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: 202560319

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.
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 (Vi) is given by:

Vi = L* Wi * Hi


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.


The Height (Hi) is given by:

HiZTi - ZBi


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)

  • 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


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


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: 202559219.



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