1503: 点到圆弧的距离

分析：

先判断点和圆心的连线是否在圆弧范围内，如果在，最短距离即到圆心的距离减去半径的绝对值；反之，为到端点的最短距离。

具体看注释

#include
using namespace std;

#define eps 1e-8
const double pi=acos(-1);

struct Point
{
double x,y;
Point(double a=0,double b=0)
{
x=a;
y=b;
}
};

Point operator - (Point a,Point b)
{
return Point(a.x-b.x,a.y-b.y);
}

double dist(Point a,Point b)
{
return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}

double multi(Point a,Point b)
{
return a.x*b.x+a.y*b.y;
}

double cross(Point a,Point b)
{
return a.x*b.y-a.y*b.x;
}

Point TriangleCircumCenter(Point a,Point b,Point c)
{
Point res;
double a1=atan2(b.y-a.y,b.x-a.x)+pi/2;
double a2=atan2(c.y-b.y,c.x-b.x)+pi/2;
double ax=(a.x+b.x)/2;
double ay=(a.y+b.y)/2;
double bx=(c.x+b.x)/2;
double by=(c.y+b.y)/2;
double r1=(sin(a2)*(ax-bx)+cos(a2)*(by-ay))/(sin(a1)*cos(a2)-sin(a2)*cos(a1));
return Point(ax+r1*cos(a1),ay+r1*sin(a1));
}

int main()
{
// freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
int x1,y1,x2,y2,x3,y3,xp,yp;
int kase=0;
while(~scanf("%d%d%d%d%d%d%d%d",&x1,&y1,&x2,&y2,&x3,&y3,&xp,&yp))
{
Point p1=Point(x1,y1);
Point p2=Point(x2,y2);
Point p3=Point(x3,y3);
Point pp=Point(xp,yp);
Point pc=TriangleCircumCenter(p1,p2,p3); //算圆心
double temp=cross(p2-p1,p3-p1);
if(temp<0) //如果是顺时针，把p1和p3点互换 { Point t=p1; p1=p3; p3=t; } double cosA=multi(p1-pc,p3-pc)/(dist(p1,pc)*dist(p3,pc)); if(fabs(cosA)>1) //如果fabs(cosA)>1，那么acos(cosA)算出的结果是不合法的
{
if(cosA<0) cosA+=eps; else cosA-=eps; } double maxd=acos(cosA); //算p1-pc与p3-pc的夹角 if(cross(p1-pc,p3-pc)<0 && fabs(cross(p1-pc,p3-pc))>eps)
maxd=2*pi-maxd;
double cosB=multi(p1-pc,pp-pc)/(dist(p1,pc)*dist(pp,pc));
if(fabs(cosB)>1)
{
if(cosB<0) cosB+=eps; else cosB-=eps; } double degree=acos(cosB); //算p1-pc与pp-pc的夹角 if(cross(p1-pc,pp-pc)<0 && fabs(cross(p1-pc,pp-pc))>eps)
degree=2*pi-degree;
if(degree<maxd)
printf("Case %d: %.3lf\n",++kase,fabs(dist(pp,pc)-dist(p1,pc)));
else
printf("Case %d: %.3lf\n",++kase,min(dist(pp,p1),dist(pp,p3)));
}
return 0;
}