How Pix4Dmapper calculates the Volume?

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

 
Note: The volume is computed using the DSM. In order to draw a new volume, the point cloud and the DSM have to be generated.
Figure 1. Volume drawn in the Volumes view.

 

 
Note: Pix4Dmapper creates the base taking into account the altitude of each vertex.
volume_base.jpg
Figure 2. The Base of the volume.

 

2. Pix4Dmapper projects a grid with GSD spacing on the base.

volume_base_grid_white.jpg
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 (Vi) is given by:

Vi = L* Wi * Hi

Where:

L= the length of the cell.
Wi = the width of the cell.
Hi = the height of the cell.

The Length (Li) and Width (Wi) are equal to the project's GSD.

L=W= GSD

The Height (Hi) is given by:

HiZTi - ZBi

Where: 

ZTi = the terrain altitude of each cell at the center of the cell.
ZBi = the base altitude of each cell at the center of the cell.

Therefore, the volume Vof cell i is given by:

V= GSD*GSD* (ZTi  - ZBi)

 
Note:
  • ZTi is the altitude of the 3D terrain corresponding to the center of the cell i.
  • ZBi is the altitude of the base surface of the volume corresponding to the center of the cell i .
volume_pixel_3d.jpg volume_pixel_element_dimensions.jpg
Figure 4: Volume of one cell of the base  

 

4. Pix4Dmapper calculates 2 volumes:

    • The Cut volume Vis the volume between the base and the 3D terrain, when the terrain is higher than the base.

Cut volume = VC VC1 + VC2 +...VCN

Where:

VC1...N = Cut volume for cell i..N

    • The Fill volume Vis the volume between the base and the terrain when the terrain is lower than the base.

Fill volume = VVF+ VF2 +...VFN

Where:

VF1...N = Fill volume for cell i...N.

 
Note: The Fill Volume is given with negative value / sign.

 

5. The Total volume is given by:

Total Volume = VT VVF

 

For more information about the error in Volume calculation: Error estimation in volume calculation.

 

 

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4 comments

  • jose soares

    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

     

  • Momtanu (Pix4D)

    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.

  • Mariya Susai

    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

  • Timothy (Pix4D)

    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

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