csuoj 1503: 点到圆弧的距离

  1 #include<cstdio>
  2 #include<cstring>
  3 #include<iostream>
  4 #include<algorithm>
  5 #include<cmath>
  6 using namespace std;
  7 const double eps = 1e-6,PI = acos(-1.0);
  8 
  9 struct Point
 10 {
 11     double x,y;
 12     friend Point operator - (Point a,Point b)
 13     {
 14         Point temp;
 15         temp.x = a.x - b.x;
 16         temp.y = a.y - b.y;
 17         return temp;
 18     }
 19 };
 20 
 21 Point p1,p2,p3,pc,pp;
 22 double r;
 23 
 24 Point get_pc1(Point p1, Point p2, Point p3)    //求圆心
 25 {
 26   Point p;
 27   if(fabs(p1.y-p2.y) > eps)      //因为计算过程中有出现(y2-y1)做分母的情况，所以这里分了两种情况讨论
 28   {
 29  //      double t1 = p3.x*p3.x - p1.x*p1.x+p3.y*p3.y-p1.y*p1.y-((p3.y-p1.y)*(p1.x*p1.x-p2.x*p2.x+p1.y*p1.y-p2.y*p2.y)) / (p2.y-p1.y);
 30    //    double t2 = 2.0*(p3.x-p1.x)-(2*(p3.y-p1.y)*(p2.x-p1.x)) / (p2.y-p1.y);
 31         double  t1 = (p2.x*p2.x-p1.x*p1.x+p2.y*p2.y-p1.y*p1.y) *(p3.y-p1.y) - (p2.y-p1.y)*(p3.x*p3.x-p1.x*p1.x+p3.y*p3.y-p1.y*p1.y);
 32         double t2 = 2.0*((p3.y-p1.y)*(p2.x-p1.x) - (p2.y-p1.y)*(p3.x-p1.x));
 33        p.x = t1 / t2;
 34        p.y = (p2.x*p2.x-p1.x*p1.x+p2.y*p2.y-p1.y*p1.y-2*(p2.x-p1.x)*p.x) / (2*(p2.y-p1.y));
 35     }
 36     else
 37     {
 38         p.x = (p2.x*p2.x-p1.x*p1.x+p2.y*p2.y-p1.y*p1.y) / (2*(p2.x-p1.x));
 39         p.y = (p3.x*p3.x-p1.x*p1.x+p3.y*p3.y-p1.y*p1.y-2*(p3.x-p1.x)*p.x) / (2*(p3.y-p1.y));
 40     }
 41     return p;
 42 }
 43 double dis(Point a,Point b)
 44 {
 45     return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y));
 46 }
 47 double mult_ca(Point p1,Point p2)   //叉乘
 48 {
 49     return p1.x * p2.y - p2.x * p1.y;
 50 }
 51 
 52 double get_ans(Point pc,Point pp,Point p1,Point p2,Point p3)
 53 {
 54     double temp = mult_ca(p2-p1,p3-p1);
 55     double f1 = atan2((p1-pc).x,(p1-pc).y);
 56     double f2 = atan2((p3-pc).x,(p3-pc).y);
 57     double f3 = atan2((p2-pc).x,(p2-pc).y);
 58     double f4 = atan2((pp-pc).x,(pp-pc).y);
 59     double ans1 = fabs(dis(pp,pc)-dis(p1,pc));
 60     double ans2 = min(dis(pp,p1),dis(pp,p3));
 61     if(temp < 0)    //顺时针给点
 62     {
 63         if(f1 < f2)      //判断区间方向，这样有利于判断p点和p2点是不是在同一个区间
 64         {
 65             if((f3 >= f1 && f3 <= f2) == (f4 >= f1 && f4 <= f2) ) return ans1;
 66             else return ans2;
 67         }
 68         else
 69         {
 70             if((f3 >= f2 && f3 <= f1) == (f4 >=f2 && f4 <= f1) ) return ans1;
 71             else return ans2;
 72         }
 73     }
 74     else
 75     {
 76         if(f2 < f1)
 77         {
 78             if((f3 >= f2 && f3 <= f1) == (f4 >= f2 && f4 <= f1) ) return ans1;
 79             else return ans2;
 80         }
 81         else
 82         {
 83             if((f3 >= f1 && f3 <= f2) == (f4 >= f1 && f4 <= f2)) return ans1;
 84             else return ans2;
 85         }
 86     }
 87 }
 88 
 89 int main()
 90 {
 91   //   freopen("in","r",stdin);
 92     int kase = 1;
 93     while(scanf("%lf%lf%lf%lf%lf%lf%lf%lf",&p1.x,&p1.y,&p2.x,&p2.y,&p3.x,&p3.y,&pp.x,&pp.y)!=EOF)
 94     {
 95         pc = get_pc1(p1,p2,p3);
 96         double ans = get_ans(pc,pp,p1,p2,p3);
 97         printf("Case %d: %.3lf\n",kase++,ans);
 98     }
 99     return 0;
100 }

 1 // Rujia Liu
 2 #include<cmath>
 3 #include<cstdio>
 4 #include<iostream>
 5 
 6 using namespace std;
 7 
 8 const double PI = acos(-1.0);
 9 const double TWO_PI = 2 * PI;
10 const double eps = 1e-6;
11 
12 inline double NormalizeAngle(double rad, double center = PI) {
13   return rad - TWO_PI * floor((rad + PI - center) / TWO_PI);
14 }
15 
16 inline int dcmp(double x) {
17   if(fabs(x) < eps) return 0; else return x < 0 ? -1 : 1;
18 }
19 
20 struct Point {
21   double x, y;
22   Point(double x=0, double y=0):x(x),y(y) { }
23 };
24 
25 typedef Point Vector;
26 
27 inline Vector operator + (Vector A, Vector B) { return Vector(A.x+B.x, A.y+B.y); }
28 inline Vector operator - (Point A, Point B) { return Vector(A.x-B.x, A.y-B.y); }
29 
30 inline double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }
31 inline double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }
32 inline double Length(Vector A) { return sqrt(Dot(A, A)); }
33 
34 // 外接圆圆心。假定三点不共线
35 Point get_circumscribed_center(Point p1, Point p2, Point p3) {
36   double bx = p2.x - p1.x;
37   double by = p2.y - p1.y;
38   double cx = p3.x - p1.x;
39   double cy = p3.y - p1.y;
40   double d = 2 * (bx * cy - by * cx);
41   Point p;
42   p.x = (cy * (bx * bx + by * by) - by * (cx * cx + cy * cy)) / d + p1.x;
43   p.y = (bx * (cx * cx + cy * cy) - cx * (bx * bx + by * by)) / d + p1.y;
44   return p;
45 }
46 
47 double DistanceToArc(Point a, Point start, Point mid, Point end) {
48   Point p = get_circumscribed_center(start, mid, end);
49   bool CCW = dcmp(Cross(mid - start, end - start)) > 0;
50   double ang_start = atan2(start.y-p.y, start.x-p.x);
51   double ang_end = atan2(end.y-p.y, end.x-p.x);
52   double r = Length(p - start);
53   double ang = atan2(a.y-p.y, a.x-p.x);
54   bool inside;
55   if(CCW) {
56     inside = NormalizeAngle(ang - ang_start) < NormalizeAngle(ang_end - ang_start);
57   } else {
58     inside = NormalizeAngle(ang - ang_end) < NormalizeAngle(ang_start - ang_end);
59   }
60   if(inside) {
61     return fabs(r - Length(p - a));
62   }
63   return min(Length(a - start), Length(a - end));
64 }
65 
66 int main() {
67   int kase = 0;
68   double x1, y1, x2, y2, x3, y3, xp, yp;
69   while(cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3 >> xp >> yp) {
70     double ans = DistanceToArc(Point(xp,yp), Point(x1,y1), Point(x2,y2), Point(x3,y3));
71     printf("Case %d: %.3lf\n", ++kase, ans);
72   }
73   return 0;
74 }