Check whether a given point lies inside a Triangle\\n

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 Δ??? = Δ??? + Δ??? + Δ???, 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.