1 typedef long double LD; | 1 // Verified: partly by geocon2013 D(1). 2 typedef complex<LD> CMP; < 3 2 > 3 // Crosspoing of a line (not lineseg!) and a circle). 4 bool line_circle(CMP la, CMP lb, CMP c, LD r, CMP* p1, CMP* p2) | 4 bool line_circle(CMP la, CMP lb, CMP c, double r, CMP* p1, CMP* p2) 5 { 5 { 6 CMP v = (lb-la) / abs(lb-la); 6 CMP v = (lb-la) / abs(lb-la); 7 CMP o = (c-la) / v; 7 CMP o = (c-la) / v; 8 if( abs(o.imag()) > r ) 8 if( abs(o.imag()) > r ) 9 return false; 9 return false; 10 LD dx = sqrt(r*r - o.imag()*o.imag()); | 10 double dx = sqrt(r*r - o.imag()*o.imag()); 11 *p1 = la + (o.real()-dx)*v; 11 *p1 = la + (o.real()-dx)*v; 12 *p2 = la + (o.real()+dx)*v; 12 *p2 = la + (o.real()+dx)*v; 13 return true; 13 return true; 14 } 14 } > 15 > 16 // Whether or not |p| is in the circle (c, r). > 17 bool pt_in_circle(CMP p, CMP c, double r) > 18 { > 19 return norm(p-c) <= r*r; > 20 } > 21 > 22 // Assuming |o| is outside (C,r), compute the two tangent points. > 23 void sessen(CMP o, CMP c, double r, CMP* p1, CMP* p2) > 24 { > 25 double len = sqrt(norm(c-o) - r*r); > 26 double theta = asin(r/abs(c-o)); > 27 > 28 if(p1) *p1 = o+(c-o)*polar(len/abs(c-o), theta); > 29 if(p2) *p2 = o+(c-o)*polar(len/abs(c-o), -theta); > 30 } > 31 > 32 // For two points |p| and |q| on (c,r), compute their distance along the circle. > 33 double d_on_c(CMP c, double r, CMP p, CMP q) > 34 { > 35 return abs(arg((p-c) / (q-c))) * r; > 36 }