XV Open Cup named after E.V. Pankratiev. GP of Siberia-Swimming

给出两个点，找到过这两个点的等角螺线，并求出中间的螺线长

$c = \frac{b}{a}$

$p = a \times c^{\frac{\theta}{angle}}$

对弧线积分

#include <bits/stdc++.h>
using namespace std;
long double eps = 1e-;
struct Point {
    long double x, y;
    Point(long double _x = , long double _y = ) {
        x = _x; y = _y;
    }
    Point operator - (const Point &b) {
        return Point(x - b.x, y - b.y);
    }
}a[];
long double Dot(Point &a, Point b) {
    return a.x * b.x + a.y * b.y;
}
long double len(Point &a) {
    return sqrt(Dot(a, a));
}
int cmp(long double x) {
    if (fabs(x) < eps) return ; return eps > ? : -;
}
int main() {
    for (int i = ; i <= ; ++ i) cin >> a[i].x >> a[i].y;
    a[] = a[] - a[];
    a[] = a[] - a[];
    long double tmp = Dot(a[], a[]);
    long double len1 = len(a[]), len2 = len(a[]);
    if (cmp(tmp - len1 * len2) == ) {
        long double ans = fabs(len1 - len2);
        cout << fixed << setprecision() << ans << '\n';
        return ;
    }
    auto sqr = [&](long double x) -> long double {
        return x * x;
    };
    long double ang = acos(tmp / len1 / len2);
    long double ans = ang * len1;
    if (cmp(len1 - len2)) {
        long double C = len2 / len1;
        ans = (C - ) / log(C) * ans;
        ans = ans * sqrt( + sqr(log(C) / ang));
    }
    cout << fixed << setprecision() << ans << '\n';
}