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.
Hi Momta,
I want to create Volumetric analysis tool in my web application. How can i do that?
We have Pix4DEngine Cloud API right now. We planned to develop our own portal for user to view and do volumetric Analysis on-the-fly. So please help us, how to do this thing with Pix4DEngine Cloud API.
With Regards
V.Mariya Susai
Hi Mariya,
There are three key portions to creating a tool like that.
The first is to define the area of interest. Whether this is through submitting a file with coordinates or clicking marks around a model you need to be able to create a polygon with those coordinates. There are many options through Potree or Three.js to create the interface for clicking/coordinate marking.
The second is the library/code piece to do the volumetric calculation. Something like this library which takes in those coordinates and calculates the volume from the DSM product is necessary. There are other mesh/volume calculators out there that was just the first I found in a cursory search.
The third item would be the infrastructure between the two. Things like creating the necessary input file from your clicks on the model, to pulling the DSM file, to running the library and reporting back to the Cloud interface widget. That may be an oversimplification but the point is there.
I hope this helps!
Yours Sincerely,
Timothy Holcombe