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Summary: IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-30, NO. 2, FEBRUARY 1983
which saved about 40 percent of computing time (van Ooste-
rom [5]).
In a discussion of this problem, Dr. F. A. Muller of the De-
partment of Physics of the University of Amsterdam pointed
out that the numerical stability involved in (5) might be
poorer than in (4). He also suggested that a more drastic
reduction might be possible by considering the triple scalar
product R1 -
(R2 X R3). While examining the various expres-
sions for Q2 alternative to (3) as described in (old) textbooks
on spherical geometry, it became apparent how this advice
could be put to use.
In Casey [4, result (359)], it is shown that
fI\ 1 + cos (a) + cos (b) + cos (c)
c 2 - 4 cos (a) cos (tb) cos (ic) (6)
with a, b, and c the arcs among A, B, and C as indicated in
Fig. 1. This can be noted as
1 + cos (Xi)
cos2 =4 Hcos ('xi)'
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