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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...
Surface Tension01:24

Surface Tension

Surface tension is defined as the force per unit length (γ) acting along the surface of a liquid. It arises due to strong intermolecular forces of attraction. A molecule located inside the bulk of the liquid is surrounded by other molecules and experiences equal forces in all directions. However, a molecule at the surface experiences unbalanced forces because there are more neighboring molecules below than above. This creates a net inward force that pulls surface molecules toward the interior,...
Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
Parallel-Axis Theorem for an Area01:12

Parallel-Axis Theorem for an Area

The moment of inertia is a fundamental concept in mechanical engineering that plays a significant role in designing rotationally symmetric objects such as flywheels, gears, and other mechanical systems. In this context, we will discuss the moment of inertia of a flywheel rotating about its centroidal axis and how it relates to the moment of inertia about an axis parallel to it.
For a flywheel approximated as a solid disc, consider an infinitesimal differential element with an arbitrary distance...

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Updated: May 20, 2026

High-speed Particle Image Velocimetry Near Surfaces
11:59

High-speed Particle Image Velocimetry Near Surfaces

Published on: June 24, 2013

A Parallel Meshless Voronoi Method for Generalized SurfaceNets.

Will Schroeder, David Thompson, Spiros Tsalikis

    IEEE Transactions on Visualization and Computer Graphics
    |May 18, 2026
    PubMed
    Summary
    This summary is machine-generated.

    A new parallel SurfaceNets algorithm visualizes discrete volumetric data from unorganized point clouds. This meshless Voronoi approach enables efficient contour extraction for variable-resolution datasets in scientific computing.

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    High-speed Particle Image Velocimetry Near Surfaces
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    04:35

    Preparation of Free-Surface Hyperbolic Water Vortices

    Published on: July 28, 2023

    Area of Science:

    • Scientific visualization
    • Computational geometry
    • Computer graphics

    Background:

    • SurfaceNets visualizes discrete volumetric scalar fields like segmentation label maps.
    • Label maps are crucial in medical computing, biology, and materials science.
    • Current methods struggle with data of highly variable resolution due to uniform spacing assumptions.

    Purpose of the Study:

    • Develop a generalized, high-performance, parallel SurfaceNets algorithm.
    • Process unorganized, labeled point clouds for visualization.
    • Overcome limitations of uniform spacing in representing variable-resolution data.

    Main Methods:

    • A scalable, meshless Voronoi approach processes each Voronoi hull independently and in parallel.
    • A hierarchical neighborhood point search metric is employed.
    • Novel topological constructs transform the meshless tessellation into a connected conformal mesh for contour extraction.

    Main Results:

    • The algorithm successfully processes unorganized, labeled point clouds.
    • Multiple valid contour surfaces can be simultaneously extracted and smoothed.
    • Parallel performance was quantified, handling large datasets (128 million hulls, 750 million tetrahedra).

    Conclusions:

    • The generalized parallel SurfaceNets algorithm effectively visualizes discrete volumetric data with variable resolution.
    • The meshless Voronoi approach offers a scalable and efficient method for contour generation.
    • The software implementation is available in the open-source Visualization Toolkit (VTK).