Cellular coverage probability is independent of base station density under stochastic geometric models

We prove that under stochastic geometric modelling of cellular networks, the coverage probability is <i>not</i> a function of base stations density, contrary to widespread belief. That is, we reveal that the base station density, $\lambda$, that is appears in a plethora of published cellular coverage probability expressions is superfluous.<br>

Cellular coverage probability is independent of base station density under stochastic geometric models

We prove that under stochastic geometric modelling of cellular networks, the coverage probability is <i>not</i> a function of base stations density, contrary to widespread belief. That is, we reveal that the base station density, $\lambda$, that is appears in a plethora of published cellular coverage probability expressions is superfluous.<br>

3D CITYLUR: MODELLING 3D CITY LAND-USE REGULATIONS TO SUPPORT ISSUING A PLANNING PERMIT

The applications and understanding of Land-use Regulations (LuR) are more communicable when they are linked to the digital representation of the physical world. In order to support issuing a planning permit and move towards the establishment of automated planning permit checks, this paper investigates how LuRs related to a planning permit process can be modelled in 3D called 3D CityLuR. 3D CityLuR serves as a 3D model for representing LuRs’ legal extents on a city scale. It is formed based on multiple geometric modelling approaches representing LuRs, which can provide a better cognitive understanding of LuRs and subsequently facilitate LuR automatic checks. To this purpose, according to LuRs’ descriptions and characteristics explained in related planning documents, key parameters representing LuRs’ extent are identified (e.g. maximum distance in overlooking or maximum allowed height in building height regulations). Accordingly, to automatically model each LuR, a geometric modelling approach (e.g. Boundary Representation (B-Rep), CSG, and extrusion) that best fits with the identified key parameters is proposed. In addition, to combine 3D CityLuR with an integrated BIM-GIS environment, the level of information need in terms of geometries and semantics is specified. Finally, the paper results in a showcase for five LuRs including building height, energy efficiency protection, overshadowing open space, overlooking, and noise impacts regulations. The showcase is a proof of concept for determining how these LuRs can be modelled in 3D and combined with 3D city models based on the selected geometric modelling approaches, identified parameters, and level of information need.

3D phytomer-based geometric modelling method for plants—the case of maize

Geometric plant modelling is crucial in in silico plants. Existing geometric modelling methods have focused on the topological structure and basic organ profiles, simplifying the morphological features. However, the models cannot effectively differentiate cultivars, limiting FSPM application in crop breeding and management. This study proposes a 3D phytomer-based geometric modelling method with maize (Zea Mays) as the representative plant. Specifically, conversion methods between skeleton and mesh models of 3D phytomer are specified. This study describes the geometric modelling of maize shoots and populations by assembling 3D phytomers. Results show that the method can quickly and efficiently construct 3D models of maize plants and populations, with the ability to show morphological, structural and functional differences among four representative cultivars. The method takes into account both the geometric modelling efficiency and 3D detail features to achieve automatic operation of geometric modelling through the standardized description of 3D phytomers. Therefore, this study provides a theoretical and technical basis for the research and application of in silico plants.

Estimating Control Points for B-Spline Surfaces Using Fully Populated Synthetic Variance–Covariance Matrices for TLS Point Clouds

A flexible approach for geometric modelling of point clouds obtained from Terrestrial Laser Scanning (TLS) is by means of B-splines. These functions have gained some popularity in the engineering geodesy as they provide a suitable basis for a spatially continuous and parametric deformation analysis. In the predominant studies on geometric modelling of point clouds by B-splines, uncorrelated and equally weighted measurements are assumed. Trying to overcome this, the elementary errors theory is applied for establishing fully populated covariance matrices of TLS observations that consider correlations in the observed point clouds. In this article, a systematic approach for establishing realistic synthetic variance–covariance matrices (SVCMs) is presented and afterward used to model TLS point clouds by B-splines. Additionally, three criteria are selected to analyze the impact of different SVCMs on the functional and stochastic components of the estimation results. Plausible levels for variances and covariances are obtained using a test specimen of several dm—dimension. It is used to identify the most dominant elementary errors under laboratory conditions. Starting values for the variance level are obtained from a TLS calibration. The impact of SVCMs with different structures and different numeric values are comparatively investigated. Main findings of the paper are that for the analyzed object size and distances, the structure of the covariance matrix does not significantly affect the location of the estimated surface control points, but their precision in terms of the corresponding standard deviations. Regarding the latter, properly setting the main diagonal terms of the SVCM is of superordinate importance compared to setting the off-diagonal ones. The investigation of some individual errors revealed that the influence of their standard deviation on the precision of the estimated parameters is primarily dependent on the scanning distance. When the distance stays the same, one-sided influences on the precision of the estimated control points can be observed with an increase in the standard deviations.