ZOJ3663_Polaris of Pandora 2012 ICPC Changchun Site I 题

先是用经纬度算，调了很久，实在不会如何用经纬度求交点，百度谷歌也找不到。用三分法求了交点，有问题。。。

不得已各种三角函数反三角函数坐标旋转神马的都用上了，硬是求出三维坐标系的各种点再算，精度都不知损到哪里去了，竟然能AC了。。。

1、算临界线的纬度

2、判断行程所在平面的“斜率”是否能与临界线相交，不相交则100.000

3、把行程平面的x方向旋转到x轴正方向算出与临界线交点，再在临界面旋转到行程面与临界面交点

4、用球面距离和z坐标结合判断计算区间。

 1 #include<stdio.h>

 2  #include<string.h>

 3  #include<stdlib.h>

 4  #include<math.h>

 5  #include<vector>

 6  #include<list>

 7  #include<algorithm>

 8  #include<iostream>

 9  using namespace std;

10  const double eps = 1e-8;

11  const double pi = acos(-1.0);

12  inline int dcmp(double x){return (x > eps) - (x < -eps);}

13  inline double pz(double x) {return dcmp(x) ? x : 0;}

14  inline double Sqr(double x) {return x * x;}

15  inline double pcs(double x) {return x > 1 ? 1 : (x < -1 ? -1 : x);}

16  struct Point3

17  {

18      double x, y, z;

19      Point3(){x = y = z = 0;}

20      Point3(double a, double b, double c){x = a, y = b, z = c;}

21      Point3 cross(Point3 p){return

22          Point3(y * p.z - p.y * z, z * p.x - x * p.z, x * p.y - y * p.x);}

23      double dot(Point3 p){return x * p.x + y * p.y + z * p.z;}

24      Point3 operator-(const Point3 &p)const{return Point3(x - p.x, y - p.y, z - p.z);}

25      Point3 operator-()const{return Point3(-x, -y, -z);}

26      Point3 operator+(const Point3 &p)const{return Point3(x + p.x, y + p.y, z + p.z);}

27      Point3 operator*(const double &b)const{return Point3(x * b, y * b, z * b);}

28      Point3 operator/(const double &b)const{return Point3(x / b, y / b, z / b);}

29      Point3 fxl(Point3 b, Point3 c){return (*this - b).cross(b - c);}

30      double Dis(Point3 b){return sqrt((*this - b).dot(*this - b));}

31      double Rdis(Point3 b, double R){return R * asin(pcs((*this).Dis(b) * 0.5 / R)) * 2;}

32      double vlen(){return sqrt(dot(*this));}

33      Point3 RotePoint(const Point3 &p, double ang)

34      {

35          return Point3((p.x - x) * cos(ang) - (p.y - y) * sin(ang) + x,

36                  (p.x - x) * sin(ang) + (p.y - y) * cos(ang) + y, p.z);

37      }

38  };

39  double R, H, lat1, lng1, lat2, lng2, lat;

40  inline double p2cross(const Point3 &a, const Point3 &b, const Point3 &c)

41  {return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y);}

42  Point3 r(0, 0, 0);

43  int main()

44  {

45      while(scanf("%lf%lf%lf%lf%lf%lf", &R, &H, &lat1, &lng1, &lat2, &lng2) != EOF)

46      {

47          double R_ = R; lat = acos(R / (R + H)); R += H;

48          lat1 += pi * 0.5, lat2 += pi * 0.5;

49          Point3 s(R * sin(lat1) * cos(lng1), R * sin(lat1) * sin(lng1), R * cos(lat1));

50          Point3 e(R * sin(lat2) * cos(lng2), R * sin(lat2) * sin(lng2), R * cos(lat2));

51          Point3 f = r.fxl(s, e);

52          double as = asin(pcs(fabs(f.cross(Point3(0, 0, 100)).vlen() / f.vlen() / 100)));

53          if(as < lat + eps) {printf("100.000\n"); continue;}

54          double len = R * sin(lat) / tan(as);

55          Point3 jd1(len, sqrt(Sqr(R_) - Sqr(len)), -R * sin(lat));

56          Point3 jd2(len, -sqrt(Sqr(R_) - Sqr(len)), -R * sin(lat));

57          if(f.z < -eps) f = -f;

58          double ang = atan2(f.y, f.x);

59          jd1 = r.RotePoint(jd1, ang), jd2 = r.RotePoint(jd2, ang);

60          double s1d = s.Rdis(jd1, R), s2d = s.Rdis(jd2, R);

61          double e1d = e.Rdis(jd1, R), e2d = e.Rdis(jd2, R);

62          double sed = s.Rdis(e, R), jd = jd1.Rdis(jd2, R);

63          if(!dcmp(s1d + e1d - sed) && !dcmp(s2d + e2d - sed))

64              printf("%.3f\n", (sed - jd) / sed * 100);

65          else if(!dcmp(s1d + e1d - sed))

66          {

67              if(e.z < s.z) printf("%.3f\n", s1d / sed * 100);

68              else printf("%.3f\n", e1d / sed * 100);

69          }

70          else if(!dcmp(s2d + e2d - sed))

71          {

72              if(e.z < s.z) printf("%.3f\n", s2d / sed * 100);

73              else printf("%.3f\n", e2d / sed * 100);

74          }

75          else printf(e.z < jd1.z ? "0.000\n" : "100.000\n");

76      }

77      return 0;

78  }