UVa12304（计算几何中圆的基本操作）

断断续续写了250多行的模拟，其间被其他事情打扰，总共花了一天才AC吧~

这道题目再次让我明白，有些事情看起来很难，实际上并没有我们想象中的那么难。当然了我主要指的不是这个题的难度……

也是初学计算几何，然后居然胆大妄为地不用刘汝佳的思路去实现这些个功能，其中有三个功能是我用自己的思路实现的吧（瞎暴力），最后果然也是自己写的出锅了。

当一个贼长的模拟题交上去一发WA时，我是欲哭无泪的……这让我怎么debug……只好不断安慰自己要用计算几何题去练习耐心。

只是没想到在不断的固执与冷静的试探之下，不到一个晚上就成功了，当然了，对拍拍出来的呗……

我的主要错误在于在我自己的实现思路里，旋转向量时应该顺时针还是逆时针是取决于输入的，而我粗暴地“一视同仁”了。还好后来发现不难改，加个正负1去control就好了~

自己的辣鸡代码贴一贴留着自己看，难得写这么长：

#include <bits/stdc++.h>
using namespace std;

struct Point
{
    double x, y;
    Point(double a = 0, double b = 0):x(a), y(b){ }
};
typedef Point Vector;

const double PI = acos(-1.0);
int dcmp(double x)
{
    if (fabs(x) < 1e-6)    return 0;
    else    return x < 0 ? -1 : 1;
}
Vector operator + (const Point &A, const Point &B) { return Vector(A.x + B.x, A.y + B.y); }
Vector operator - (const Point &A, const Point &B) { return Vector(A.x - B.x, A.y - B.y); }
Vector operator * (const Point &A, double p) { return Vector(A.x * p, A.y * p); }
Vector operator / (const Point &A, double p) { return Vector(A.x / p, A.y / p); }
bool operator < (const Point &A, const Point &B) { return dcmp(A.x - B.x) < 0 || (dcmp(A.x - B.x) == 0 && dcmp(A.y - B.y) < 0); }
bool operator == (const Point &A, const Point &B) { return dcmp(A.x - B.x) == 0 && dcmp(A.y - B.y) == 0; }

double Cross(Vector A, Vector B) { return A.x * B.y - A.y * B.x; }
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)); }
Vector Normal(Vector A) { double L = Length(A); return Vector(-A.y / L, A.x / L); }
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 Get_Line_Intersect(Point P, Vector v, Point Q, Vector w)
{
    Point u = P - Q;
    double t = Cross(w, u) / Cross(v, w);
    return P + v*t;
}

double Distance_to_Line(Point P, Point A, Point B)
{
    Vector v1 = P - A, v2 = B - A;
    return fabs(Cross(v1, v2) / Length(v2));
}

struct Circle
{
    Point c;
    double r;
    // Circle(Point a = (0, 0), double x = 0):c(a), r(x){}
    Point point(double seta) { return Point(c.x + cos(seta)*r, c.y + sin(seta)*r); }
};

struct Line
{
    Point p;
    Vector v;
    Line(Point p, Vector v):p(p), v(v) { }

    Point point(double t) { return p + v*t; }
    Line move(double d) { return Line(p + Normal(v)*d, v); }
};

double formattedAngle(Vector A)
{ 
    double a = atan2(A.y, A.x) / PI * 180; 
    if (dcmp(a) < 0)    a += 180;
    if (dcmp(a - 180) >= 0)    a -= 180;    
    return a;
}

int getTangents(Point P, Circle C, vector<double> &v)
{
    Vector u = C.c - P;
    double d = Length(u);

    if (dcmp(d - C.r) < 0)    return 0;
    else if (dcmp(d - C.r) == 0)
    {
        v.push_back(formattedAngle(Rotate(u, PI/2)));
        return 1;
    }
    else
    {
        double a = asin(C.r / d);
        v.push_back(formattedAngle(Rotate(u, a)));
        v.push_back(formattedAngle(Rotate(u, -a)));
        return 2;
    }
}

void get_Line_Circle_Intersection(Line L, Circle C, vector<Point> &ans)
{
    double t1, t2;
    double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y;
    double e = a*a + c*c, f = 2*(a*b + c*d), g = b*b + d*d - C.r*C.r;
    double delta = f*f - 4*e*g;
    
    if (dcmp(delta) < 0)    return;
    else if (dcmp(delta) == 0)
    {
        t1 = t2 = -f/2/e;
        ans.push_back(L.point(t1));
    }
    else
    {
        t1 = (-f + sqrt(delta)) / 2 / e;
        t2 = (-f - sqrt(delta)) / 2 / e;
        ans.push_back(L.point(t1)), ans.push_back(L.point(t2));
    }
}

inline double angle(Vector A) { return atan2(A.y, A.x); }

int get_Circle_Circle_Intersection(Circle C1, Circle C2, vector<Point> &v)
{
    double d = Length(C1.c - C2.c);
    if (dcmp(d) == 0)
    {
        if (dcmp(C1.r - C2.r) == 0)    return -1;
        return 0;
    }
    if (dcmp(C1.r + C2.r - d) < 0)    return 0;
    if (dcmp(fabs(C1.r - C2.r) - d) > 0)    return 0;

    double a = angle(C2.c - C1.c);
    double da = acos((C1.r*C1.r + d*d - C2.r*C2.r) / (2*C1.r*d));
    Point p1 = C1.point(a - da), p2 = C1.point(a + da);

    v.push_back(p1);
    if (p1 == p2)    return 1;
    v.push_back(p2);
    return 2;
}

void CircumscribedCircle()
{
    Point P[3];
    for (int i = 0; i < 3; i++)    scanf("%lf%lf", &P[i].x, &P[i].y);

    Point c = Get_Line_Intersect((P[0] + P[1])/2, Rotate(P[1] - P[0], PI/2), (P[2] + P[0])/2, Rotate(P[2] - P[0], -PI/2));

    printf("(%.6lf,%.6lf,%.6lf)
", c.x, c.y, Length(c - P[0]));
}

void InscribedCircle()
{
    Point P[3];
    for (int i = 0; i < 3; i++)    scanf("%lf%lf", &P[i].x, &P[i].y);

    Vector v1 = Rotate(P[1] - P[0], (Cross(P[2] - P[0], P[1] - P[0]) > 0 ? -1 : 1) * Angle(P[1]-P[0], P[2]-P[0]) / 2);
    Vector v2 = Rotate(P[0] - P[1], (Cross(P[2] - P[1], P[0] - P[1]) > 0 ? -1 : 1) * Angle(P[0]-P[1], P[2]-P[1]) / 2);
    Point c = Get_Line_Intersect(P[0], v1, P[1], v2);

    printf("(%.6lf,%.6lf,%.6lf)
", c.x, c.y, Distance_to_Line(c, P[0], P[1]));    
}

void TangentLineThroughPoint()
{
    Circle C;
    Point P;
    vector<double> v;
    scanf("%lf%lf%lf", &C.c.x, &C.c.y, &C.r);
    scanf("%lf%lf", &P.x, &P.y);

    printf("[");
    if (getTangents(P, C, v))    sort(v.begin(), v.end()), printf("%.6lf", v[0]);
    if (v.size() == 2)    printf(",%.6lf", v[1]);
    printf("]
");
}

void CircleThroughAPointAndTangentToALineWithRadius()
{
    Circle P;
    Point A, B;
    scanf("%lf%lf%lf%lf%lf%lf%lf", &P.c.x, &P.c.y, &A.x, &A.y, &B.x, &B.y, &P.r);

    Line original(A, B - A);
    vector<Point> v;
    get_Line_Circle_Intersection(original.move(P.r), P, v);
    get_Line_Circle_Intersection(original.move(-P.r), P, v);
    sort(v.begin(), v.end());

    printf("[");
    if (v.size())    printf("(%.6lf,%.6lf)", v[0].x, v[0].y);
    for (int i = 1; i < v.size(); i++)    printf(",(%.6lf,%.6lf)", v[i].x, v[i].y);
    printf("]
");
}

inline Point e_to_go(Vector A, double len) { return A / Length(A) * len; }

void CircleTangentToTwoLinesWithRadius()
{
    Point A, B, C ,D;
    double r;
    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);

    vector<Point> v;
    int control = Cross(B - A, D - C) < 0 ? -1 : 1;

    Point P = Get_Line_Intersect(A, B-A, C, D-C);
    double seta = Angle(B - A, D - C)/2;
    Vector v1 = Rotate(B - A, control*seta);
    Vector v2 = Rotate(B - A, -control*(PI/2 - seta));

    v.push_back(P + e_to_go(v1, r/sin(seta)));
    v.push_back(P - e_to_go(v1, r/sin(seta)));
    v.push_back(P + e_to_go(v2, r/cos(seta)));
    v.push_back(P - e_to_go(v2, r/cos(seta)));
    sort(v.begin(), v.end());

    for (int i = 0; i < v.size(); i++)
        printf("%c(%.6lf,%.6lf)", ",["[i == 0], v[i].x, v[i].y);
    printf("]
");
}

void CircleTangentToTwoDisjointCirclesWithRadius()
{
    Circle C1, C2;
    double r;
    scanf("%lf%lf%lf %lf%lf%lf %lf", &C1.c.x, &C1.c.y, &C1.r, &C2.c.x, &C2.c.y, &C2.r, &r);
    C1.r += r, C2.r += r;
    vector<Point> v;
    get_Circle_Circle_Intersection(C1, C2, v);
    sort(v.begin(), v.end());

    if (!v.size())    printf("[");
    for (int i = 0; i < v.size(); i++)
        printf("%c(%.6lf,%.6lf)", ",["[i == 0], v[i].x, v[i].y);
    printf("]
");
}

int main()
{
    string s;
    while (cin >> s)
    {
        if (s.length() < 19)    InscribedCircle();
        else
        {
            switch(s[18])
            {
                case 'e':
                    CircumscribedCircle(); break;
                case 'P':
                    TangentLineThroughPoint(); break;
                case 't':
                    CircleThroughAPointAndTangentToALineWithRadius(); break;
                case 'L':
                    CircleTangentToTwoLinesWithRadius(); break;
                case 'D':
                    CircleTangentToTwoDisjointCirclesWithRadius(); break;
                default : break;
            }
        }
    }
    return 0;
}