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Check whether a given point lies inside a Triangle
Three points of a triangle are given; another point P is also given to check whether the point P is inside the triangle or not.
To solve the problem, let consider the points of the triangle are A, B, and C. When the area of triangle Δ𝐴𝐵𝐶 = Δ𝐴𝐵𝑃 + Δ𝑃𝐵𝐶 + Δ𝐴𝑃𝐶, then the point P is inside the triangle.
Input and Output
Input:
Points of the triangle {(0, 0), (20, 0), (10, 30)} and point p (10, 15) to check.
Output:
Point is inside the triangle.Algorithm
isInside(p1, p2, p3, p)
Input: Three points of a triangle, the point p to check.
Output: True, when p is inside the triangle.
Begin area := area of triangle(p1, p2, p3) area1 := area of triangle(p, p2, p3) area2 := area of triangle(p1, p, p3) area3 := area of triangle(p1, p2, p) if area = (area1 + area2 + area3), then return true else return false End
Example
#include <iostream>
#include<cmath>
using namespace std;
struct Point {
int x, y;
};
float triangleArea(Point p1, Point p2, Point p3) { //find area of triangle formed by p1, p2 and p3
return abs((p1.x*(p2.y-p3.y) + p2.x*(p3.y-p1.y)+ p3.x*(p1.yp2.y))/2.0);
}
bool isInside(Point p1, Point p2, Point p3, Point p) { //check whether p is inside or outside
float area = triangleArea (p1, p2, p3); //area of triangle ABC
float area1 = triangleArea (p, p2, p3); //area of PBC
float area2 = triangleArea (p1, p, p3); //area of APC
float area3 = triangleArea (p1, p2, p); //area of ABP
return (area == area1 + area2 + area3); //when three triangles are forming the whole triangle
}
int main() {
Point p1={0, 0}, p2={20, 0}, p3={10, 30};
Point p = {10, 15};
if (isInside(p1, p2, p3, p))
cout << "Point is inside the triangle.";
else
cout << "Point is not inside the triangle";
}Output
Point is inside the triangle.
Updated on: 17-Jun-2020
2K+ Views
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