C++ Programming Code Examples
C++ > Computer Graphics Code Examples
Check if a Point d lies Inside or Outside a Circle Defined by Points a, b, c in a Plane
/* Check if a Point d lies Inside or Outside a Circle Defined by Points a, b, c in a Plane
This is a C++ Program to Check if a Point d lies Inside or Outside a Circle Defined by Points a, b, c in a Plane. For any point t (xt, yt) on the plane, its position with respect to the circle defined by 3 points (x1, y1) , (x2, y2), (x3, y3).
s = (x-xt)^2 + (y-yt)^2 - r*r
If s < 0, t lies inside the circle; if s > 0, t lies outside the circle; if s = 0, t lies on the circle. */
#include<time.h>
#include<stdlib.h>
#include<iostream>
#include<math.h>
using namespace std;
const int LOW = 0;
const int HIGH = 10;
int main(int argc, char **argv)
{
time_t seconds;
time(&seconds);
srand((unsigned int) seconds);
double x1, x2, y1, y2, x3, y3;
double m1, m2, c1, c2, r;
x1 = rand() % (HIGH - LOW + 1) + LOW;
x2 = rand() % (HIGH - LOW + 1) + LOW;
x3 = rand() % (HIGH - LOW + 1) + LOW;
y1 = rand() % (HIGH - LOW + 1) + LOW;
y2 = rand() % (HIGH - LOW + 1) + LOW;
y3 = rand() % (HIGH - LOW + 1) + LOW;
m1 = (y1 - y2) / (x1 - x2);
m2 = (y3 - y2) / (x3 - x2);
c1 = ((m1 * m2 * (y3 - y1)) + (m1 * (x2 + x3)) - (m2 * (x1 + x2))) / (2
* (m1 - m2));
c2 = ((((x1 + x2) / 2) - c1) / (-1 * m1)) + ((y1 + y2) / 2);
r = sqrt(((x3 - c1) * (x3 - c1)) + ((y3 - c2) * (y3 - c2)));
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 : <x>,<y>";
int x, y;
cin >> x;
cin >> y;
double s = ((x - c1) * (x - c1)) + ((y - c2) * (y - c1)) - (r * r);
if (s < 0)
cout << "\nThe point lies inside the circle";
else if (s > 0)
cout << "\nThe point lies outside the circle";
else
cout << "\nThe point lies on the circle";
return 0;
}
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