## 3 Results
### Numerical Example  
Figure 10 shows a real topographic map for a plot of land on which a house is to be built. The topographic map of the land was drawn up by a topometric engineer, with specific high-precision equipment, called in specialized terms \"station.\" For small areas of land, the station is successively placed and GPS 3D coordinates are measured relative to a fixed position (in our situation it is a terminal in the Black Sea area located at a distance of approximately 717 km). The first chosen points of the topographic survey are those that describe the contour of the plot of land. In our case, the terrain contour is described by the 15 points (numbered in black). These points are inventoried and noted in a table (coordinate inventory) located on the topographic map. The following points will describe the contour of the level elevations, the positioning of the access road, the position of the neighboring houses (they are marked on the map in red together with the elevation), etc. In the case of lands with a high slope, such as the one exemplified, the measured points must be thickened for a greater accuracy of tracing the level curves (in total we have over 100 such points). The designer receives in electronic format a topographic map similar to the one in Figure 10. On this topographic support, the designer will place the designed building on the scale, having to respect a series of rigors imposed by law, among which: the minimum distance from the property limit and/or from the road axis as in Figure 11. Once the construction is located, the new contour will appear on the topographic map described by a few new points (minimum 4, in the example, for the description of the contour, 6 points are used). A situation plan is drawn up in which, according to the legislation, the 2D coordinates of the corners of the construction must be specified (see Table 1) together with the elevation of the horizontal excavation/filling plane. In Figure 11, this elevation is denoted by CTA and is estimated at 707 m by the designer. A good determination of this elevation is not easy, especially if the terrain has a high slope. A detail of Figure 11 is presented in Figure 12 illustrating the points \(\text{A}_{11}^{2},\text{A}_{12}^{2},\text{A}_{21}^{2},\) and \(\text{A}_{22}^{2}\) found using the algorithm AIPS. Table 2 presents the coordinates of the points \(\text{A}_{11}^{k},\text{A}_{12}^{k},\text{A}_{21}^{k},\text{and}\ \text{A}_{22}^{k}\) calculated for each point \(\text{Q}_{k}\) (k = 1, 2,..., 6) by applying AIPS. Using A2 SSTPC2L and (26), the elevation for each point \(\text{Q}_{k}\) (k = 1, 2,..., 6) is calculated. Usually, for the dimensions of the project to be in accordance with the real construction, before commencing all the construction works, a plot is made on the field of the future building. For this purpose, the ground tracing is performed. The corners of the house are very precisely marked (the Q points). In our example, the provided measured elevations of the 6 points are presented in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Points** & **E (m)** & **N (m)** \\ \hline Q\({}_{1}\) & 552,749.248 & 456,578.380 \\ Q\({}_{2}\) & 552,754.270 & 456,571.835 \\ Q\({}_{3}\) & 552,766.210 & 456,580.997 \\ Q\({}_{4}\) & 552,760.244 & 456,588.772 \\ Q\({}_{5}\) & 552,754.733 & 456,584.542 \\ Q\({}_{6}\) & 552,753.385 & 456,581.554 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The x and y coordinates of the Q points. Figure 10: Topographic map. Figure 11: Situation plan. Figure 12: Detail of Figure 11 for Q2. As seen in Table 3, the estimated elevation and the measured one for each Q point are very close. The difference between them is less than 2 cm. Using the coordinates of the points Q\({}_{\rm k}\) (k = 1, 2,..., 6) from Table 1, Bresenham, and, then flood fill algorithms were applied resulting in 803 points located inside the perimeter of the house. The elevations of these points were calculated using A2 SSTPC2L and (26).