ACM計算幾何--三角形問題
阿新 • • 發佈:2019-01-26
#include <math.h> struct point{double x,y;}; struct line{point a,b;}; double distance(point p1,point p2){ return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y)); } point intersection(line u,line v){ point ret=u.a; double t=((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x)) /((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x)); ret.x+=(u.b.x-u.a.x)*t; ret.y+=(u.b.y-u.a.y)*t; return ret; } //外心 point circumcenter(point a,point b,point c){ line u,v; u.a.x=(a.x+b.x)/2; u.a.y=(a.y+b.y)/2; u.b.x=u.a.x-a.y+b.y; u.b.y=u.a.y+a.x-b.x; v.a.x=(a.x+c.x)/2; v.a.y=(a.y+c.y)/2; v.b.x=v.a.x-a.y+c.y; v.b.y=v.a.y+a.x-c.x; return intersection(u,v); } //內心 point incenter(point a,point b,point c){ line u,v; double m,n; u.a=a; m=atan2(b.y-a.y,b.x-a.x); n=atan2(c.y-a.y,c.x-a.x); u.b.x=u.a.x+cos((m+n)/2); u.b.y=u.a.y+sin((m+n)/2); v.a=b; m=atan2(a.y-b.y,a.x-b.x); n=atan2(c.y-b.y,c.x-b.x); v.b.x=v.a.x+cos((m+n)/2); v.b.y=v.a.y+sin((m+n)/2); return intersection(u,v); } //垂心 point perpencenter(point a,point b,point c){ line u,v; u.a=c; u.b.x=u.a.x-a.y+b.y; u.b.y=u.a.y+a.x-b.x; v.a=b; v.b.x=v.a.x-a.y+c.y; v.b.y=v.a.y+a.x-c.x; return intersection(u,v); } //重心 //到三角形三頂點距離的平方和最小的點 //三角形內到三邊距離之積最大的點 point barycenter(point a,point b,point c){ line u,v; u.a.x=(a.x+b.x)/2; u.a.y=(a.y+b.y)/2; u.b=c; v.a.x=(a.x+c.x)/2; v.a.y=(a.y+c.y)/2; v.b=b; return intersection(u,v); } //費馬點 //到三角形三頂點距離之和最小的點 point fermentpoint(point a,point b,point c){ point u,v; double step=fabs(a.x)+fabs(a.y)+fabs(b.x)+fabs(b.y)+fabs(c.x)+fabs(c.y); int i,j,k; u.x=(a.x+b.x+c.x)/3; u.y=(a.y+b.y+c.y)/3; while (step>1e-10) for (k=0;k<10;step/=2,k++) for (i=-1;i<=1;i++) for (j=-1;j<=1;j++){ v.x=u.x+step*i; v.y=u.y+step*j; if (distance(u,a)+distance(u,b)+distance(u,c)>distance(v,a)+distance(v,b)+distance(v,c)) u=v; } return u; } //求曲率半徑 三角形內最大可圍成面積 #include<iostream> #include<cmath> using namespace std; const double pi=3.14159265358979; int main() { double a,b,c,d,p,s,r,ans,R,x,l; int T=0; while(cin>>a>>b>>c>>d&&a+b+c+d) { T++; l=a+b+c; p=l/2; s=sqrt(p*(p-a)*(p-b)*(p-c)); R= s /p; if (d >= l) ans = s; else if(2*pi*R>=d) ans=d*d/(4*pi); else { r = (l-d)/((l/R)-(2*pi)); x = r*r*s/(R*R); ans = s - x + pi * r * r; } printf("Case %d: %.2lf\n",T,ans); } return 0; }