计算几何：直线与圆的交点 三角形的内切圆和外接圆(5252: Triangle to Hexagon)

http://exam.upc.edu.cn/problem.php?id=5252

斜截式表示的直线方程

求三角形的内切圆和外接圆

求直线与直线交点，直线与圆交点

#include <bits/stdc++.h>
using namespace std;
const long double EPS = 0.0000001;

// a == b return 0
// a > b return 1
// a < b return -1
inline int cmp(long double a, long double b) {
    if(abs(a - b) < EPS) return 0;
    return a > b? 1: -1;
}
struct point {
    long double x, y;
    void print() {
        printf(" (%.4Lf, %.4Lf)
", x, y);
    }
};
struct line {
    long double k, b;
    bool isk = true;
    line() {}
    line(long double x1, long double y1, long double x2, long double y2) {
        if(!cmp(x1, x2)) {
            isk = false;
            b = x1;
        } else {
            isk = true;
            k = (y1 - y2) / (x1 - x2);
            b = y1 - k * x1;
        }
    }
    line(point a, point b) {
        *this = line(a.x, a.y, b.x, b.y);
    }
    void print() {
        printf(" k = %.4Lf, b = %.4Lf
", k, b);
    }
};
struct circle {
    point o;
    long double r;
    void print() {
        printf(" center:(%.4Lf, %.4Lf) rad: %.4Lf
", o.x, o.y, r);
    }
};
inline long double dist (point a, point b) {
    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}
circle getWjc(point a, point b, point c) {
    long double a1 = b.x - a.x, b1 = b.y - a.y, c1 = (a1*a1 + b1*b1)/2;
    long double a2 = c.x - a.x, b2 = c.y - a.y, c2 = (a2*a2 + b2*b2)/2;
    long double d = a1 * b2 - a2 * b1;
    circle cir;
    cir.o.x = a.x + (c1*b2 - c2*b1)/d;
    cir.o.y = a.y + (a1*c2 - a2*c1)/d;
    cir.r = dist(cir.o, a);
    return cir;
}
circle getNqc(point a, point b, point c) {
    long double C = dist(a, b);
    long double B = dist(a, c);
    long double A = dist(b, c);
    circle cir;
    cir.o.x = (A*a.x + B*b.x + C*c.x) / (A + B + C);
    cir.o.y = (A*a.y + B*b.y + C*c.y) / (A + B + C);
    cir.r = sqrt((A + B - C)*(A - B + C)*(-A + B + C) / (A + B + C)) / 2;
    return cir;
}
pair<point, point> getPoint(circle cir, line l) {
    pair<point, point> ans;
    if(l.isk) {
        long double x0 = cir.o.x;
        long double y0 = cir.o.y;
        long double a = (1 + l.k * l.k);
        long double b = (2*l.k*(l.b-y0)-2*x0);
        long double c = (x0*x0+(l.b-y0)*(l.b-y0)-cir.r*cir.r);
        long double deta = b * b - 4 * a * c;
        long double x1 = ( - b - sqrt(deta)) / (2 * a);
        long double x2 = ( - b + sqrt(deta)) / (2 * a);
        long double y1 = l.k*x1+l.b;
        long double y2 = l.k*x2+l.b;
        ans.first.x = x1;
        ans.first.y = y1;
        ans.second.x = x2;
        ans.second.y = y2;
    } else {
        long double x0 = cir.o.x;
        long double y0 = cir.o.y;
        long double y1 = y0 - sqrt(cir.r*cir.r - (l.b - x0) * (l.b - x0));
        long double y2 = y0 + sqrt(cir.r*cir.r - (l.b - x0) * (l.b - x0));
        ans.first.x = l.b;
        ans.first.y = y1;
        ans.second.x = l.b;
        ans.second.y = y2;
    }
    return ans;
}
point getPoint(line l1, line l2) {
    point ans;
    if( ((!l1.isk) && (!l2.isk)) || (l1.isk && l2.isk && !cmp(l1.k, l2.k)) ) {
        cerr << "RONG!!!!" << endl; exit(-1);
    } else {
        if(!l2.isk) swap(l1, l2);
        if(l1.isk) {
            long double b1 = l1.b;
            long double b2 = l2.b;
            long double k1 = l1.k;
            long double k2 = l2.k;
            long double x = (b2 - b1) / (k1 - k2);
            long double y = k1*x+b1;
            ans.x = x;
            ans.y = y;
        } else {
            long double x = l1.b;
            long double y = l2.k * x + l2.b;
            ans.x = x;
            ans.y = y;
        }
    }
    return ans;
}
point myGetPoint(circle cir, line l, point p) {
    pair<point, point> points = getPoint(cir, l);
    long double d1 = dist(points.first, p);
    long double d2 = dist(points.second, p);
    if(d1 > d2) return points.first;
    else return points.second;
}
int main()
{
    //freopen("in.txt", "r", stdin);
    ios::sync_with_stdio(false);
    int p; cin >> p;
    while(p--) {
        int k; cin >> k; cout << k << ' ';
        long double bx, cx, cy;  cin >> bx >> cx >> cy;
        point A, B, C;
        A.x = 0; A.y = 0;
        B.x = bx; B.y = 0;
        C.x = cx; C.y = cy;
        circle nqy = getNqc(A, B, C); //nqy.print();
        circle wjy = getWjc(A, B, C); //wjy.print();
        point I = nqy.o;
        line CP(C, I);
        line AM(A, I);
        line BN(B, I);
        point P = myGetPoint(wjy, CP, C);
        point M = myGetPoint(wjy, AM, A);
        point N = myGetPoint(wjy, BN, B);
        line PN(P, N);
        line NM(N, M);
        line MP(M, P);
        line AB(A, B);
        line BC(B, C);
        line CA(C, A);
        point E = getPoint(PN, AB);
        point F = getPoint(CA, PN);
        point G = getPoint(NM, CA);
        point H = getPoint(NM, BC);
        point J = getPoint(BC, MP);
        point K = getPoint(AB, MP);
        cout.flags(ios::fixed);
        cout.precision(4);
        cout << dist(E, F) << ' ';
        cout << dist(F, G) << ' ';
        cout << dist(G, H) << ' ';
        cout << dist(H, J) << ' ';
        cout << dist(J, K) << ' ';
        cout << dist(K, E) << endl;
    }
    return 0;
}