How to determine if a point is in a 2D triangle? [closed]

Answer 1

Honestly it is as simple as Simon P Steven's answer however with that approach you don't have a solid control on whether you want the points on the edges of the triangle to be included or not.

My approach is a little different but very basic. Consider the following triangle;

In order to have the point in the triangle we have to satisfy 3 conditions

1. ACE angle (green) should be smaller than ACB angle (red)
2. ECB angle (blue) should be smaller than ACB angle (red)
3. Point E and Point C shoud have the same sign when their x and y values are applied to the equation of the |AB| line.

In this method you have full control to include or exclude the point on the edges individually. So you may check if a point is in the triangle including only the |AC| edge for instance.

So my solution in JavaScript would be as follows;

function isInTriangle(t,p){

  function isInBorder(a,b,c,p){
    var m = (a.y - b.y) / (a.x - b.x);                     // calculate the slope
    return Math.sign(p.y - m*p.x + m*a.x - a.y) === Math.sign(c.y - m*c.x + m*a.x - a.y);
  }
  
  function findAngle(a,b,c){                               // calculate the C angle from 3 points.
    var ca = Math.hypot(c.x-a.x, c.y-a.y),                 // ca edge length
        cb = Math.hypot(c.x-b.x, c.y-b.y),                 // cb edge length
        ab = Math.hypot(a.x-b.x, a.y-b.y);                 // ab edge length
    return Math.acos((ca*ca + cb*cb - ab*ab) / (2*ca*cb)); // return the C angle
  }

  var pas = t.slice(1)
             .map(tp => findAngle(p,tp,t[0])),             // find the angle between (p,t[0]) with (t[1],t[0]) & (t[2],t[0])
       ta = findAngle(t[1],t[2],t[0]);
  return pas[0] < ta && pas[1] < ta && isInBorder(t[1],t[2],t[0],p);
}

var triangle = [{x:3, y:4},{x:10, y:8},{x:6, y:10}],
      point1 = {x:3, y:9},
      point2 = {x:7, y:9};

console.log(isInTriangle(triangle,point1));
console.log(isInTriangle(triangle,point2));