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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.

Geometric features such as cylinders and planes are important objects of interest in terrestrial laser scanner surveys of complex scenes. The quality of the objects modelled from the laser scanner data is a function of many variables and geometric network design plays a key role in maximizing precision. The expected precision can be predicted at the planning stage from simulations of the environment to be scanned. However, this practice can incur a high computational load, even if performed in 2D rather than in 3D. In this paper, a closed-form solution to estimate geometric object precision is proposed as an efficient first order network design tool. It models the laser scanner measurement process with an observation distribution function that is introduced into the least-squares normal equations. Parameter precision is evaluated directly by solving a few (three to six) integrals and inverting the normal equations matrix. The method is presented for two cases of a circle lying in the horizontal plane and a 2D line scanned from a single location. Both a simplified circle model and a more general circle model are explored. The method is then extended using the summation of normals method to allow precision estimation from the combination of multiple scans from different locations. Results from many real datasets, 95 circles and 30 lines, show that the distributions of the range observations and derived Cartesian coordinates follow model predictions. Moreover, results demonstrate that the method can predict circle parameter standard deviations within 4%–6% of the experimental values. The agreement is at the 10% level for a very specific case due to inherent high parameter correlation. The agreement of line parameter standard deviations is much greater, approximately 0.1%. The results show the method can be a valuable tool to predict feature quality with minimal computational requirements. The method is beneficial to not only laser scanner network design but could also be to instantaneous 2D map construction performed for SLAM-based surveys.