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 Lenght (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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2 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.

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