The area 积分积分

 1 #include <iostream>
 2 #include <math.h>
 3 #include <stdio.h>
 4 #include <string.h>
 5 using namespace std;
 6 struct point
 7 {
 8     double x,y;
 9 } p1,p2,p3;
10 double a,b,c,a1,b1;
11 double F(double x)
12 {
13     return fabs(a*(x-b)*(x-b)+c-a1*x-b1);
14 }
15 void init()
16 {
17     b = p1.x;
18     c = p1.y;
19     a = (p2.y - c) / (p2.x - b) / (p2.x - b);
20     a1 = (p3.y - p2.y) / (p3.x - p2.x);
21     b1 = p2.y - a1 * p2.x;
22     //cout<<a<<"   "<<b<<"    "<<c<<" "<<a1<<" "<<b1<<" "<<endl;
23 }
24 //三点辛普森公式
25 double simpson(double width,double fa,double fb,double fc)
26 {
27     return (fb+fa+4*fc)*width/6;
28 }
29 
30 //自适应simpson公式递归过程
31 double asr(double a,double b,double eps,double A)
32 {
33     double c=(a+b)/2;
34     double fa,fb,fc,L,R;
35     fa=F(a);
36     fb=F(b);
37     fc=F(c);
38     L=simpson(c-a,fa,fc,F((c+a)/2));
39     R=simpson(b-c,fc,fb,F((b+c)/2));
40     if(fabs(L+R-A)<=15*eps) return L+R+(L+R-A)/15;
41     return asr(a,c,eps/2,L)+asr(c,b,eps/2,R);
42 }
43 double asr1(double a,double b,double eps)
44 {
45     return asr(a,b,eps,simpson(b-a,F(a),F(b),F((b+a)/2)));
46 }
47 int main()
48 {
49     int t;
50     scanf("%d",&t);
51     while(t--)
52     {
53         scanf("%lf%lf",&p1.x,&p1.y);
54         scanf("%lf%lf",&p2.x,&p2.y);
55         scanf("%lf%lf",&p3.x,&p3.y);
56         init();
57         printf("%.2lf\n",asr1(p2.x,p3.x,0.0000001));
58     }
59 }