**m**denotes the movement direction (e.g. projected onto the x-z plane) and

**n**the terrain normal at the current position, then

**r**:=

**m**cross

**n**

denotes the side vector perpendicular to both

**m**and

**n**. Then

**f**:=

**n**cross

**r**

denotes the forward vector that can be used as look-along vector as requested. It usually need to be normalized, though.

If, on the other hand, the normal isn't available because you're working with a height map, then this topic may help you. (Please notice that my first posts therein haven't considered triangulation correctly, but down from post #15 inclusive things are done well). After computing the height at the current position and the height a bit in direction of the movement vector, then the normalized difference vector is the result.

BTW: To be pedantic: A bi-normal is a construct that can be computed at locations on a line. In case of a surface the correct term is bi-tangent.