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A RATIONAL ALGEBRAIC FORMULATION OF THE PROBLEM OF RELATIVE ORIENTATION
Author(s) -
Thompson E. H.
Publication year - 1959
Publication title -
the photogrammetric record
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 51
eISSN - 1477-9730
pISSN - 0031-868X
DOI - 10.1111/j.1477-9730.1959.tb01267.x
Subject(s) - mathematics , orientation (vector space) , algebraic equation , matrix (chemical analysis) , context (archaeology) , algebraic number , set (abstract data type) , orthogonal matrix , order (exchange) , orthogonal functions , algebra over a field , pure mathematics , mathematical analysis , geometry , orthogonal basis , computer science , paleontology , physics , materials science , finance , quantum mechanics , nonlinear system , economics , composite material , biology , programming language
The problem of relative orientation involves the determination of the elements of at least one orthogonal matrix. Hitherto a difficulty has arisen in that, in this context, orthogonal matrices have not been expressed in terms of three independent parameters without the use of circular functions. In this paper a more tractable form of the orthogonal matrix is used to set up a rational algebraic equation expressing the relative orientation condition. This equation turns out to be of the third order in the five unknowns. A set of such equations may be solved by a rapidly converging process of iteration.