Lidar Volume Calculation

1. NTWIST Inc
Artificial Intelligence for Industrial Excellence
Point cloud Data and
Volume Calculation

2. Introduction
Stockpile in Mining–
• A mine stockpile is a pile or heap of material (such as
ore, gravel, or sand) that has been extracted from a
mine and stored for further processing.
• The main purpose of a mine stockpile is to ensure
that there is a steady supply of material available
for processing or shipping, and to prevent the mine
from running out of material.
• Stockpile volume calculation is important for the mining
industry as it allows the operators to track the amount
of material being extracted and stored, and to plan for
future production and shipment.
• The volume of a stockpile can be affected by various
factors such as weather conditions, compaction,
and material degradation. Therefore it's important to
have a good monitoring system to track the volume
changes.

3. Shortcomings: Resolution
Resolution:
• Our current stockpile model uses a resolution of 1m by 1m with Voxel variable set to
0.05 for creating mesh.
• If the terrain is uneven, or has higher variability in z-coordinate, a larger resolution or
large voxel meshing may lead to inaccurate volume calculation.
• If the resolution is too high, More computation power, hence more time is required.
• An optimization is required for our case: computing volume from point cloud data of
stockpile.

4. Shortcomings: Primitive LiDAR
LiDAR Scan – Side View
Primitive:
• The Primitive LiDAR scan or dynamic base level for a LiDAR scan plays
crucial role in determining the volume of the material.
• For a same LiDAR scan, in Fig. A the Volume is overshoots the real value,
due to inconsideration of the “real ground”. A stockpile area can have a
inclined ground surface, more than usual, so much so that the trucks can
reach different levels of a pile from different sides.
• To resolve this either we need to have a correct primitive LiDAR scan
with no material in the stockpile or have a dynamic datum depending on
the sectors of the stockpile.
Fig. A
Fig. B

5. Thank you

6. Volume Calculations
• The shoelace formula: (Gauss area formula) formula is used to
calculate the area of a simple polygon. The formula is based on
the idea of treating the polygon as a curved shape and breaking
it down into a series of line segments.
• V = (z1+z2+z3)*(x1*y2-x2*y1+x2*y3-x3*y2+x3*y1-x1*y3)/6
• It applies to simple closed polygon with no self-intersections, as
well as it is easy to implement and numerically stable.
• It can be used for both convex and concave polygons, and it's a
common method used in computational geometry.
• For Triangle --This method involves taking the dot product
of the vector formed by the coordinates of one vertex of
the triangle with the cross product of the vectors formed
by the coordinates of the other two vertices.