c2)<&&dcmp(c3)*dcmp(c4)< ;
 }

 bool  OnSegment(Point P,Point A,Point B)  //判断一个点是否在一条线段上
 {
     return dcmp(Cross(P-A, P-B))==&&dcmp(Dot(P-A,P-B))<;
 }

 double PolygonArea(Point *p,int n)  //多边形的有向面积
 {
     double area=;

     for(int i=;i<n-;i++)
     {
         area+=Cross(p[i]-p[], p[i+]-p[]);
     }
     return area/;

 }

 Point  read_point()   //输入点
 {
     Point P;
     scanf("%lf%lf",&P.x,&P.y);
     return  P;
 }

 int n;
 Point L[][][];
 double x[];   //  存放离散化的x坐标

 int main()
 {
     double X,H,B;
     int cas=;
     while(cin>>n && n)
     {
         int c=;
         for(int i=;i<n;i++)
         {
             scanf("%lf%lf%lf",&X,&H,&B);
             L[i][][]=Point(X-B*0.5,);
             L[i][][]=L[i][][]=Point(X,H);
             L[i][][]=Point(X+B*0.5,);

             x[c++]=X-B*0.5;
             x[c++]=X;
             x[c++]=X+B*0.5;
         }
             for(int i=;i<n;i++)
                 for(int a=;a<;a++)
                     for(int j=i+;j<n;j++)
                         for(int b=;b<;b++)
                         {
                             Point A=L[i][a][];
                             Point B=L[i][a][];
                             Point C=L[j][b][];
                             Point D=L[j][b][];

                             if(SegmentProperIntersection(A, B, C, D))
                             {
                                 x[c++]=GetLineIntersection(A, B-A, C, D-C).x;
                             }
                         }

         sort(x,x+c);
         c=unique(x, x+c)-x; //unique()函数去重函数，在头文件algorithm中
         double ans=;
         Point lastp=Point(x[],);

         for(int i=;i<c;i++)
         {
             Point P=Point(x[i],);
             Vector v=Vector(,);
             double maxy=-;
             Point inter;

             for(int j=;j<n;j++)
                 for(int a=;a<;a++)
                 {
                     Point A=L[j][a][];
                     Point B=L[j][a][];
                     if(dcmp(A.x-x[i])<=&&dcmp(B.x-x[i])>=)
                     {
                         inter=GetLineIntersection(A, B-A, P, v);
                         maxy=max(maxy,inter.y);
                     }
                 }
             if(i>&&(dcmp(maxy)>||dcmp(lastp.y)>))   ans+=Length(Point(x[i],maxy)-lastp);
             lastp=Point(x[i],maxy);
         }
         printf("Case %d: %.0f\n\n",++cas,ans);
     }
 }