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Related Concept Videos

Mesh Analysis01:20

Mesh Analysis

Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
Mesh Analysis with Current Sources01:10

Mesh Analysis with Current Sources

Mesh analysis becomes simpler when analyzing circuits with current sources, whether independent or dependent. The presence of current sources reduces the number of equations required for analysis. Two cases illustrate this:
Current Source in One Mesh: The analysis process is straightforward when a current source is found in only one mesh within the circuit. Mesh currents are assigned as usual, with the mesh containing the current source excluded from the analysis. Kirchhoff's voltage law (KVL)...
Uniform Depth Channel Flow01:27

Uniform Depth Channel Flow

Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant cross-section...
Finding Volume Using Cross-Sectional Area01:24

Finding Volume Using Cross-Sectional Area

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...
Mesh Analysis for AC Circuits01:12

Mesh Analysis for AC Circuits

In the domain of radio communication, the significance of impedance matching must be considered. It is crucial to ensure the efficient transmission of signals between radio transmitters and receivers. Achieving this balance involves using impedance-matching circuits, with one fundamental configuration comprising a resistor, capacitor, and inductor.
The process of harmonizing these impedances begins with a clear understanding of the input and output signals. Once these signals are known, the...
Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...

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Updated: Jun 2, 2026

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

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

Published on: April 26, 2016

Quality Multi-domain Meshing for Volumetric Data.

Qin Zhang1, Bharadwaj Subramanian, Guoliang Xu

  • 1Institute for Computational Engineering and Sciences, the University of Texas, Austin, TX 78712.

Proceedings of the ... International Conference on Biomedical Engineering and Informatics. International Conference on Biomedical Engineering and Informatics
|May 6, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method for creating high-quality, multi-domain meshes from volumetric data. The approach ensures meshes are free from intersections, making them suitable for advanced computations in science and engineering.

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Area of Science:

  • Computational geometry
  • Scientific visualization
  • Numerical analysis

Background:

  • Multi-domain meshing is crucial for simulations in medicine, biology, and geology.
  • Existing methods often struggle with generating high-quality, intersection-free meshes for complex volumetric data.

Purpose of the Study:

  • To develop a robust pipeline for generating high-quality multi-domain meshes from volumetric data.
  • To ensure the resulting meshes are free from self- and inter-domain intersections.
  • To provide a user-controlled separation for sub-meshes.

Main Methods:

  • Generating a point cloud from a preliminary mesh of domain boundaries.
  • Employing a higher-order level-set method for sub-mesh generation.
  • Utilizing geometric flow for mesh smoothing.
  • Developing a novel approach to detect and curate intersections using volumetric data.
  • Implementing a user-defined gap threshold for sub-mesh separation.

Main Results:

  • A high-quality, multi-domain mesh is produced.
  • The mesh is guaranteed to be free from self- and inter-domain intersections.
  • Sub-mesh separation is controllable via a gap threshold parameter.
  • The pipeline is efficiently implemented and demonstrated with sample meshes.

Conclusions:

  • The proposed method effectively generates high-quality, intersection-free multi-domain meshes.
  • The resulting meshes are suitable for finite element and boundary element computations.
  • This approach enhances the usability of volumetric data for scientific simulations.