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Open-configuration portable X-ray computed tomography (CT) is a technology that enables the volumetric inspections of regions of interest on large parts. The open-configuration aspect of X-ray CT allows it to be portable and applicable to large and irregular parts that are not conducive to conventional CT booth setups or ring geometry. The inherent problem with the open-configuration setup is the lack of mechanical controls that determine the geometry between the X-ray source, detector, and part. As a result, the focus of this article is a prerequisite technique to self-determine the X-ray shot geometry from the X-ray shot itself. Additional difficulties pertaining to self-determined shot geometry is that there are nine system unknowns for every X-ray shot as compared to conventional CT that has nine system unknowns total. To address these problems, the technique presented here has three unique features: 1) it consists of only a few known constellation markers; 2) it exploits geometry to break the problem into many to find the global optimum solution; and 3) it reprojects a 3-D model of the reference constellation for final geometry refinement. A comparison study is provided to demonstrate the advantages of this solution over random basin hopping, a general-purpose global optimization technique. After performing this process for every shot, results show that the geometric error is satisfactorily low for successful CT reconstruction.