**Proposition 8.1.1**: *The herd space of a flock F is determined by any three of its functions whose associated points are not collinear.*

*Pf*: Let f_{P}, f_{Q}, and f_{R} be three functions of the herd space of F where P =(x_{P},y_{P},z_{P},0), Q = (x_{Q},y_{Q},z_{Q},0) and R = (x_{R},y_{R},z_{R},0) are non-collinear points of W = 0. For each value of the parameter t (indexing the planes of F), the points (x_{P},y_{P},z_{P},-f_{P}(t)), (x_{Q},y_{Q},z_{Q},-f_{Q}(t)), (x_{R},y_{R},z_{R},-f_{R}(t)) are non-collinear points in by the definition of the herd space functions. Thus, , and hence all the planes of F are determined by these three functions. Given the indexed planes, the functions at all the other points of W = 0 are determined.