Proof of Tienstra's Formula for an External Observation Point

Abstract

As a continuation of the writers' previous work on establishment of Tienstra's formula via finite-element ideas for an internal observation point, the formula is proven for the case where the observation point lies outside the control triangle. Because of the loss of “rotational symmetry” in the present case, this proof differs from the previous one as more formulas have to be derived, and “reflection symmetry” of the new configuration becomes an important aid throughout the derivation. Furthermore, the lengthy computer algebra needed to complete the previous proof has a much simpler counterpart here, requiring only one line of computer simplification.