Entering or Exiting Value

We can classify if entering or exiting value by using inner product.

Let be the line

and be the normal vector(outward).

If , the parameter t is entering.

If , the parameter t is exiting.

Example

Let P = (1,3), Q = (-4,2) while the edge equation is x+2y-4 = 0. Determine if the vector from P to Q is entering or exiting the edge.

We can determine n from the equation ax + by + c = o, where n = (a,b). Therfore, n = (1,2).

Q-P = (-4-1,2-3) = (-5,-1).

n(Q-P) = (1,2) * (-5,-1) = -5-2 = -7 which is less than 0.

So, this line is entering the edge.

From P. Asokarathinam -- see details 27.11.1996