How PIX4Dmapper calculates the Volume

This article explains how PIX4Dmapper calculate a volume by providing the functions being used within PIX4Dmapper.

PIX4Dmapper calculates the volume as follows:

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.

volume

Note: PIX4Dmapper creates the base taking into account the altitude of each vertex.

volume_base

2. PIX4Dmapper projects a grid with GSD spacing on the base.

volume_base_grid_white

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 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_Bi = the base altitude of each cell at the center of the cell.

Therefore, the volume V_iof cell i is given by:

V_i= GSD*GSD* (Z_Ti- Z_Bi)

Note:

Z_Ti is the altitude of the 3D terrain corresponding to the center of the cell i.
Z_Bi is the altitude of the base surface of the volume corresponding to the center of the cell i .

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_C₁+ V_C₂ +...V_C_N

Where:

V_C_1...N = Cut volume for cell i..N

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

Fill volume = V_F= V_F₁+ V_F2 +...V_F_N

Where:

V_F_1...N = Fill volume for cell i...N.

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

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.