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| #include <cstdio>
#include <iostream>
#include <cmath>
#include <algorithm>
long long read()
{
char last = '+', ch = getchar();
while (ch < '0' || ch > '9') last = ch, ch = getchar();
long long tmp = 0;
while (ch >= '0' && ch <= '9') tmp = tmp * 10 + ch - 48, ch = getchar();
if (last == '-') tmp = -tmp;
return tmp;
}
struct point
{
double x, y;
};
struct circle
{
point o;
double r;
};
const double eps = 1e-12;
const double pi = acos(-1);
const int _n = 100 + 10;
int T, n;
circle ci[_n];
int now, nxt;
double angle, nxtangle, ndl;
double ans;
double abss(double x)
{
return x > 0 ? x : -x;
}
bool equal(double x, double y)
{
return abss(x - y) < eps;
}
double ad(double ang)
{
if (ang < 0.0)
{
ang += 2 * pi;
}
if (ang - 2 * pi > eps)
{
ang -= 2 * pi;
}
if (equal(ang, 0.0))
{
ang = 2 * pi;
}
return ang;
}
double a(point x, point y)
{
double ang;
if (equal(x.x, y.x))
{
if (x.y - y.y > eps)
{
ang = pi / 2 * 3;
}
else
{
ang = pi / 2;
}
}
else
{
ang = atan((y.y - x.y) / (y.x - x.x));
if (x.x - y.x > eps)
{
ang = ang + pi;
}
}
return ad(ang);
}
double d(point x, point y)
{
return sqrt((x.x - y.x) * (x.x - y.x) + (x.y - y.y) * (x.y - y.y));
}
double dl(circle c1, circle c2)
{
double dis = d(c1.o, c2.o);
double dr = abss(c1.r - c2.r);
return sqrt(dis * dis - dr * dr);
}
bool comp(circle x, circle y)
{
return x.r - y.r > eps;
}
void calc(int i1, int i2)
{
circle c1 = ci[i1];
circle c2 = ci[i2];
double del;
if (equal(c1.r, c2.r))
{
del = pi / 2;
}
else
{
if (c1.r - c2.r > eps)
{
del = acos((c1.r - c2.r) / d(c1.o, c2.o));
}
else
{
del = asin((c2.r - c1.r) / d(c1.o, c2.o)) + pi / 2;
}
}
double ali = a(c1.o, c2.o);
double ang = ad(ali - del);
if (ang - angle > eps)
{
if (nxtangle - ang > eps)
{
nxtangle = ang;
nxt = i2;
ndl = dl(c1, c2);
}
else
{
if (equal(ang, nxtangle) && dl(c1, c2) - ndl > eps)
{
nxtangle = ang;
nxt = i2;
ndl = dl(c1, c2);
}
}
}
ang = ad(ali + del);
if (ang - angle > eps)
{
if (nxtangle - ang > eps)
{
nxtangle = ang;
nxt = i2;
ndl = dl(c1, c2);
}
else
{
if (equal(ang, nxtangle) && dl(c1, c2) - ndl > eps)
{
nxtangle = ang;
nxt = i2;
ndl = dl(c1, c2);
}
}
}
}
void solve()
{
scanf("%d", &n);
for (int i = 1; i <= n; i++)
{
ci[i].o.x = (double)1.0 * read();
ci[i].o.y = (double)1.0 * read();
ci[i].r = (double)1.0 * read();
}
std::sort(ci + 1, ci + n + 1, comp);
int nn = 1;
for (int i = 2; i <= n; i++)
{
bool F = true;
for (int j = 1; j <= nn; j++)
{
double dis = d(ci[j].o, ci[i].o);
if (ci[j].r - ci[i].r - dis > eps || equal(ci[i].r + dis, ci[j].r))
{
F = false;
break;
}
}
if (F == true)
{
nn++;
ci[nn] = ci[i];
}
}
n = nn;
if (n == 1)
{
printf("%.10lf\n", (double)(2 * pi * ci[1].r));
return;
}
double right = -1000000000.0;
for (int i = 1; i <= n; i++)
{
if (ci[i].o.x + ci[i].r - right > eps)
{
right = ci[i].o.x + ci[i].r;
now = i;
}
else
{
if (equal(ci[i].o.x + ci[i].r, right) && ci[i].o.y - ci[now].o.y > eps)
{
now = i;
}
}
}
ans = 0.0;
angle = 0.0;
int beg = now;
while (true)
{
nxtangle = 1000000000.0;
nxt = now;
ndl = 1000000000.0;
for (int i = 1; i <= n; i++)
{
if (i != now)
{
calc(now, i);
}
}
double dang = nxtangle - angle;
ans = ans + dang * ci[now].r;
ans = ans + ndl;
angle = nxtangle;
now = nxt;
if (now == beg)
{
break;
}
}
ans = ans + (2 * pi - angle) * ci[now].r;
printf("%.10lf\n", (double)ans);
}
int main()
{
scanf("%d", &T);
while (T--)
{
solve();
}
return 0;
}
|