 Planar orientation test

For planar points $A,B,P$, the sign of $(B-A)\times (P-A)$, using the two-dimensional cross product, determines which side of the directed line from $A$ to $B$ contains $P$. Zero means collinearity. A point is strictly inside a nondegenerate triangle exactly when these signs for its three cyclically ordered sides are all strictly positive or all strictly negative.