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Related Concept Videos

Finding Volume Using Cross-Sectional Area01:24

Finding Volume Using Cross-Sectional Area

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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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Metal ions can be separated from one another by complexation with organic ligands–the chelating agent– to form uncharged chelates. Here, the chelating agent must contain hydrophobic groups and behave as a weak acid, losing a proton to bind with the metal. Since most organic ligands used in this process are insoluble or undergo oxidation in the aqueous phase, the chelating agent is initially added to the organic phase and extracted into the aqueous phase. The metal-ligand complex is...
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The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
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Related Experiment Video

Updated: Apr 29, 2026

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
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[An automatic extraction algorithm for individual tree crown projection area and volume based on 3D point cloud

Wei-Heng Xu, Zhong-Ke Feng, Zhi-Fang Su

    Guang Pu Xue Yu Guang Pu Fen Xi = Guang Pu
    |May 15, 2014
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    Summary
    This summary is machine-generated.

    This study introduces an automated method using 3D laser scanning to accurately measure tree crown projection area and volume, overcoming limitations of traditional forestry measurements for biomass estimation.

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    Area of Science:

    • Forestry Science
    • Remote Sensing
    • Computer Vision

    Background:

    • Traditional methods for measuring tree crown projection area and volume are prone to significant errors due to complex tree structures.
    • Accurate measurements are crucial for biomass estimation and other forestry applications.
    • Existing methods struggle with validation due to inherent inaccuracies.

    Purpose of the Study:

    • To develop an automatic, non-destructive method for extracting tree crown projection area and volume.
    • To overcome the limitations of conventional measurement techniques for complex tree morphologies.
    • To implement computer-based algorithms for objective and precise forest mensuration.

    Main Methods:

    • Utilized terrestrial three-dimensional laser scanning (FARO Photon120) for data acquisition.
    • Applied a plane scattered data point convex hull algorithm for crown projection area calculation.
    • Employed slice segmentation and accumulation algorithms for tree crown volume estimation.
    • Developed algorithms in VC++6.0 and Matlab7.0 for processing high-resolution 3D LIDAR point cloud data.

    Main Results:

    • Achieved high correlation coefficients: 0.964 for crown projection area and 0.960 for crown volume.
    • The new method demonstrated a high degree of accuracy compared to conventional techniques.
    • Identified deviations attributed to the irregular silhouettes of tree crowns, highlighting the new method's sensitivity to actual shape.

    Conclusions:

    • The automated 3D laser scanning method provides accurate and efficient extraction of tree crown projection and volume.
    • Proposed improvements include using multi-point projections and shape-specific volume formulas for enhanced accuracy.
    • This technique offers a valuable reference for tree crown structure studies and precision forestry.