Orthogonal matrix package program (ORTMATPAC) for the WANG-700
Abstract
ORTMATPAC is a first attempt to make available to users of the WING 700 desk calculator a few routines for fundamental analytical-geometric and analytical-photogrammetric problems.
Basically three different type of routines are contained: (1) Trigonometric functions, such as, SIN, COS, ARCTAN, together with conversion functions from degrees, minutes, seconds, or from gons to radians and vice versa. These functions were taken from SURVTRIGPACK, the idea behind them being to use only radians for angles during any type of computations. Degrees or gons are required only for I/O-operations.
(2) Storing and recalling elements of vectors and matrices. Presently, matrices are confined to size 3 x 3. It was considered as fundamentally important to keep these two routines as general as possible; i.e., to influence from outside the position of the arrays to be acted upon.
(3) For manipulating spatial rotations at the present stage two routines for determining an orthogonal 3 x 3 matrix from 3 independent orientation angles and vice versa, are available. Although similar programs could have been incorporated relatively easy, it was felt to make use of the sequence (ɯ,ᶲ, қ) of rotations only. Whereas for aerial photogrammetric purposes the sequence as such is mostly immaterial, terrestrial photogrammetric formulation require it that way. At a later time, similar routines for the sequence (ɯ,ᶲ, қ) and for the Rodriguez parameters are intended to be included.
It is hoped that the program package will serve some needs of the photogrammertrist who wants quick results for his problems that are not worthwhile to be solved by larger computers.