Detect collsion between Point (e.g. Mouse) with a Triangle (3 Points)

To detect a collision between an point and a triangle we need to calculate some areas

Area of a Triangle

First we need to calculate the area of the original triangle with the Heron’s Formula

F = sqrt(s(s-a)(s-b)(s-c))
s = (a+b+c)/2

where a,b,c are the sides of the triangle and s is the semiperimeter

Area of each Triangle with the Point

Now we calculate the 3 areas with the Point and the Triangle. The Area’s are: ABP, ACP and BCP.

BCP = abs((Bx-Px)*(Cy-Py) - (By-Py)*(Cx-Px))
ACP = abs((Ax-Px)*(Cy-Py) - (Ay-Py)*(Cx-Px))
ABP = abs((Ax-Px)*(By-Py) - (Ay-Py)*(Bx-Px))

Check if the Point is inside the Triangle

Now we check if the Point is inside the Triangle by checking if the sum of the 3 areas is equal to the area of the original triangle.

if (ABP + ACP + BCP) == F:
return True
else:
return False