## 2 Materials and Methods
### Layout of a Project Point and Accuracy Evaluation  
Construction layout or stake-out is one of the most important missions of the surveying engineer, with the purpose of ensuring the designed geometries of the engineering structure, by satisfying the required accuracies from the project [2; 22; 23; 24; 25]. Although modern GNSS systems have the capability of point stake-out with an accuracy of \(\approx\)2 cm in the right  
Figure 3: Graphical abstract of the site layout plan process. conditions, construction surveys and layouts are made using total stations. The principle behind a total station stake-out is the polar coordinates method, which consist of calculating and determining the position of a horizontal angle and a distance from a set of two control points (or geodetic points). The two control points are used for instrument stationing and orientation (or bearing), and all calculations regarding the layout of the construction are made in accordance to the established layout network. It was opted for the GNSS technology for the creation of the layout network, because of the efficiency, the lower cost price, and the short time to perform the measurements. In the case of classical methods of determining new geodetic points, by means of resection or traverse networks, the current great deficiency is the lack of reliable control points or geodetic points, almost completely destroyed in the past decades [13]. The layout elements (horizontal angle and a distance) are calculated using the known coordinates of the layout network and the designed coordinates of the construction, as follows (example for layout point H7; Figure 4):  
\[\mathrm{tg}\theta_{\mathrm{St1-St2}}=\frac{\Delta Y_{\mathrm{St1-St2}}}{ \Delta X_{\mathrm{St1-St2}}}\Rightarrow\theta_{\mathrm{St1-St2}}=\mathrm{atan} \frac{Y_{\mathrm{St2}}-Y_{\mathrm{St1}}}{X_{\mathrm{St2}}-X_{\mathrm{St1}}}, \tag{1}\]  
\[\mathrm{tg}\theta_{\mathrm{St1-H7}}=\frac{\Delta Y_{\mathrm{St1-H7}}}{ \Delta X_{\mathrm{St1-H7}}}\Rightarrow\theta_{\mathrm{St1-H7}}=\mathrm{atan} \frac{Y_{\mathrm{H7}}-Y_{\mathrm{St1}}}{X_{\mathrm{H7}}-X_{\mathrm{St1}}}, \tag{2}\]  
\[\omega_{\mathrm{H7}}=(400^{8}-\theta_{\mathrm{St1-St2}})+\theta_{\mathrm{St1- H7}}, \tag{3}\]  
\[D_{\mathrm{St1-H7}}=\sqrt{\Delta X^{2}+\Delta Y^{2}}, \tag{4}\]  
In order to ensure an accurate and efficient layout of the construction points, a retrospective of the measurement errors, required accuracy and the construction tolerances must be taken into account [2; 21; 22]. The type of building and the building technology are also important aspects, as the components and structural elements used to construct buildings are often fabricated, assembled or built on site, often by hand, in conditions that may be less than ideal. Errorless measurements are impossible, thus it is mandatory to satisfy the recommended accuracies through the \"achieved point standard deviation\" which is defined by the product of the errors derived from known point coordinates and the layout measurements. In order to assure the required accuracy, the achieved accuracy must be smaller than the required one. Based on the type of construction and the characteristics of the engineering structure, the required point standard deviation (\(\pm\mu_{P}\)) should be: \(\mu_{P}=\pm\)(1-2) cm for the majority of layout construction projects that use a monobloc structure with build on site structural elements (reinforced concrete); \(\mu_{P}=\pm\)(2-5) mm for prefabricated and assembled structural elements; \(\mu_{P}=\pm\)(1-2) mm for precise machine guidance and complex structures [2; 26; 27]. It is the surveying engineer's mission to identify the required accuracy and plan the layout process in accordance. Figure 4: Polar coordinates for layout point H7 and the topographic quadrants for the calculus.