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-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 << '\n';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 << '\n';
}

转载于:https://www.cnblogs.com/tempestT/p/10673163.html

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