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First order geometric network design is an important quality assurance process for terrestrial laser scanning of complex built environments for the construction of digital as-built models. A key design task is the determination of a set of instrument locations or viewpoints that provide complete site coverage while meeting quality criteria. Although simplified point precision measures are often used in this regard, precision measures for common geometric objects found in the built environment—planes, cylinders and spheres—are arguably more relevant indicators of as-built model quality. The computation of such measures at the design stage—which is not currently done—requires generation of artificial observations by ray casting, which can be a dissuasive factor for their adoption. This paper presents models for the rigorous computation of geometric object precision without the need for ray casting. Instead, a model for the 2D distribution of angular observations is coupled with candidate viewpoint-object geometry to derive the covariance matrix of parameters. Three-dimensional models are developed and tested for vertical cylinders, spheres and vertical, horizontal and tilted planes. Precision estimates from real experimental data were used as the reference for assessing the accuracy of the predicted precision—specifically the standard deviation—of the parameters of these objects. Results show that the mean accuracy of the model-predicted precision was 4.3% (of the read data value) or better for the planes, regardless of plane orientation. The mean accuracy of the cylinders was up to 6.2%. Larger differences were found for some datasets due to incomplete object coverage with the reference data, not due to the model. Mean precision for the spheres was similar, up to 6.1%, following adoption of a new model for deriving the angular scanning limits. The computational advantage of the proposed method over precision estimates from simulated, high-resolution point clouds is also demonstrated. The CPU time required to estimate precision can be reduced by up to three orders of magnitude. These results demonstrate the utility of the derived models for efficiently determining object precision in 3D network design in support of scanning surveys for reality capture.