ASC7 Problem F. Little Mammoth

题目大意

求矩形和圆的交

简要题解

嚯嚯嚯，我会暴力积分！

调了一整天参数，Wrong Answer on Test 2.

爆粗口了，真是没办法，谁叫我弱呢。。

老老实实写精确做法吧。

其实要求的就是三角形和圆的交嘛，9种情况全部讨论一下就好~

啊摔！去你大爷的，你知道这有多难写吗？？

有向面积大法好~

来看三张图就明白了~

来源地址

然后就愉快地写呗~

好久没写计算几何了，不过好像我都会实现欸。

然后写完了，好开心~

然后对拍，拍一次错一次，爆粗口×2

要知道我为这道傻缺题已经花了两天了。

血的教训：计算几何千万不要觉得是对的就写，细节会让你明白，你写的全是错的。

所以，有板子就上板子，现推什么的出错的概率太高了。

写完后我发现，这道题我写的调试代码长度是源代码长度的两倍。。爆粗口×3

最坑的地方就是有相交时的处理，GeoGebra是个好软件，可也架不住我个智障选手啊。。

拍了n次，画了n张图，然后发现愚蠢的错误爆n次粗口，然后在图书馆众目睽睽之下抽自己n次耳光。

终于Accept了~ 

#include <bits/stdc++.h>
using namespace std;
namespace my_header {
#define pb push_back
#define mp make_pair
#define pir pair<int, int>
#define vec vector<int>
#define pc putchar
#define clr(t) memset(t, 0, sizeof t)
#define pse(t, v) memset(t, v, sizeof t)
#define bl puts("")
#define wn(x) wr(x), bl
#define ws(x) wr(x), pc(' ')
    const int INF = 0x3f3f3f3f;
    typedef long long LL;
    typedef double DB;
    inline char gchar() {
        char ret = getchar();
        for(; (ret == '
' || ret == '
' || ret == ' ') && ret != EOF; ret = getchar());
        return ret; }
    template<class T> inline void fr(T &ret, char c = ' ', int flg = 1) {
        for(c = getchar(); (c < '0' || '9' < c) && c != '-'; c = getchar());
        if (c == '-') { flg = -1; c = getchar(); }
        for(ret = 0; '0' <= c && c <= '9'; c = getchar())
            ret = ret * 10 + c - '0';
        ret = ret * flg; }
    inline int fr() { int t; fr(t); return t; }
    template<class T> inline void fr(T&a, T&b) { fr(a), fr(b); }
    template<class T> inline void fr(T&a, T&b, T&c) { fr(a), fr(b), fr(c); }
    template<class T> inline char wr(T a, int b = 10, bool p = 1) {
        return a < 0 ? pc('-'), wr(-a, b, 0) : (a == 0 ? (p ? pc('0') : p) : 
            (wr(a/b, b, 0), pc('0' + a % b)));
    }
    template<class T> inline void wt(T a) { wn(a); }
    template<class T> inline void wt(T a, T b) { ws(a), wn(b); }
    template<class T> inline void wt(T a, T b, T c) { ws(a), ws(b), wn(c); }
    template<class T> inline void wt(T a, T b, T c, T d) { ws(a), ws(b), ws(c), wn(d); }
    template<class T> inline T gcd(T a, T b) {
        return b == 0 ? a : gcd(b, a % b); }
    template<class T> inline T fpw(T b, T i, T _m, T r = 1) {
        for(; i; i >>= 1, b = b * b % _m)
            if(i & 1) r = r * b % _m;
        return r; }
};
using namespace my_header;


const DB PI = 3.1415926535897932384626;
const DB EPS = 1e-6;
int sgn(DB x) {
    return x < -EPS ? -1 : EPS < x;
}

#define Vector Point
struct Point {
    DB x, y;
    Point() {}
    Point(DB x, DB y):x(x), y(y) {}
    Vector operator + (Vector);
    Vector operator - (Vector);
    Vector operator * (DB);
    Vector operator / (DB);
    DB getCross(Vector);
    DB getDot(Vector);
    DB getLength();
    DB getAngle(Vector);
    Vector getNorm();
    Vector Rotate(DB);
};

    
struct Circle {
    Point o;
    DB r;
    DB getSectorArea(DB);
    vector<Point> getSegmentIntersection(Point, Point);
};

DB getSegmentCirlcleProjectionArea(Circle, Point, Point);
DB getTriangleCircleIntersectionArea(Circle, Point, Point, Point);
bool onSegment(Point, Point, Point);

int main() {
#ifdef lol
    freopen("F.in", "r", stdin);
    freopen("F.out", "w", stdout);
#else
    freopen("mammoth.in", "r", stdin);
    freopen("mammoth.out", "w", stdout);
#endif

    Circle c;
    Point a, b;
    cin >> c.o.x >> c.o.y >> c.r;
    cin >> a.x >> a.y;
    cin >> b.x >> b.y;
    if (b.x < a.x) swap(a.x, b.x);
    if (b.y < a.y) swap(a.y, b.y);

    DB ans = 0;
    ans += getTriangleCircleIntersectionArea(c, a, Point(a.x, b.y), b);
    ans += getTriangleCircleIntersectionArea(c, a, Point(b.x, a.y), b);
    printf("%.8lf
", ans);
    return 0;
}

DB getSegmentCirlcleProjectionArea(Circle C, Point a, Point b) {
    vector<Point> t = C.getSegmentIntersection(a, b);
    if (t.size() == 0) {
        if ((a - C.o).getLength() < C.r + EPS && (b - C.o).getLength() < C.r + EPS)
            return (a - C.o).getCross(b - C.o) / 2;
        return C.getSectorArea((a - C.o).getAngle(b - C.o));
    }
    if (t.size() == 1) {
        Point c = t.at(0);
        if ((a - C.o).getLength() <= C.r) {
            return C.getSectorArea((c - C.o).getAngle(b - C.o)) + (a - C.o).getCross(c - C.o) / 2;
        }
        else {
            return C.getSectorArea((a - C.o).getAngle(c - C.o)) + (c - C.o).getCross(b - C.o) / 2;
        }
    }
    return C.getSectorArea((a - C.o).getAngle(t[0] - C.o)) + (t[0] - C.o).getCross(t[1] - C.o) / 2 + C.getSectorArea((t[1] - C.o).getAngle(b - C.o));
}

DB getTriangleCircleIntersectionArea(Circle C, Point a, Point b, Point c) {
    DB res = 0;
    res += getSegmentCirlcleProjectionArea(C, a, b);
    res += getSegmentCirlcleProjectionArea(C, b, c);
    res += getSegmentCirlcleProjectionArea(C, c, a);
    return fabs(res);
}

Vector Vector::operator + (Vector b) {
    return Vector(x + b.x, y + b.y);
}
Vector Vector::operator - (Vector b) {
    return Vector(x - b.x, y - b.y);
}
Vector Vector::operator * (DB b) {
    return Vector(x * b, y * b);
}
Vector Vector::operator / (DB b) {
    return Vector(x / b, y / b);
}
DB Vector::getCross(Vector b) {
    return x * b.y - y * b.x;
}
DB Vector::getDot(Vector b) {
    return x * b.x + y * b.y;
}
DB Vector::getLength() {
    return sqrt(this->getDot(*this));
}
Vector Vector::Rotate(DB ang) {
    DB c = cos(ang), s = sin(ang);
    return Vector(c * x - s * y, s * x + c * y);
}
Vector Vector::getNorm() {
    DB l = this->getLength();
    return Vector(x / l, y / l);
}
DB Vector::getAngle(Vector b) {
    DB t = atan2(b.y, b.x) - atan2(y, x);
    while (t > PI)
        t -= 2 * PI;
    while (t < -PI)
        t += 2 * PI;
    return t;
}

bool onSegment(Point a, Point b, Point c) {
    return sgn((c - a).getDot(b - a)) > 0 && sgn((c - b).getDot(a - b)) > 0;
}

DB Circle::getSectorArea(DB ang) {
    return ang * r * r / 2;
}
vector<Point> Circle::getSegmentIntersection(Point a, Point b) {
    vector<Point> res;
    Point p = a + (b - a).getNorm() * (b - a).getDot(o - a) / (b - a).getLength();
    if ((p - o).getLength() >= r)
        return res;
    DB d = sqrt(r * r - (p - o).getDot(p - o));
    Vector tmp = (b - a).getNorm() * d;
    if (onSegment(a, b, p - tmp))
        res.push_back(p - tmp);
    if (onSegment(a, b, p + tmp))
        res.push_back(p + tmp);
    return res;
}