BZOJ1209 [HNOI2004]最佳包裹 三维凸包 计算几何

欢迎访问~原文出处——博客园-zhouzhendong

去博客园看该题解

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题目传送门 - BZOJ1209

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题目概括

　　给出立体的n个点。求三维凸包面积。

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题解

　　增量法，看了一天，还是没有完全懂。

　　上板子！

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代码

#include <cstring>
#include <cstdio>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <ctime>
using namespace std;
const double Eps=1e-8;
const int N=100+5;
int Dcmp(double x){
	if (fabs(x)<Eps)
		return 0;
	return x<0?-1:1;
}
struct Point{
	double x,y,z;
	Point (){}
	Point (double x_,double y_,double z_){
		x=x_,y=y_,z=z_;
	}
}P[N],p[N];
Point operator - (Point a,Point b){
	return Point(a.x-b.x,a.y-b.y,a.z-b.z);
}
Point operator + (Point a,Point b){
	return Point(a.x+b.x,a.y+b.y,a.z+b.z);
}
Point operator * (Point a,double x){
	return Point(a.x*x,a.y*x,a.z*x);
}
Point operator / (Point a,double x){
	return Point(a.x/x,a.y/x,a.z/x);
}
Point cross(Point a,Point b){
	return Point(a.y*b.z-a.z*b.y,a.z*b.x-a.x*b.z,a.x*b.y-a.y*b.x);
}
Point cross(Point a,Point b,Point c){
	return cross(b-a,c-a);
}
double Dot(Point a,Point b){
	return a.x*b.x+a.y*b.y+a.z*b.z;
}
double Length(Point P){
	return sqrt(Dot(P,P));
}
double rand01(){
	return (double)rand()/(double)RAND_MAX;
}
double randEps(){
	return (rand01()-0.5)*Eps;
}
Point add_noise(Point P){
	return Point(P.x+randEps(),P.y+randEps(),P.z+randEps());
}
struct Face{
	int v[3];
	Face(){}
	Face(int a,int b,int c){
		v[0]=a,v[1]=b,v[2]=c;
	}
	Point Normal(Point *P){
		return cross(P[v[0]],P[v[1]],P[v[2]]);
	}
	int CanSee(Point *P,int i){
		return Dot(P[i]-P[v[0]],Normal(P))>0?1:0;
	}
};
struct ConvexHull{
	vector <Face> cur;
	bool vis[N][N];
	void Increment(Point *P,int n){
		vector <Face> next;
		memset(vis,0,sizeof vis);
		for (int i=1;i<=n;i++)
			P[i]=add_noise(P[i]);
		cur.clear();
		cur.push_back(Face(1,2,3));
		cur.push_back(Face(3,2,1));
		for (int i=4;i<=n;i++){
			next.clear();
			for (int j=0;j<cur.size();j++){
				Face F=cur[j];
				int res=F.CanSee(P,i);
				if (!res)
					next.push_back(F);
				for (int k=0;k<3;k++)
					vis[F.v[k]][F.v[(k+1)%3]]=res;
			}
			for (int j=0;j<cur.size();j++)
				for (int k=0;k<3;k++){
					int a=cur[j].v[k],b=cur[j].v[(k+1)%3];
					if (vis[a][b]&&!vis[b][a])
						next.push_back(Face(a,b,i));
				}
			cur=next;
		}
	}
	double Area(Point a,Point b,Point c){
		return 0.5*Length(cross(a,b,c));
	}
	double Area(Face F,Point *P){
		return Area(P[F.v[0]],P[F.v[1]],P[F.v[2]]);
	}
	double Area(Point *P){
		double Answer=0;
		for (int i=0;i<cur.size();i++)
			Answer+=Area(cur[i],P);
		return Answer;
	}
}Hull;
int n;
int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++){
		scanf("%lf%lf%lf",&P[i].x,&P[i].y,&P[i].z);
		p[i]=P[i];
	}
	Hull.Increment(p,n);
	printf("%.6lf",Hull.Area(P));
	return 0;
}