uva 11836 - Star War（几何）

题目链接：uva 11836 - Star War

就三种情况，点到线段，点到面，线段到线段。

#include <cstdio>#include <cstring>#include <cmath>#include <cstdlib>#include <vector>#include <algorithm>using namespace std;const double eps = 1e-6;inline int dcmp (double x) { if (fabs(x) < eps) return 0; else return x < 0 ? -1 : 1; }struct Point3 {double x, y, z;Point3 (double x = 0, double y = 0, double z = 0): x(x), y(y), z(z) {}bool operator < (const Point3& u) const { return dcmp(x-u.x)<0 || (dcmp(x-u.x)==0 && dcmp(y-u.y)<0) || (dcmp(x-u.x)==0 && dcmp(y-u.y)==0 && dcmp(z-u.z) < 0); }bool operator > (const Point3& u) const { return u < (*this); }bool operator == (const Point3& u) const { return !(u < (*this) || (*this) < u); }bool operator != (const Point3& u) const { return !((*this) == u); }Point3 operator + (const Point3& u) const { return Point3(x+u.x, y+u.y, z+u.z); }Point3 operator - (const Point3& u) const { return Point3(x-u.x, y-u.y, z-u.z); }Point3 operator * (const double u) const { return Point3(x*u, y*u, z*u); }Point3 operator / (const double u) const { return Point3(x/u, y/u, z/u); }void read () { scanf("%lf%lf%lf", &x, &y, &z); }};typedef Point3 Vector3;namespace Vectorial {double getDot(Vector3 a, Vector3 b) { return a.x*b.x + a.y*b.y + a.z*b.z; }double getLength(Vector3 a) { return sqrt(getDot(a, a)); }double getAngle(Vector3 a, Vector3 b) { return acos(getDot(a, b) / getLength(a) / getLength(b)); }Vector3 getCross (Vector3 a, Vector3 b) { return Vector3(a.y*b.z-a.z*b.y, a.z*b.x-a.x*b.z, a.x*b.y-a.y*b.x); }Vector3 getNormal(Point3 a, Point3 b, Point3 c) {  Vector3 u = a-b, v = b-c;Vector3 k = getCross(u, v);return k / getLength(k);}double getDistancePointToPlane (Point3 p, Point3 p0, Vector3 v) { return fabs(getDot(p-p0, v)); }Point3 getPlaneProjection (Point3 p, Point3 p0, Vector3 v) { return p - v * getDot(p-p0, v); }};namespace Linear {using namespace Vectorial;double getDistancePointToLine(Point3 p, Point3 a, Point3 b) {Vector3 v1 = b-a, v2 = p-a;return getLength(getCross(v1,v2)) / getLength(v1);}double getDistancePointToSegment(Point3 p, Point3 a, Point3 b) {if (a == b) return getLength(p-a);Vector3 v1 = b-a, v2 = p-a, v3 = p-b;if (dcmp(getDot(v1, v2)) < 0) return getLength(v2);else if (dcmp(getDot(v1, v3)) > 0) return getLength(v3);else return getLength(getCross(v1, v2)) / getLength(v1);}bool getPointLineToLine (Point3 a, Vector3 u, Point3 b, Vector3 v, double& s) {double p = getDot(u, u) * getDot(v, v) - getDot(u, v) * getDot(u, v);if (dcmp(p) == 0) return false;double q = getDot(u, v) * getDot(v, a-b) - getDot(v, v) * getDot(u, a-b);s = q/p;return true;}double getDistanceLineToLine (Point3 a, Vector3 u, Point3 b, Vector3 v) {double s, t;bool flag1 = getPointLineToLine(a, u, b, v, s);bool flag2 = getPointLineToLine(b, v, a, u, t);if (flag1 && flag2) {Point3 p = a + u * s, q = b + v * t;return getLength(p-q);}return 0;}double getDistanceSegmentToSegment(Point3 a, Point3 b, Point3 c, Point3 d) {double s, t;bool flag1 = getPointLineToLine(a, b-a, c, d-c, s);bool flag2 = getPointLineToLine(c, d-c, a, b-a, t);if (flag1 && flag2 && dcmp(s) > 0 && dcmp(s- 1) < 0 && dcmp(t) > 0 && dcmp(t-1) < 0) {Vector3 u = b-a, v = d-c;Point3 p = a + u * s, q = c + v * t;return getLength(p-q);} else {double ans = 1e20;ans = min(ans, getDistancePointToSegment(a, c, d));ans = min(ans, getDistancePointToSegment(b, c, d));ans = min(ans, getDistancePointToSegment(c, a, b));ans = min(ans, getDistancePointToSegment(d, a, b));return ans;}}};namespace Triangular {using namespace Vectorial;double getArea (Point3 a, Point3 b, Point3 c) { return getLength(getCross(b-a, c-a)); }bool onTriangle (Point3 p, Point3 a, Point3 b, Point3 c) {double area1 = getArea(p, a, b);double area2 = getArea(p, b, c);double area3 = getArea(p, c, a);return dcmp(area1 + area2 + area3 - getArea(a, b, c)) == 0;}bool haveIntersectionTriSeg (Point3 p0, Point3 p1, Point3 p2, Point3 a, Point3 b, Point3& p) {Vector3 v = getCross(p1-p0, p2-p0);if (dcmp(getDot(v, b-a)) == 0) return false;else {double t = getDot(v, p0 - a) / getDot(v, b-a);if (dcmp(t) < 0 || dcmp(t-2) > 0) return false;p = a + (b-a) * t;return onTriangle(p, p0, p1, p2);}}};struct Face {int v[3];Face (int a = 0, int b = 0, int c = 0) { v[0] = a, v[1] = b, v[2] = c;}Vector3 normal (Point3 *p) const { return Vectorial::getCross(p[v[1]] - p[v[0]], p[v[2]]-p[v[0]]); }int cansee (Point3 *p, int i) const {return Vectorial::getDot(p[i]-p[v[0]], normal(p)) > 0 ? 1 : 0;}};namespace Polygonal {using namespace Vectorial;/* 有向体积，是4边形的6倍 */double getVolume (Point3 a, Point3 b, Point3 c, Point3 d) { return fabs(getDot(d-a, getCross(b-a, c-a)) / 6); }int vis[1005][1005];double rand01() { return rand() / (double) RAND_MAX; }double randeps() { return (rand01() - 0.5) * eps; }Point3 addNoise(Point3 p) { return Point3(p.x+randeps(), p.y+randeps(), p.z+randeps()); }vector<Face> CH3D (Point3 *o, int n, Point3* p) {for (int i = 0; i < n; i++) p[i] = addNoise(o[i]);memset(vis, -1, sizeof(vis));vector<Face> cur;cur.push_back(Face(0, 1, 2));cur.push_back(Face(2, 1, 0));for (int i = 3; i < n; i++) {vector<Face> net;for (int j = 0; j < cur.size(); j++) {Face& f = cur[j];int res = f.cansee(p, i);if (!res) net.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] && vis[a][b])net.push_back(Face(a, b, i));}}cur = net;}return cur;}Point3 getCenter (const vector<Face>& f, Point3* p) {int n = f.size();double sv = 0, sx = 0, sy = 0, sz = 0;for (int i = 0; i < n; i++) {double v = getVolume(Point3(0, 0, 0), p[f[i].v[0]], p[f[i].v[1]], p[f[i].v[2]]);sv += v;sx += (p[f[i].v[0]].x + p[f[i].v[1]].x + p[f[i].v[2]].x) * v;sy += (p[f[i].v[0]].y + p[f[i].v[1]].y + p[f[i].v[2]].y) * v;sz += (p[f[i].v[0]].z + p[f[i].v[1]].z + p[f[i].v[2]].z) * v;}return Point3(sx/sv/4, sy/sv/4, sz/sv/4);}};using namespace Linear;using namespace Triangular;using namespace Polygonal;Point3 A[5], B[5];double getDistancePointToTriangle(Point3 p, Point3 a, Point3 b, Point3 c) {double ret = 1e20;ret = min(ret, getDistancePointToSegment(p, a, b));ret = min(ret, getDistancePointToSegment(p, b, c));ret = min(ret, getDistancePointToSegment(p, c, a));Vector3 v = getNormal(a, b, c);Point3 tmp = getPlaneProjection(p, a, v);if (onTriangle(tmp, a, b, c)) ret = min(ret, getDistancePointToPlane(p, a, v));return ret;}double solve () {double ret = 1e20;for (int i = 0; i < 4; i++) {for (int j = i+1; j < 4; j++)for (int x = 0; x < 4; x++)for (int y = x+1; y < 4; y++)ret = min(ret, getDistanceSegmentToSegment(A[i], A[j], B[x], B[y]));}for (int i = 0; i < 4; i++) {for (int j = 0; j < 4; j++) {int a = (j+1)%4, b = (j+2)%4;ret = min(ret, getDistancePointToTriangle(A[i], B[j], B[a], B[b]));ret = min(ret, getDistancePointToTriangle(B[i], A[j], A[a], A[b]));}}return ret;}int main () {int cas;scanf("%d", &cas);while (cas--) {for (int i = 0; i < 4; i++) A[i].read();for (int i = 0; i < 4; i++) B[i].read();printf("%.2lf\n", solve());}return 0;}