Pix4Dmapper calculates the volume following:
1. The user draws a volume in the Volumes view. For more information about how to draw a Volume: How to draw a Volume
Figure 1. Volume drawn in the Volumes view. |
Figure 2. The Base of the volume. |
2. Pix4Dmapper projects a grid with GSD spacing on the base.
Figure 3. Projected grid on the base of the volume: This drawing is a sketch and does not depict the real dimensions of the grid. The grid has very small interval (the GSD). |
3. For each cell i of the grid, its volume (V_{i}) is given by:
V_{i }= L_{i }* W_{i} * H_{i}
Where:
L_{i }= the length of the cell.
W_{i} = the width of the cell.
H_{i} = the height of the cell.
The Lenght (Li) and Width (Wi) are equal to the project's GSD.
L_{i }=W_{i }= GSD_{}
The Height (H_{i}) is given by:
H_{i} = Z_{Ti }- Z_{Bi}
Where:
Z_{Ti} = the terrain altitude of each cell at the center of the cell.
Z_{Bi} = the base altitude of each cell at the center of the cell.
Therefore, the volume V_{i }of cell i is given by:
V_{i }= GSD*GSD* (Z_{Ti }- Z_{Bi})
Figure 4: Volume of one cell of the base |
4. Pix4Dmapper calculates 2 volumes:
- The Cut volume V_{c }is the volume between the base and the 3D terrain, when the terrain is higher than the base.
Cut volume = V_{C }= V_{C}_{1 }+ V_{C}_{2} +...V_{C}_{N}
Where:
V_{C}_{1...N} = Cut volume for cell i..N
- The Fill volume V_{F }is the volume between the base and the terrain when the terrain is lower than the base.
Fill volume = V_{F }= V_{F}_{1 }+ V_{F2} +...V_{F}_{N}
Where:
V_{F}_{1...N} = Fill volume for cell i...N.
5. The Total volume is given by:
Total Volume = V_{T }= V_{C }+ V_{F}
For more information about the error in Volume calculation: Error estimation in volume calculation.
I have gone through all the mechanism in calculating the volume with Pix4D after the step 3 is processed. I do understand how it works in general, however, I have a specific question regarding the height of cell. As given in this equation :
Vi = Li*Wi*Hi ; where Vi = Volume
Li=Length
Wi = width
Hi= height
It is explained that, Li*Wi= GSD. I have understood this concept and can visualized it. However, in order to trigger the Hi or the height of the cell, what is the simple explanation regarding this. since, for instance, the stockpile measurement when the shape is irregular. How do the Pix4D draw the length out of this equation.
Your explanation is highly appreciated
Hi Jose,
The GSD of each cell is multiplied by the height at the center of the cell. The GSDs are always small enough, so we just consider the height at the center as even if the shape is irregular, the height will not vary a lot. The smaller the GSDs, more accurate is the volume calculated.