UVA12304_2D Geometry 110 in 1!

各种点线与圆的关系。

1、三角形外接圆：求各边中垂线交点；

2、三角形内切圆：定比分点构造等腰三角形求角平分线，求两角平分线交点；

3、定点到圆切线：点到圆心斜率加减切线夹角，处理结果的表示范围；

4、切直线、过定点的圆：点在线上是两个对称的圆，否则圆在点线确定的双曲线上，利用双曲线性质构造直角梯形，然后利用向量与定比分点求；

5、与两相交直线相切的圆：分别将直线朝不同方向平移半径距离求交点；

6、两相离圆的公共外切圆：三圆心连线构成三角形，所求圆心做三角形的高，余弦定理+定比分点求出各项数据。

特殊情况进行特判求值。

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>
#include<algorithm>
using namespace std;
const double eps = 1e-10;
const double pi = acos(-1.0);
char buf[100];
char task[6][100] = {
    "CircumscribedCircle",
    "InscribedCircle",
    "TangentLineThroughPoint",
    "CircleThroughAPointAndTangentToALineWithRadius",
    "CircleTangentToTwoLinesWithRadius",
    "CircleTangentToTwoDisjointCirclesWithRadius"
    };
inline double Sqr(double x)
{return x * x;}
inline int dcmp(double x)
{
    if(x > eps) return 1;
    return x < -eps ? -1 : 0;
}
inline double pz(double x)
{return dcmp(x) ? x : 0;}
struct Point
{
    double x, y;
    Point(){x = y = 0;}
    Point(double a, double b)
    {x = a, y = b;}
    Point operator-(const Point &b)const
    {return Point(x - b.x, y - b.y);}
    Point operator+(const Point &b)const
    {return Point(x + b.x, y + b.y);}
    Point operator-()
    {return Point(-x, -y);}
    Point operator*(const double &b)const
    {return Point(x * b, y * b);}
    double dot(const Point &b)const
    {return x * b.x + y * b.y;}
    double cross(const Point &b, const Point &c)const
    {return (b.x - x) * (c.y - y) - (c.x - x) * (b.y - y);}
    double Dis(const Point &b)const
    {return sqrt((*this - b).dot(*this - b));}
    bool operator<(const Point &b)const
    {
        if(!dcmp(x - b.x)) return y < b.y;
        return x < b.x;
    }
    bool operator>(const Point &b)const
    {return b < *this;}
};
inline double min(double a, double b)
{return a < b ? a : b;}
inline double max(double a, double b)
{return a > b ? a : b;}
inline Point min(Point a, Point b)
{return a < b ? a : b;}
inline Point max(Point a, Point b)
{return a > b ? a : b;}
Point CrossPoint(Point a, Point b, Point c, Point d)
{
    double u = a.cross(b, c), v = b.cross(a, d);
    return Point((c.x * v + d.x * u) / (u + v), (c.y * v + d.y * u) / (u + v));
}
int Task(char *s)
{
    for(int i = 0; i < 6; ++ i)
        if(!strcmp(s, task[i])) return i;
}

void CC()   //外接圆
{
    Point a, b, c, ab, ac, r;
    scanf("%lf%lf%lf%lf%lf%lf", &a.x, &a.y, &b.x, &b.y, &c.x, &c.y);
    ab = (a + b) * 0.5, ac = (a + c) * 0.5;
    r = CrossPoint(ab, Point(ab.x + a.y - b.y, ab.y + b.x - a.x), 
        ac, Point(ac.x + a.y - c.y, ac.y + c.x - a.x));
    printf("(%.6f,%.6f,%.6f)\n", 
        eps + pz(r.x), eps + pz(r.y), eps + pz(r.Dis(a)));
}
void IC()   //内切圆
{
    Point a, b, c, apf, bpf, r;
    scanf("%lf%lf%lf%lf%lf%lf", &a.x, &a.y, &b.x, &b.y, &c.x, &c.y);
    double la = b.Dis(c), lb = a.Dis(c), lc = a.Dis(b), p = (la + lb + lc) * 0.5;
    apf = (c + a + (b - a) * (lb / lc)) * 0.5;
    bpf = (c + b + (a - b) * (la / lc)) * 0.5;
    r = CrossPoint(a, apf, b, bpf);
    printf("(%.6f,%.6f,%.6f)\n", eps + pz(r.x), eps + pz(r.y), 
        eps + pz(sqrt(p * (p - la) * (p - lb) * (p - lc)) * 2 / (la + lb + lc)));
}
double ManageDeg(double x)
{
    while(x < -eps) x += pi;
    while(x > pi - eps) x -= pi;
    return x;
}
void TLTP() //点到圆切线
{
    Point a, r;
    double R, ang, ang1, ang2;
    scanf("%lf%lf%lf%lf%lf", &r.x, &r.y, &R, &a.x, &a.y);
    ang = atan2(r.y - a.y, r.x - a.x);
    switch(dcmp(a.Dis(r) - R))
    {
        case 0:
            printf("[%.6f]\n", eps + pz(ManageDeg(ang + pi * 0.5) / pi * 180));
            break;
        case 1:
            ang1 = ManageDeg(ang + asin(R / a.Dis(r))) / pi * 180;
            ang2 = ManageDeg(ang - asin(R / a.Dis(r))) / pi * 180;
            printf("[%.6f,%.6f]\n", eps + pz(min(ang1, ang2)), 
                eps + pz(max(ang1, ang2)));
            break;
        default:
            printf("[]\n");
    }
}
void CTAPATTAWR()//切直线且经定点、半径定值的圆
{
    Point p, a, b, pcl, pcz, r1, r2, xl;
    double R, rcp;
    scanf("%lf%lf%lf%lf%lf%lf%lf", &p.x, &p.y, &a.x, &a.y, &b.x, &b.y, &R);
    pcl = Point(p.x + a.y - b.y, p.y + b.x - a.x);//pcl-p 垂线向量
    pcz = CrossPoint(p, pcl, a, b);//垂足
    if(!dcmp(p.cross(a, b)))
    {
        r1 = p + (pcl - p) * (R / p.Dis(pcl));
        r2 = p - (pcl - p) * (R / p.Dis(pcl));
        printf("[(%.6f,%.6f),", eps + pz(min(r1, r2).x), eps + pz(min(r1, r2).y));
        printf("(%.6f,%.6f)]\n", eps + pz(max(r1, r2).x), eps + pz(max(r1, r2).y));
    }
    else if(!dcmp(R - p.Dis(pcz) * 0.5))
    {
        r1 = (p + pcz) * 0.5;
        printf("[(%.6f,%.6f)]\n", eps + pz(r1.x), eps + pz(r1.y));
    }
    else if(dcmp(R - p.Dis(pcz) * 0.5) > 0)//利用双曲线性质，构造直角梯形求解。
    {
        rcp = sqrt(R * R - Sqr(R - p.Dis(pcz)));//直角梯形的高。。。
        r1 = pcz + (a - b) * (rcp / (a.Dis(b))) + (p - pcz) * (R / p.Dis(pcz));
        r2 = pcz - (a - b) * (rcp / (a.Dis(b))) + (p - pcz) * (R / p.Dis(pcz));
        printf("[(%.6f,%.6f),", eps + pz(min(r1, r2).x), eps + pz(min(r1, r2).y));
        printf("(%.6f,%.6f)]\n", eps + pz(max(r1, r2).x), eps + pz(max(r1, r2).y));
    }
    else printf("[]\n");

}
void CTTTLWR()//与两相交直线相切的圆
{
    Point a, b, c, d, A, B, C, D, jd, xl1, xl2, r[4];
    double R, R_, ang, l1, l2;
    scanf("%lf%lf%lf%lf%lf%lf%lf%lf%lf", 
        &a.x, &a.y, &b.x, &b.y, &c.x, &c.y, &d.x, &d.y, &R);
    xl1 = Point(a.y - b.y, b.x - a.x); xl1 = xl1 * (R / sqrt(xl1.dot(xl1)));
    xl2 = Point(c.y - d.y, d.x - c.x); xl2 = xl2 * (R / sqrt(xl2.dot(xl2)));
    r[0] = CrossPoint(a + xl1, b + xl1, c + xl2, d + xl2);
    r[1] = CrossPoint(a + xl1, b + xl1, c - xl2, d - xl2);
    r[2] = CrossPoint(a - xl1, b - xl1, c + xl2, d + xl2);
    r[3] = CrossPoint(a - xl1, b - xl1, c - xl2, d - xl2);
    sort(r, r + 4);
    printf("[");
    for(int i = 0; i < 4; ++ i)
    {
        if(i)printf(",");
        printf("(%.6f,%.6f)", eps + pz(r[i].x), eps + pz(r[i].y));
    }
    printf("]\n");
}
void CTTTDCWR()//两相离圆的公共外切圆
{
    Point r1, r2, r[2], zd, xl;
    double R1, R2, R, len;
    scanf("%lf%lf%lf%lf%lf%lf%lf", &r1.x, &r1.y, &R1, &r2.x, &r2.y, &R2, &R);
    if(!dcmp(R + R1 + R + R2 - r1.Dis(r2)))
    {
        r[0] = r1 + (r2 - r1) * ((R + R1) / (R + R1 + R + R2));
        printf("[(%.6f,%.6f)]\n", eps + pz(r[0].x), eps + pz(r[0].y));
    }
    else if(dcmp(R + R1 + R + R2 - r1.Dis(r2)) > 0)
    {
        zd = r1 + (r2 - r1) * (((R + R1) * (Sqr(R + R1) + Sqr(r1.Dis(r2)) - Sqr(R + R2)) * 
            0.5 / (R + R1) / r1.Dis(r2)) / r1.Dis(r2));//对称圆心的中点
        len = sqrt(Sqr(R + R1) - Sqr(zd.Dis(r1)));//zd到所求圆心距离
        xl = Point(r1.y - r2.y, r2.x - r1.x);//zd到所求圆心的向量
        r[0] = zd + xl * (len / sqrt(xl.dot(xl)));
        r[1] = zd - xl * (len / sqrt(xl.dot(xl)));
        sort(r, r + 2);
        printf("[(%.6f,%.6f),(%.6f,%.6f)]\n", 
            eps + pz(r[0].x), eps + pz(r[0].y), eps + pz(r[1].x), eps + pz(r[1].y));
    }
    else printf("[]\n");
}
int main()
{
    while(scanf("%s", buf) != EOF)
    {
        switch(Task(buf))
        {
            case 0: CC();break;
            case 1: IC();break;
            case 2: TLTP();break;
            case 3: CTAPATTAWR();break;
            case 4: CTTTLWR();break;
            case 5: CTTTDCWR();break;
        }
    }
    return 0;
}