Triangle point¶

In this example we will see how to determine if a point is inside a triangle.

We shall start by defining the Triangle class.

Algorithm¶

  • The Triangle class calculates several values during initialization, such as bax, bay, cax, cay, ax, ay, and den.
  • These values are derived from the coordinates of the triangle's vertices (p1, p2, p3).
  • The isInside method then takes a point p as input and uses these pre-calculated values to compute two barycentric coordinates, w1 and w2.

The point p is considered inside the triangle if the following conditions are met:

  1. w1 <= 0.0
  2. w2 >= 0.0
  3. (w1 + w2) >= 1.0

This method determines if the point lies within the triangle's boundaries based on its barycentric coordinates relative to the triangle's vertices.

In [4]:
class Triangle:
    
    def __init__(self, p1, p2, p3):
        self.bax = p2[0] - p1[0]
        self.bay = p2[1] - p1[1]
        self.cax = p3[0] - p1[0]
        self.cay = p3[1] - p1[1]
        self.ay = p1[1]
        self.ax = p1[0] * self.cay
        self.den = self.bay * self.cax - self.bax * self.cay
        
    def isInside(self, p):
        w1 = self.ax + (p[1] - self.ay) - p[0] * self.cay
        w1 /= self.den
        w2 = p[1] - self.ay - w1 * self.bay
        w2 /= self.cay
        return w1 <=0.0 and w2 >=0.0 and (w1 + w2)>=1.0

Driver Code¶

In [5]:
if __name__ == "__main__":
    tr = Triangle((4.0, -4.0), (12.0, 6.0), (16.0, -2.0))
    points = [
        (4.0, -6.0),
        (6.0, 4.0),
        (6.0, -2.0),
        (8.0, -2.0),
        (10.0, 2.0),
        (10.0, -4.0),
        (12.0, 2.0),
        (12.0, -2.0),
        (12.0, -4.0),
        (14.0, -4.0),
        (14.0, 0.0)
    ]
    for p in points:
        if(tr.isInside(p)):
            print(p,"is inside the triangle")
        else:
            print(p,"is outside the triangle")

(4.0, -6.0) is outside the triangle
(6.0, 4.0) is outside the triangle
(6.0, -2.0) is inside the triangle
(8.0, -2.0) is inside the triangle
(10.0, 2.0) is inside the triangle
(10.0, -4.0) is outside the triangle
(12.0, 2.0) is inside the triangle
(12.0, -2.0) is inside the triangle
(12.0, -4.0) is outside the triangle
(14.0, -4.0) is outside the triangle
(14.0, 0.0) is inside the triangle

Actual triangle on graph¶

triangle