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3D Convex Hull
#include <iostream>
#include <vector>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <cassert>
using namespace std;
#define MAXN 1010
typedef long long vtype;
/* Basic 3D vector implementation */
struct vec3 {
vec3() { X[0] = X[1] = X[2] = 0; }
vec3(vtype x, vtype y, vtype z) { X[0] = x; X[1] = y; X[2] = z; }
/* 3D cross product */
vec3 operator*(const vec3& v) const {
return vec3(X[1] * v.X[2] - X[2] * v.X[1],
X[2] * v.X[0] - X[0] * v.X[2],
X[0] * v.X[1] - X[1] * v.X[0]);
}
vec3 operator-(const vec3& v) const {
return vec3(X[0] - v.X[0], X[1] - v.X[1], X[2] - v.X[2]);
}
vec3 operator-() const {
return vec3(-X[0], -X[1], -X[2]);
}
vtype dot(const vec3& v) const {
return X[0] * v.X[0] + X[1] * v.X[1] + X[2] * v.X[2];
}
vtype X[3];
};
/* Original points in the input. */
vec3 A[MAXN];
/* E[i][j] indicates which (up to two) other points combine with the edge i and
* j to make a face in the hull. Only defined when i < j.
*/
struct twoset {
void insert(int x) { (a == -1 ? a : b) = x; }
bool contains(int x) { return a == x || b == x; }
void erase(int x) { (a == x ? a : b) = -1; }
int size() { return (a != -1) + (b != -1); }
int a, b;
} E[MAXN][MAXN];
struct face {
vec3 norm;
vtype disc;
int I[3];
};
/* Compute the half plane {x : c^T norm < disc}
* defined by the three points A[i], A[j], A[k] where
* A[inside_i] is considered to be on the 'interior' side of the face. */
face make_face(int i, int j, int k, int inside_i) {
E[i][j].insert(k); E[i][k].insert(j); E[j][k].insert(i);
face f;
f.I[0] = i; f.I[1] = j; f.I[2] = k;
f.norm = (A[j] - A[i]) * (A[k] - A[i]);
f.disc = f.norm.dot(A[i]);
if(f.norm.dot(A[inside_i]) > f.disc) {
f.norm = -f.norm;
f.disc = -f.disc;
}
return f;
}
int main() {
int N;
for(cin >> N; N; cin >> N) {
for(int i = 0; i < N; i++) {
cin >> A[i].X[0] >> A[i].X[1] >> A[i].X[2];
}
/* Initially construct the hull as containing only the first four points. */
face f;
vector<face> faces;
memset(E, -1, sizeof(E));
for(int i = 0; i < 4; i++)
for(int j = i + 1; j < 4; j++)
for(int k = j + 1; k < 4; k++) {
faces.push_back(make_face(i, j, k, 6 - i - j - k));
}
/* Now add a point into the hull one at a time. */
for(int i = 4; i < N; i++) {
/* Find and delete all faces with their outside 'illuminated' by this
* point. */
for(int j = 0; j < faces.size(); j++) {
f = faces[j];
if(f.norm.dot(A[i]) > f.disc) {
E[f.I[0]][f.I[1]].erase(f.I[2]);
E[f.I[0]][f.I[2]].erase(f.I[1]);
E[f.I[1]][f.I[2]].erase(f.I[0]);
faces[j--] = faces.back();
faces.resize(faces.size() - 1);
}
}
/* Now for any edge still in the hull that is only part of one face
* add another face containing the new point and that edge to the hull. */
int nfaces = faces.size();
for(int j = 0; j < nfaces; j++) {
f = faces[j];
for(int a = 0; a < 3; a++) for(int b = a + 1; b < 3; b++) {
int c = 3 - a - b;
if(E[f.I[a]][f.I[b]].size() == 2) continue;
faces.push_back(make_face(f.I[a], f.I[b], i, f.I[c]));
}
}
}
/* Answer each of the queries. Compute the minimum distance of each query
* point to each face of the hull. */
int Q; cin >> Q;
for(int i = 0; i < Q; i++) {
vec3 v; cin >> v.X[0] >> v.X[1] >> v.X[2];
double dist = 1e300;
for(int i = 0; i < faces.size(); i++) {
vtype d = faces[i].disc - faces[i].norm.dot(v);
dist = min(dist, 1. * d / sqrt(faces[i].norm.dot(faces[i].norm)));
}
printf("%.4f\n", dist);
}
}
}
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