uva 11178 Morley's Theorem (2D Geometry)

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2119

　　在uva跪了一个下午后提交这题，AC了。这题更简单，就是套入几何模板，求出交点就可以了。

　　这题测试通过了几何模板中的相交判断并求出交点等几个函数。

代码如下：

View Code

#include <cstdio>
#include <cstring>
#include <cmath>
#include <vector>
#include <iostream>
#include <algorithm>

using namespace std;

#define REP(i, n) for (int i = 0; i < (n); i++)

struct Point {
double x, y;
Point() {}
Point(double x, double y) : x(x), y(y) {}
} ;
template<class T> T sqr(T x) { return x * x;}

// basic calculations
typedef Point Vec;
Vec operator + (Vec a, Vec b) { return Vec(a.x + b.x, a.y + b.y);}
Vec operator - (Vec a, Vec b) { return Vec(a.x - b.x, a.y - b.y);}
Vec operator * (Vec a, double p) { return Vec(a.x * p, a.y * p);}
Vec operator / (Vec a, double p) { return Vec(a.x / p, a.y / p);}

const double eps = 1e-8;
int sgn(double x) { return fabs(x) < eps ? 0 : (x < 0 ? -1 : 1);}
bool operator < (Point a, Point b) { return a.x < b.x || (a.x == b.x && a.y < b.y);}
bool operator == (Point a, Point b) { return sgn(a.x - b.x) == 0 && sgn(a.y - b.y) == 0;}

double dotDet(Vec a, Vec b) { return a.x * b.x + a.y * b.y;}
double vecLen(Vec x) { return sqrt(sqr(x.x) + sqr(x.y));}
double angle(Vec a, Vec b) { return acos(dotDet(a, b) / vecLen(a) / vecLen(b));}
double crossDet(Vec a, Vec b) { return a.x * b.y - a.y * b.x;}
double triArea(Point a, Point b, Point c) { return fabs(crossDet(b - a, c - a));}
Vec rotate(Vec x, double rad) { return Vec(x.x * cos(rad) - x.y * sin(rad), x.x * sin(rad) + x.y * cos(rad));}
Vec normal(Vec x) {
double len = vecLen(x);
return Vec(- x.y / len, x.x / len);
}

struct Line {
Point s, t;
Line() {}
Line(Point s, Point t) : s(s), t(t) {}
} ;
typedef Line Seg;

bool onSeg(Point x, Point a, Point b) { return sgn(crossDet(a - x, b - x)) == 0 && sgn(dotDet(a - x, b - x)) < 0;}
bool onSeg(Point x, Seg s) { return onSeg(x, s.s, s.t);}
// 0 : not intersect
// 1 : proper intersect
// 2 : improper intersect
int segIntersect(Point a, Point c, Point b, Point d) {
Vec v1 = b - a, v2 = c - b, v3 = d - c, v4 = a - d;
int a_bc = sgn(crossDet(v1, v2));
int b_cd = sgn(crossDet(v2, v3));
int c_da = sgn(crossDet(v3, v4));
int d_ab = sgn(crossDet(v4, v1));
if (a_bc * c_da > 0 && b_cd * d_ab > 0) return 1;
if (onSeg(b, a, c) && c_da) return 2;
if (onSeg(c, b, d) && d_ab) return 2;
if (onSeg(d, c, a) && a_bc) return 2;
if (onSeg(a, d, b) && b_cd) return 2;
return 0;
}
int segIntersect(Seg a, Seg b) { return segIntersect(a.s, a.t, b.s, b.t);}

// point of the intersection of 2 lines
Point lineIntersect(Point P, Vec v, Point Q, Vec w) {
Vec u = P - Q;
double t = crossDet(w, u) / crossDet(v, w);
return P + v * t;
}
Point lineIntersect(Line a, Line b) { return lineIntersect(a.s, a.t - a.s, b.s, b.t - b.s);}

// directed distance
double pt2Line(Point x, Point a, Point b) {
Vec v1 = b - a, v2 = x - a;
return crossDet(v1, v2) / vecLen(v1);
}
double pt2Line(Point x, Line L) { return pt2Line(x, L.s, L.t);}

double pt2Seg(Point x, Point a, Point b) {
if (a == b) return vecLen(x - a);
Vec v1 = b - a, v2 = x - a, v3 = x - b;
if (sgn(dotDet(v1, v2)) < 0) return vecLen(v2);
if (sgn(dotDet(v1, v3)) > 0) return vecLen(v3);
return fabs(crossDet(v1, v2)) / vecLen(v1);
}
double pt2Seg(Point x, Seg s) { return pt2Seg(x, s.s, s.t);}

struct Poly {
vector<Point> pt;
Poly() {}
Poly(vector<Point> pt) : pt(pt) {}
double area() {
double ret = 0.0;
int sz = pt.size();
for (int i = 1; i < sz; i++) {
ret += crossDet(pt[i], pt[i - 1]);
}
return fabs(ret / 2.0);
}
} ;

/****************** template above *******************/

Point p[3];

Point cal(Point a, Point b, Point c) {
double angB = fabs(angle(c - b, a - b) / 3.0);
double angC = fabs(angle(b - c, a - c) / 3.0);
Vec v1, v2;
v1 = rotate(c - b, angB);
v2 = rotate(b - c, -angC);
//    return lineIntersect(Line(b, b + v1), Line(c, c + v2));
return lineIntersect(b, v1, c, v2);
}

int main() {
//    freopen("in", "r", stdin);
int n;
cin >> n;
while (n--) {
for (int i = 0; i < 3; i++) {
cin >> p[i].x >> p[i].y;
}
for (int i = 0; i < 3; i++) {
Point tmp = cal(p[i % 3], p[(i + 1) % 3], p[(i + 2) % 3]);
if (i) putchar(' ');
printf("%.10f %.10f", tmp.x, tmp.y);
}
cout << endl;
}
return 0;
}

——written by Lyon