UVA 11178 Morley's Theorem （计算直线交点 + 向量旋转）

 

这题是刘汝佳老师书里的例题。P259

想了解二维几何基础的可以 戳

 

#include <bits/stdc++.h>
#define LL long long
#define mem(i, j) memset(i, j, sizeof(i))
#define rep(i, j, k) for(int i = j; i <= k; i++)
#define dep(i, j, k) for(int i = k; i >= j; i--)
#define pb push_back
#define make make_pair
#define INF INT_MAX
#define inf LLONG_MAX
#define PI acos(-1)
using namespace std;

const int N = 1e6 + 5;

struct Point {
    double x, y;
    Point(double x = 0, double y = 0) : x(x), y(y) { } /// 构造函数
};

typedef Point Vector;
/// 向量+向量=向量， 点+向量=向量
Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }
///点-点=向量
Vector operator - (Point A, Point B) { return Vector(A.x - B.x, A.y - B.y); }
///向量*数=向量
Vector operator * (Vector A, double p) { return Vector(A.x * p, A.y * p); }
///向量/数=向量
Vector operator / (Vector A, double p) { return Vector(A.x / p, A.y / p); }

const double eps = 1e-10;
int dcmp(double x) {
    if(fabs(x) < eps) return 0; else return x < 0 ? -1 : 1;
}

bool operator == (const Point& a, const Point &b) {
    return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
}

double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }
double Length(Vector A) { return sqrt(Dot(A, A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }
Vector Rotate(Vector A, double rad) {
    return Vector(A.x*cos(rad) - A.y*sin(rad), A.x*sin(rad) + A.y*cos(rad));
}

Point GetLineIntersection(Point P, Vector v, Point Q, Vector w) {
    Vector u = P - Q;
    double t = Cross(w, u) / Cross(v, w);
    return P + v * t;
}

Point getD(Point A, Point B, Point C) {
    Vector V1 = C - B;
    double a1 = Angle(A - B, V1);
    V1 = Rotate(V1, a1 / 3.0);

    Vector V2 = B - C;
    double a2 = Angle(A - C, V2);
    V2 = Rotate(V2, -a2 / 3.0);

    return GetLineIntersection(B, V1, C, V2);
}

int main() {
    int _; scanf("%d", &_);
    while(_--) {
        Point A, B, C, D, E, F;
        scanf("%lf %lf", &A.x, &A.y);
        scanf("%lf %lf", &B.x, &B.y);
        scanf("%lf %lf", &C.x, &C.y);
        D = getD(A, B, C);
        E = getD(B, C, A);
        F = getD(C, A, B);
        printf("%.6f %.6f %.6f %.6f %.6f %.6f\n", D.x, D.y, E.x, E.y, F.x, F.y);
    }
    return 0;
}