The area

最新推荐文章于 2024-06-24 18:02:24 发布

xuehuhu1

最新推荐文章于 2024-06-24 18:02:24 发布

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分类专栏：计算几何

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本文介绍了一种通过给定三个交点坐标来计算由抛物线和直线围成的土地面积的方法。利用输入的顶点及两个交点坐标，通过解析几何原理计算出特定区域的面积。

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Ignatius bought a land last week, but he didn't know the area of the land because the land is enclosed by a parabola and a straight line. The picture below shows the area. Now given all the intersectant points shows in the picture, can you tell Ignatius the area of the land?

Note: The point P1 in the picture is the vertex of the parabola.

Input

The input contains several test cases. The first line of the input is a single integer T which is the number of test cases. T test cases follow.
Each test case contains three intersectant points which shows in the picture, they are given in the order of P1, P2, P3. Each point is described by two floating-point numbers X and Y(0.0<=X,Y<=1000.0).

Output

For each test case, you should output the area of the land, the result should be rounded to 2 decimal places.

Sample Input

2
5.000000 5.000000
0.000000 0.000000
10.000000 0.000000
10.000000 10.000000
1.000000 1.000000
14.000000 8.222222

Sample Output

33.33
40.69

最为基础的计算几何，但是要注意公式千万不要推错了。。。，还有避免一个错误x^3-y^3!=(x-y)^3;

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;

struct point{
double x,y;
}p1,p2,p3;

void solve(){
double e=(p3.y-p2.y)/(p3.x-p2.x);
double f=p2.y-p2.x*e;
double k=p2.x-p1.x;
k=pow(k,2);
double a=(p2.y-p1.y)/k;
double b=-2*a*p1.x;
double c=a*p1.x*p1.x+p1.y;
double t=p3.x;
double s1=(a/3)*t*t*t+(b-e)/2*t*t+(c-f)*t;//注意数学上的合并，x^3-y^3!=(x-y)^3
t=p2.x;
double s2=(a/3)*t*t*t+(b-e)/2*t*t+(c-f)*t;
printf("%.2f\n",s1-s2);
}
int main(){
int n;
while(cin>>n){
while(n-->0){
cin>>p1.x>>p1.y>>p2.x>>p2.y>>p3.x>>p3.y;
solve();
}

}
}