用于检查点d在平面中由点a，b，c定义的圆的内部还是外部的C ++程序
我们将考虑使用C++程序通过使用等式检查点d是否位于平面中由点a，b，c定义的圆的内部或外部
s = (x-xt)^2 + (y-yt)^2 – r*r
其中，对于平面上的任何点t(xt,yt)，其相对于由3个点(x1,y1)，(x2,y2)，(x3,y3)定义的圆的位置。
对于s<0，t位于圆内。
对于s>0，t位于圆的外面。
对于s=0，t位于圆上。
算法
Begin
Take the points at input.
Declare constant L = 0 and H = 20
Declare the variables of the equation.
For generating equation, generate random numbers for coefficient of x and y by using rand at every time of compilation.
Calculate the center of the circle.
Calculate the radius of the circle.
Calculate s.
if s < 0, print point lies inside the circle.
else if s >0, print point lies outside the circle.
else if s = 0, print point lies on the circle.
End范例程式码
#include<time.h>
#include<stdlib.h>
#include<iostream>
#include<math.h>
using namespace std;
const int L= 0;
const int H = 20;
int main(int argc, char **argv) {
time_t s;
time(&s);
srand((unsigned int) s);
double x1, x2, y1, y2, x3, y3;
double a1, a2, c1, c2, r;
x1 = rand() % (H - L+ 1) + L;
x2 = rand() % (H - L + 1) + L;
x3 = rand() % (H- L + 1) + L;
y1 = rand() % (H- L + 1) + L;
y2 = rand() % (H- L+ 1) + L;
y3 = rand() % (H- L + 1) + L;
a1 = (y1 - y2) / (x1 - x2);
a2 = (y3 - y2) / (x3 - x2);
c1 = ((a1 * a2 * (y3 - y1)) + (a1 * (x2 + x3)) - (a2 * (x1 + x2))) / (2 * (a1 - a2));//calculate center of circle
c2 = ((((x1 + x2) / 2) - c1) / (-1 * a1)) + ((y1 + y2) / 2);//calculate center of circle
r = sqrt(((x3 - c1) * (x3 - c1)) + ((y3 - c2) * (y3 - c2)));//calcultate radius
cout << "The points on the circle are: (" << x1 << ", " << y1 << "), (" << x2 << ", " << y2 << "), (" << x3 << ", " << y3 << ")";
cout << "\nThe center of the circle is (" << c1 << ", " << c2 << ") and radius is " << r;
cout << "\nEnter the point : ";
int u, v;
cin >>u;
cin >>v;
double s1 = ((u - c1) * (u - c1)) + ((v - c2) * (v - c1)) - (r * r);
if (s1 < 0)
cout << "\nThe point lies inside the circle";
else if (s1 >0)
cout << "\nThe point lies outside the circle";
else
cout << "\nThe point lies on the circle";
return 0;
}输出结果
The points on the circle are: (8, 4), (9, 17), (5, 9) The center of the circle is (12.6364, 10.8182) and radius is 7.84983 Enter the point : 7 6 The point lies outside the circle