lib/Documentation/docs-sonyckson/p3.cpp

   1 // PROBLEMA DE GEOMETIRA, 2 cortes en una torta, y calcula el volumen de cada pedazo :D
   2
   3 #include <algorithm>
   4 #include <vector>
   5 #include <set>
   6 #include <string>
   7 #include <fstream>
   8 #include <iostream>
   9 #include <iomanip>
  10 #include <map>
  11 #include <stack>
  12 #include <sstream>
  13 #include <queue>
  14
  15 #include <cmath>
  16 #include <cstdio>
  17 #include <cctype>
  18 #include <cstdlib>
  19 #include <cstring>
  20
  21 #define REP(i, n) for(int i=0;i<int(n);i++)
  22 #define foreach(it, c)  for(typeof((c).begin()) it = (c).begin();it!=(c).end();++it)
  23 #define ALL(x)   (x).begin(),(x).end()
  24 #define SORT(x) sort(ALL(x))
  25 using namespace std;
  26 #define VI vector<int>
  27 #define VS vector<string>
  28 #define PB push_back
  29 typedef struct{
  30         double x, y;
  31 }point;
  32 typedef struct{
  33         double a, b, c;
  34 }line;
  35 #define EPS 1e-7
  36 int signo(double a){
  37         if( a >= 0.0 ) return 1;
  38         return -1;
  39 }
  40 double prodcruz(point p1, point p2, point p3){
  41         double x1, x2, y1, y2;
  42         x1 = p2.x-p1.x; x2 = p3.x-p1.x;
  43         y1 = p2.y-p1.y; y2 = p3.y-p1.y;
  44         return fabs(x1*y2-x2*y1)/2.0;
  45 }
  46 double prodcruz2(point p1, point p2, point p3){
  47         double x1, x2, y1, y2;
  48         x1 = p2.x-p1.x; x2 = p3.x-p1.x;
  49         y1 = p2.y-p1.y; y2 = p3.y-p1.y;
  50         return (x1*y2-x2*y1)/2.0;
  51 }
  52 int equal(double a, double b){if( fabs(a-b) < EPS) return 1; return 0;}
  53 void points_to_line(point p1, point p2, line & l){
  54         if(equal(p1.x, p2.x)){
  55                 l.a = 1;
  56                 l.b = 0;
  57                 l.c = -p1.x;
  58         }else{
  59                 l.b = 1;
  60                 l.a = -(p1.y-p2.y)/(p1.x-p2.x);
  61                 l.c = -(l.a*p1.x)-(l.b*p1.y);
  62         }
  63 }
  64 double R;
  65 double dist(point p1, point p2){
  66         double ax, ay;
  67         ax = p1.x-p2.x;
  68         ay = p1.y-p2.y;
  69         return sqrt(ax*ax+ay*ay);
  70 }
  71 double area(point p1, point p2, point p3){
  72         double a, b, c;
  73         point p;
  74         p.x = 0.0; p.y = 0.0;
  75         a = dist(p2,p1);
  76         b = dist(p2,p);
  77         c = dist(p1,p);
  78         double aux = a*a-b*b-c*c;
  79         aux /= (-2.0*b*c);
  80         double angle = acos(aux);
  81         double prop = angle/(acos(-1)*2.0);
  82         if( signo(prodcruz2(p1,p2,p3)) == signo(prodcruz2(p1,p2,p))){
  83                 prop *= (acos(-1)*R*R);
  84                 prop -= prodcruz(p1,p2,p);
  85                 prop += prodcruz(p1,p2,p3);
  86         }else{
  87                 prop =  1.0-prop;
  88                 prop *= (acos(-1)*R*R);
  89                 prop += prodcruz(p1,p2,p);
  90                 prop += prodcruz(p1,p2,p3);
  91         }
  92         return prop;
  93 }
  94 void intersection_point(line l1, line l2, point &p){
  95         p.x = (l2.b*l1.c-l1.b*l2.c) / (l2.a*l1.b-l1.a*l2.b);
  96         if( fabs(l1.b) > EPS )
  97                 p.y = -(l1.a*p.x+l1.c)/l1.b;
  98         else
  99                 p.y = -(l2.a*p.x+l2.c)/l2.b;
 100 }
 101 double cuad(double a) { return a*a;}
 102 double complementox(double x, line l){
 103         double y =  sqrt(cuad(R)-cuad(x));
 104         if( !equal(l.a*x+l.b*y+l.c, 0.0) ) return -y;
 105         return y;
 106 }
 107 double complementoy(double y, line l){
 108         double x =  sqrt(cuad(R)-cuad(y));
 109         if( !equal(l.a*x+l.b*y+l.c, 0.0) ) return -x;
 110         return x;
 111 }
 112 void line_to_points(line l, point &p1, point &p2){
 113         if(equal(l.b, 0.0)){
 114                 double a , b, c;
 115                 a = cuad(l.b)/cuad(l.a)+1.0;
 116                 b = (2.0*l.c*l.b)/cuad(l.a);
 117                 c = cuad(l.c)/cuad(l.a)-cuad(R);
 118                 p1.y = (-b+sqrt(b*b-4.0*a*c))/(2.0*a);
 119                 p2.y = (-b-sqrt(b*b-4.0*a*c))/(2.0*a);
 120                 p1.x = complementoy(p1.y, l);
 121                 p2.x = complementoy(p2.y, l);
 122         }else{
 123                 double a, b, c;
 124                 a = cuad(l.a)/cuad(l.b)+1.0;
 125                 b = (2.0*l.c*l.a)/cuad(l.b);
 126                 c = cuad(l.c)/cuad(l.b)-cuad(R);
 127                 p1.x = (-b+sqrt(b*b-4.0*a*c))/(2.0*a);
 128                 p2.x = (-b-sqrt(b*b-4.0*a*c))/(2.0*a);
 129                 p1.y = complementox(p1.x, l);
 130                 p2.y = complementox(p2.x, l);
 131         }
 132 }
 133 int main(){
 134         int i , j, k;
 135         int radio, h;
 136         while(scanf("%i %i", &radio, &h) != EOF){
 137                 R = (double)radio;
 138                 double x[4], y[4];
 139                 REP(i, 4)scanf("%lf %lf", &x[i], &y[i]);
 140                 point p[4];
 141                 REP(i, 4)p[i].x = x[i], p[i].y = y[i];
 142                 line l1, l2;
 143                 points_to_line(p[0], p[1], l1);
 144                 points_to_line(p[2], p[3], l2);
 145                 line_to_points(l1, p[0], p[1]);
 146                 line_to_points(l2, p[2], p[3]);
 147                 point P;
 148                 intersection_point(l1, l2, P);
 149                 double areas[4];
 150                 areas[0] = area(p[0], p[2], P);
 151                 areas[1] = area(p[0], p[3], P);
 152                 areas[2] = area(p[1], p[2], P);
 153                 areas[3] = area(p[1], p[3], P);
 154                 sort(areas, areas+4);
 155                 printf("%.2lf %.2lf\n", (areas[3])*(double)h, (areas[0])*(double)h);
 156         }
 157         return 0;
 158 }