## 3 Methodology
### Cartographic Scale-Variant Flight Planning  
A map is a symbolic representation of specific characteristics of an area depicted on a flat surface and includes qualitative and quantitative information about the world in a simple, visual way. To understand maps properly specific parameters need to be understood thoroughly, with the map scale being the most important parameter of them. In this context, the most critical step to address in the 3D mapping of a geosite is defining the visualization's appropriate cartographic scale, which directly affects the UAS flight planning. Furthermore, the geographical area to be mapped should be defined as it affects the selection of the drone, endurance capabilities, and sensor characteristics. The required ground sampling distance (GSD) relies on the map's cartographic scale on which the 3D geovisualization will be placed as an AR item. Thus, the sizes of the features of interest are correlated by map production processes that are necessarily approximate. These processes result in a variety of error effects that apply to geometric details on a map. Figure 2: Methodology flow chart: flight planning, data acquisition, data processing, 3D geovisualization and the software that was used. The cartographic scale (sc) of derivative maps is based on the flight height (h) and focal length (fl) in aerial data acquisition and is calculated using Equation (1) [63]. \[\text{sc}=\text{fl}/\text{h} \tag{1}\]  
According to [PERSON], \"The rule is: divide the denominator of the map scale by 1,000 to obtain the detectable size in meters. The resolution is one-half of this amount\" [64]. This makes the spatial resolution the most critical parameter when mapping. The spatial resolution of the produced DSM and orthomosaics from the UAS data processing is inseparably linked to the GSD of the images. Thus, they are directly affected by the flight altitude and image characteristics (resolution, sensor size, and focal length). As GSD is driven by the spatial scale of the AR 3D geovisualization, the flight parameters and the image selection and settings require trade-offs for survey optimization in order to achieve the best parameterization. The GSD of the images is calculated using Equation (2) [65]. \[\text{GSD}=(\text{sw}^{*}\text{h})/(\text{fl}^{*}\text{iw}) \tag{2}\]  
where GSD is ground sampling distance (m), sw is sensor width (mm), h is the flight height (m), fl is the focal length (mm), and iw is image width (pixels). For this study, considering that the cartographic product's selected scale was 1:400, the acceptable spatial error was calculated to be 10 cm. Furthermore, based on the human eye's visual acuity that is 1% of a millimeter, the smaller spatial entity visually detectable in a map with a scale of 1:400 is 10 cm. In this case, the acceptable spatial error for all raster derivatives of aerial data (DSM and orthomosaic) is GSD/3 [66] thus 3.33 cm. Using this value, the maximum flight altitude was calculated using Equation (2) at 100 m. When designing the scale-variant flights three heights were selected using 100 m as an altitude threshold, which gives images that need a spatial resolution of 3 cm. The three selected heights were 60 m, 80 m, and 100 m. The first flight altitude chosen was 100 m as it was the height that produced the smallest amount of aerial images that had the desirable GSD. The 60 m flight altitude selected was the value at which the curve began to flatten, meaning that was the value where the drone could acquire the minimum number of images to cover the selected area with the lowest spatial resolution (1.8 cm). Moreover, the 80 m was finally selected as the third flight altitude as an intermediate height between 60 m and 100 m.  
Another significant parameter in flight planning is the determination of the forward and side image overlap, particularly for structure-from-motion (SfM) photogrammetric reconstructions, which require features observed in multiple images for developing DSMs, orthomosaics, and 3D models.