# POJ 2225 / ZOJ 1438 / UVA 1438 Asteroids --三维凸包，求多面体重心

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <set>
#define Mod 1000000007
#define eps 1e-8
#define lll __int64
#define ll long long
using namespace std;
#define N 100007
#define MAXV 505

//三维点
struct pt{
double x, y, z;
pt(){}
pt(double _x, double _y, double _z): x(_x), y(_y), z(_z){}
pt operator - (const pt p1){return pt(x - p1.x, y - p1.y, z - p1.z);}
pt operator * (pt p){return pt(y*p.z-z*p.y, z*p.x-x*p.z, x*p.y-y*p.x);}        //叉乘
double operator ^ (pt p){return x*p.x+y*p.y+z*p.z;}                            //点乘
};

//pt operator - (const pt p,const pt p1){return pt(p.x - p1.x, p.y - p1.y, p.z - p1.z);}
//pt operator ** (pt p,pt p1){return pt(p.y*p1.z-p.z*p1.y, p.z*p1.x-p.x*p1.z, p.x*p1.y-p.y*p1.x);}        //叉乘
//double operator ^^ (pt p1,pt p){return p1.x*p.x+p1.y*p.y+p1.z*p.z;}

struct _3DCH{
struct fac{
int a, b, c;    //表示凸包一个面上三个点的编号
bool ok;        //表示该面是否属于最终凸包中的面
};

int n;    //初始点数
pt P[MAXV];    //初始点

int cnt;    //凸包表面的三角形数
fac F[MAXV*8]; //凸包表面的三角形

int to[MAXV][MAXV];

double vlen(pt a){return sqrt(a.x*a.x+a.y*a.y+a.z*a.z);}    //向量长度
double area(pt a, pt b, pt c){return vlen((b-a)*(c-a));}    //三角形面积*2
double volume(pt a, pt b, pt c, pt d){return (b-a)*(c-a)^(d-a);}    //四面体有向体积*6

//正：点在面同向
double ptof(pt &p, fac &f){
pt m = P[f.b]-P[f.a], n = P[f.c]-P[f.a], t = p-P[f.a];
return (m * n) ^ t;
}
pt pvec(fac s) {
pt k1 = (P[s.a]-P[s.b]), k2 = (P[s.b]-P[s.c]);
return (k1*k2);
}
double ptoplane(pt p,fac s){
return fabs(pvec(s)^(p-P[s.a]))/vlen(pvec(s));
}

void deal(int p, int a, int b){
int f = to[a][b];
if (F[f].ok){
if (ptof(P[p], F[f]) > eps)
dfs(p, f);
else{
to[p][b] = to[a][p] = to[b][a] = cnt;
}
}
}

void dfs(int p, int cur){
F[cur].ok = 0;
deal(p, F[cur].b, F[cur].a);
deal(p, F[cur].c, F[cur].b);
deal(p, F[cur].a, F[cur].c);
}

bool same(int s, int t){
pt &a = P[F[s].a], &b = P[F[s].b], &c = P[F[s].c];
return fabs(volume(a, b, c, P[F[t].a])) < eps && fabs(volume(a, b, c, P[F[t].b])) < eps && fabs(volume(a, b, c, P[F[t].c])) < eps;
}

//构建三维凸包
void construct(){
cnt = 0;
if (n < 4)
return;

/*********此段是为了保证前四个点不公面，若已保证，可去掉********/
bool sb = 1;
//使前两点不公点
for (int i = 1; i < n; i++){
if (vlen(P[0] - P[i]) > eps){
swap(P[1], P[i]);
sb = 0;
break;
}
}
if (sb)return;

sb = 1;
//使前三点不公线
for (int i = 2; i < n; i++){
if (vlen((P[0] - P[1]) * (P[1] - P[i])) > eps){
swap(P[2], P[i]);
sb = 0;
break;
}
}
if (sb)return;

sb = 1;
//使前四点不共面
for (int i = 3; i < n; i++){
if (fabs((P[0] - P[1]) * (P[1] - P[2]) ^ (P[0] - P[i])) > eps){
swap(P[3], P[i]);
sb = 0;
break;
}
}
if (sb)return;
/*********此段是为了保证前四个点不公面********/

for (int i = 0; i < 4; i++){
}

for (int i = 4; i < n; i++){
for (int j = 0; j < cnt; j++){
if (F[j].ok && ptof(P[i], F[j]) > eps){
dfs(i, j);
break;
}
}
}
int tmp = cnt;
cnt = 0;
for (int i = 0; i < tmp; i++){
if (F[i].ok){
F[cnt++] = F[i];
}
}
}

//表面积
double area(){
double ret = 0.0;
for (int i = 0; i < cnt; i++){
ret += area(P[F[i].a], P[F[i].b], P[F[i].c]);
}
return ret / 2.0;
}

//体积
double volume(){
pt O(0, 0, 0);
double ret = 0.0;
for (int i = 0; i < cnt; i++) {
ret += volume(O, P[F[i].a], P[F[i].b], P[F[i].c]);
}
return fabs(ret / 6.0);
}

pt BaryCenter() {
pt O(0, 0, 0);
double ret = 0.0,sumvolume = 0.0, sumx = 0.0, sumy = 0.0, sumz = 0.0;
for(int i=0;i<cnt;i++) {
double Vol = volume(O, P[F[i].a], P[F[i].b], P[F[i].c]);
sumvolume += Vol;
sumx += (P[F[i].a].x + P[F[i].b].x + P[F[i].c].x)*Vol;
sumy += (P[F[i].a].y + P[F[i].b].y + P[F[i].c].y)*Vol;
sumz += (P[F[i].a].z + P[F[i].b].z + P[F[i].c].z)*Vol;
}
return pt(sumx/sumvolume/4, sumy/sumvolume/4, sumz/sumvolume/4);
}

//表面三角形数
int facetCnt_tri(){
return cnt;
}

//表面多边形数
int facetCnt(){
int ans = 0;
for (int i = 0; i < cnt; i++){
bool nb = 1;
for (int j = 0; j < i; j++){
if (same(i, j)){
nb = 0;
break;
}
}
ans += nb;
}
return ans;
}
};

_3DCH hull,hull2;    //内有大数组，不易放在函数内

int main()
{
while (scanf("%d", &hull.n)!=EOF){
for (int i = 0; i < hull.n; i++)
scanf("%lf%lf%lf", &hull.P[i].x, &hull.P[i].y, &hull.P[i].z);
hull.construct();
pt bc1 = hull.BaryCenter();
scanf("%d",&hull2.n);
for (int i = 0; i < hull2.n; i++)
scanf("%lf%lf%lf", &hull2.P[i].x, &hull2.P[i].y, &hull2.P[i].z);
hull2.construct();
pt bc2 = hull2.BaryCenter();
//printf("BARY1: %.2f %.2f %.2f\n",bc1.x,bc1.y,bc1.z);
//printf("BARY2: %.2f %.2f %.2f\n",bc2.x,bc2.y,bc2.z);
double dis1 = Mod, dis2 = Mod;
for (int i = 0; i < hull.cnt; i++)
dis1 = min(dis1,fabs(hull.ptoplane(bc1,hull.F[i])));
for (int i = 0; i < hull2.cnt; i++)
dis2 = min(dis2,fabs(hull2.ptoplane(bc2,hull2.F[i])));
printf("%.6f\n",dis1+dis2);
}
return 0;
}
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posted @ 2015-03-05 23:04 whatbeg 阅读(...) 评论(...) 编辑 收藏