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

Posted 2021-02-15 tempestt

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

$c = frac{b}{a}$

$p = a imes c^{frac{ heta}{angle}}$

对弧线积分

 

#include <bits/stdc++.h>
using namespace std;
long double eps = 1e-8;
struct Point {
    long double x, y;
    Point(long double _x = 0, long double _y = 0) {
        x = _x; y = _y;
    } 
    Point operator - (const Point &b) {
        return Point(x - b.x, y - b.y);
    }
}a[4];
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 0; return eps > 0? 1: -1;
}
int main() {
    for (int i = 1; i <= 3; ++ i) cin >> a[i].x >> a[i].y;
    a[1] = a[1] - a[3];
    a[2] = a[2] - a[3];
    long double tmp = Dot(a[1], a[2]);
    long double len1 = len(a[1]), len2 = len(a[2]);
    if (cmp(tmp - len1 * len2) == 0) {
        long double ans = fabs(len1 - len2);
        cout << fixed << setprecision(12) << ans << ‘
‘;
        return 0;
    }
    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 - 1) / log(C) * ans; 
        ans = ans * sqrt(1 + sqr(log(C) / ang));
    }
    cout << fixed << setprecision(12) << ans << ‘
‘;
}