The complex source point method converts an omnidirectional source diffraction solution into a beam solution by an appropriate choice of complex source coordinates. In so doing shadow and reflection boundary singularities of the geometrical theory of diffraction become non-singular, in general. Thus the suggestion that, for certain parameters, transition region functions are unnecessary. Here numerical results from uniform and asymptotic solutions for beam diffraction by half-planes and wedges indicate this is so only if diffraction is negligible. Convenient uniform expressions are shown to provide accurate far field values for all parameters.