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Related Concept Videos

Calculation of Volume of Solids by Integration01:27

Calculation of Volume of Solids by Integration

Volume calculation often begins with simple geometric solids. For example, the volume of a rectangular box is obtained by multiplying the area of its base by its height. This straightforward approach relies on the fact that the cross-sectional area of the box remains constant throughout its length. Many real-world objects, however, do not have uniform cross-sections, and their volumes cannot be determined using elementary geometric formulas.To address this limitation, the Slicing Method...
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Topographic surveying is critical for documenting the Earth's surface, focusing on capturing elevations, slopes, and natural and man-made features. It is essential in construction planning, water resource management, and land-use analysis. The primary outcome of such surveys is a topographic map, which uses contour lines to visually represent the shape and slope of the terrain, providing valuable insights into the landscape's characteristics.Contour lines are fundamental to understanding the...
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For solids whose cross-sectional areas vary in a predictable way, volume can be determined by integrating these areas along an axis perpendicular to the slices. This approach is particularly useful for polyhedral solids, where classical geometric formulas may not be immediately applicable. A tetrahedron provides a clear example of how cross-sectional integration can be applied to a three-dimensional object with continuously changing geometry.Consider a tetrahedron with height h and a base that...

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Updated: May 28, 2026

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
09:37

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Published on: April 26, 2016

3D Perception-Based Adaptive Point Cloud Simplification and Slicing for Soil Compaction Pit Volume Calculation.

Chuang Han1,2, Jiayu Wei1, Tao Shen1

  • 1The School of Measurement, Control Technology and Communication Engineering, Harbin University of Science and Technology, Harbin 150080, China.

Sensors (Basel, Switzerland)
|May 27, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new framework for accurately measuring excavated pit volumes in subgrade compaction quality assessment. The method enhances point cloud data processing for improved precision in construction quality control.

Keywords:
3D point cloudadaptive point cloud thinningcomputer visionerror analysissubgrade engineeringvolume measurement

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Area of Science:

  • Geotechnical Engineering
  • Computer Vision
  • Geomatics

Background:

  • Accurate volume measurement of excavated pits is crucial for subgrade compaction quality assessment.
  • Challenges include non-uniform point clouds, environmental noise, and complex boundaries.
  • Existing methods struggle with precision and robustness in real-world conditions.

Purpose of the Study:

  • To develop a robust volume detection framework for excavated pits.
  • To improve the accuracy and reliability of sensor-based automated subgrade compaction quality measurement.
  • To address limitations of current point cloud processing techniques.

Main Methods:

  • Pose normalization using RANSAC plane fitting and rigid body transformation.
  • Gradient adaptive simplification for point cloud refinement.
  • Piecewise-cubic polynomial fitting for cross-sectional area calculation.
  • Median Absolute Deviation (MAD) based dynamic outlier removal.
  • Hybrid volume aggregation using Simpson's rule and frustum compensation.

Main Results:

  • The proposed algorithm achieves an average relative volume error of less than 0.8% on simulated pits.
  • Demonstrated superior performance compared to traditional volume measurement methods.
  • Significantly improved robustness and precision in handling noisy and irregular data.

Conclusions:

  • The developed framework effectively addresses challenges in excavated pit volume measurement.
  • Offers a significant advancement for sensor-based automated subgrade compaction quality assessment.
  • Provides a precise and reliable solution for construction quality control.