## Volume measurement

PIX4Dsurvey's volume measurement is using the triangulated method between the volume's base polygon and the surface defined by a local TIN in the resolution of the project GSD. This method connects all the vertices and triangulates the volume above and below the base surface.

**IN THIS ARTICLE**

How to create a new volume

How to compute the volume

How PIX4Dsurvey calculates the Volume measurement

## How to create a new volume

- On the
*Tools*bar, select the volume measurement tool by clicking on .Volume measurement selection.

- To draw a Volume, left-click on points in the 3D view. Right-click or press Enter to complete the polygon.
- (Optional) To mark the vertices more accurately, select the volume by clicking on it. Then you can correct the position of each vertex in the 3D view, on images, or using the vertex editor.

After drawing the volume, details about the volume measurement are displayed. More specifically:

- Name of the volume and name of the layer the volume belongs to. The name of the volume layer and color of visualization can be edited.
- 3D perimeter, 3D area, minimum and maximum elevation will be displayed according to the drawn polygon.
Display of volume measurement details, after drawing the volume.

## How to compute the volume

Once the volume is drawn, click **Compute **in *Measurements* to trigger the volume computation.

Compute the cut/fill volume measurements by clicking on **Compute** button.

After volume measurements are completed, cut/fill volume and error are displayed.

Cut/fill volume and error are computed after the completion of volume measurements.

More specifically:

**Cut volume [units**Volume that is above the volume base. The volume is measured between the volume base and the surface.^{3}]:**Fill volume [units**: Volume that is below the volume base. The volume is measured between the volume base and the surface.^{3}]**Total volume [units**The total volume (cut + fill volume).^{3}]:

## How PIX4Dsurvey calculates the Volume measurement

PIX4Dsurvey calculates the volume as follows:

1. A new volume is drawn. For more information on how to draw a volume: How to create a new volume.

A volume is drawn.

The base of the volume.

2. PIX4Dsurvey projects a grid with GSD spacing on the base.

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

*the width of the cell.*

_{i}=*H*the height of the cell.

_{i}=The Length (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*= the base altitude of each cell at the center of the cell.

_{Bi}Therefore, the volume *V _{i}*of cell i is given by:

*V _{i }= GSD*GSD* (Z_{Ti }- Z_{Bi})*

Volume of one cell of the base |

4. PIX4Dsurvey calculates 2 volumes:

- The Cut volume
*V*is the volume between the base and the 3D terrain, when the terrain is higher than the base._{c}

*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*is the volume between the base and the terrain when the terrain is lower than the base._{F }

*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}
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