Given the triangle with vertices (a,b,c):

c

/ \

/ \

/ \

a - - - b

Which is then subdivided into four triangles by halving each of the edges:

c

/ \

/ \

ca / \ bc

/\ - - - /\

/ \ / \

/ \ / \

a- - - - ab - - - -b

Wich results in four triangles (a, ab, ca), (b, bc, ab), (c, ca, bc), (ab, bc, ca).

Now given a point p. How do I determine in which triangle p lies, given that p is within the outer triangle (a, b, c)?

Currently I intend to use ab as the origin. Check whether it is to the left of right of the line "ca - ab" using the perp of "ca - ab" and checking the sign against the dot product of "ab - a" and the perp vector and the vector "p - ab". If it is the same or the dot product is zero then it must be in (a, ab, ca)... Continue with this procedure with the other outer triangles (b, ba, ab) & (c, ca, ba). In the end if it didn't match with these it must be contained within the inner triangle (ab, bc, ca).

Is there a better way to do it?