124 lines
4.9 KiB
C++
124 lines
4.9 KiB
C++
#include <iostream>
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#include <cstdio>
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#include <cstring>
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#include <cstdlib>
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#include <cmath>
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#include <algorithm>
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#define eps 1e-8
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using namespace std;
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#define N 100017
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struct Point{
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double x,y;
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Point(double x=0, double y=0):x(x),y(y) {}
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void input() { scanf("%lf%lf",&x,&y); }
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};
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typedef Point Vector;
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struct Circle{
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Point c;
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double r;
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Circle(){}
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Circle(Point c,double r):c(c),r(r) {}
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Point point(double a) { return Point(c.x + cos(a)*r, c.y + sin(a)*r); }
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void input() { scanf("%lf%lf%lf",&c.x,&c.y,&r); }
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};
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int dcmp(double x) {
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if(x < -eps) return -1;
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if(x > eps) return 1;
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return 0;
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}
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template <class T> T sqr(T x) { return x * x;}
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Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }
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Vector operator - (Vector A, Vector B) { return Vector(A.x - B.x, A.y - B.y); }
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Vector operator * (Vector A, double p) { return Vector(A.x*p, A.y*p); }
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Vector operator / (Vector A, double p) { return Vector(A.x/p, A.y/p); }
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bool operator < (const Point& a, const Point& b) { return a.x < b.x || (a.x == b.x && a.y < b.y); }
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bool operator >= (const Point& a, const Point& b) { return a.x >= b.x && a.y >= b.y; }
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bool operator <= (const Point& a, const Point& b) { return a.x <= b.x && a.y <= b.y; }
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bool operator == (const Point& a, const Point& b) { return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0; }
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double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }
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double Length(Vector A) { return sqrt(Dot(A, A)); }
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double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
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double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }
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Vector VectorUnit(Vector x){ return x / Length(x);}
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Vector Normal(Vector x) { return Point(-x.y, x.x) / Length(x);}
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double angle(Vector v) { return atan2(v.y, v.x); }
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bool OnSegment(Point P, Point A, Point B) {
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return dcmp(Cross(A-P,B-P)) == 0 && dcmp(Dot(A-P,B-P)) < 0;
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}
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double DistanceToSeg(Point P, Point A, Point B)
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{
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if(A == B) return Length(P-A);
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Vector v1 = B-A, v2 = P-A, v3 = P-B;
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if(dcmp(Dot(v1, v2)) < 0) return Length(v2);
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if(dcmp(Dot(v1, v3)) > 0) return Length(v3);
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return fabs(Cross(v1, v2)) / Length(v1);
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}
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double DistanceToLine(Point P, Point A, Point B){
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Vector v1 = B-A, v2 = P-A;
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return fabs(Cross(v1,v2)) / Length(v1);
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}
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Point DisP(Point A, Point B){
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return Length(B-A);
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}
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bool SegmentIntersection(Point A,Point B,Point C,Point D) {
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return max(A.x,B.x) >= min(C.x,D.x) &&
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max(C.x,D.x) >= min(A.x,B.x) &&
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max(A.y,B.y) >= min(C.y,D.y) &&
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max(C.y,D.y) >= min(A.y,B.y) &&
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dcmp(Cross(C-A,B-A)*Cross(D-A,B-A)) <= 0 &&
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dcmp(Cross(A-C,D-C)*Cross(B-C,D-C)) <= 0;
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}
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Point Zero = Point(0,0);
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double TriAngleCircleInsection(Circle C, Point A, Point B)
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{
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Vector OA = A-C.c, OB = B-C.c;
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Vector BA = A-B, BC = C.c-B;
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Vector AB = B-A, AC = C.c-A;
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double DOA = Length(OA), DOB = Length(OB),DAB = Length(AB), r = C.r;
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if(dcmp(Cross(OA,OB)) == 0) return 0;
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if(dcmp(DOA-C.r) < 0 && dcmp(DOB-C.r) < 0) return Cross(OA,OB)*0.5;
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else if(DOB < r && DOA >= r) {
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double x = (Dot(BA,BC) + sqrt(r*r*DAB*DAB-Cross(BA,BC)*Cross(BA,BC)))/DAB;
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double TS = Cross(OA,OB)*0.5;
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return asin(TS*(1-x/DAB)*2/r/DOA)*r*r*0.5+TS*x/DAB;
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}
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else if(DOB >= r && DOA < r) {
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double y = (Dot(AB,AC)+sqrt(r*r*DAB*DAB-Cross(AB,AC)*Cross(AB,AC)))/DAB;
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double TS = Cross(OA,OB)*0.5;
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return asin(TS*(1-y/DAB)*2/r/DOB)*r*r*0.5+TS*y/DAB;
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}
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else if(fabs(Cross(OA,OB)) >= r*DAB || Dot(AB,AC) <= 0 || Dot(BA,BC) <= 0) {
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if(Dot(OA,OB) < 0) {
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if(Cross(OA,OB) < 0) return (-acos(-1.0)-asin(Cross(OA,OB)/DOA/DOB))*r*r*0.5;
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else return ( acos(-1.0)-asin(Cross(OA,OB)/DOA/DOB))*r*r*0.5;
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}
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else return asin(Cross(OA,OB)/DOA/DOB)*r*r*0.5;
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}
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else {
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double x = (Dot(BA,BC)+sqrt(r*r*DAB*DAB-Cross(BA,BC)*Cross(BA,BC)))/DAB;
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double y = (Dot(AB,AC)+sqrt(r*r*DAB*DAB-Cross(AB,AC)*Cross(AB,AC)))/DAB;
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double TS = Cross(OA,OB)*0.5;
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return (asin(TS*(1-x/DAB)*2/r/DOA)+asin(TS*(1-y/DAB)*2/r/DOB))*r*r*0.5 + TS*((x+y)/DAB-1);
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}
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}
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Point p[507],A,B;
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int main()
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{
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int n,i,j,cs = 1;
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double k;
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while(scanf("%d%lf",&n,&k)!=EOF)
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{
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for(i=1;i<=n;i++) p[i].input();
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A.input(), B.input(), p[n+1] = p[1];
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double D = (2.0*k*k*A.x-2.0*B.x)/(1.0-k*k);
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double E = (2.0*k*k*A.y-2.0*B.y)/(1.0-k*k);
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double F = (B.x*B.x+B.y*B.y-k*k*(A.x*A.x+A.y*A.y))/(1.0-k*k);
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Circle C = Circle(Point(-D*0.5,-E*0.5),sqrt(D*D+E*E-4.0*F)*0.5);
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double ans = 0.0;
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for(i=1;i<=n;i++)
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ans += TriAngleCircleInsection(C, p[i], p[i+1]);
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printf("Case %d: %.10f\n",cs++,fabs(ans));
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}
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return 0;
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}
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