A Signal Flow Graph Approach to the Resolution of Spherical Triangles Using CORDIC
Abstract
Jack Volder’s original motivation for the COordinate DIgital Computer (CORDIC) was the real-time digital solution of spherical triangle equations employed in airborne navigation, for which he presented a solution flow diagram without detailing its construction. In fact, without a strong guidance, it is not easy to express the solutions of linear algebraic problems such as those involved when solving spherical triangles as cascades of CORDIC operations—called by Volder CORDIC solution-flow diagrams—and thus to devise a system solution on CORDIC processing units. As it gives a bird’s eye view of the system design problem, a signal flow graph representation of the underlying system of linear equations provides such guidance; the operations leading to the problem solution are uncovered by performing a sequence of partial flow reversals on the graph. The approach is illustrated by the problem where two sides and the included angle of a spherical triangle are given, called SAS problem, that is encountered in applications as diverse as air navigation, lattice filters for adaptive processing, and dexterous robotic hands. The solutions thus obtained are at least as efficient as existing ones, whenever available.