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Related Concept Videos

Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Graphical Representation of Inequalities01:28

Graphical Representation of Inequalities

The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all points...
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a cylinder...
Test for Homogeneity01:23

Test for Homogeneity

The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can be stated as...
Area Between Curves: Problem Solving01:27

Area Between Curves: Problem Solving

A region can be enclosed by three curves: a square root function, a reflected cube root function, and a linear function. The linear function intersects each of the other two curves, and these intersection points determine where the boundary of the enclosed region changes. Because different curves serve as the upper and lower boundaries in different parts of the graph, the area cannot be found using a single setup over the entire interval.To compute the area, the region is first divided into two...

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Related Experiment Video

Updated: May 29, 2026

Long-term Video Tracking of Cohoused Aquatic Animals: A Case Study of the Daily Locomotor Activity of the Norway Lobster (Nephrops norvegicus)
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A convex hull inclusion test.

T Bailey1, J Cowles

  • 1Department of Computer Science, University of Wyoming, Laramie, WY 82071.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method to describe the inside of a convex hull for point sets. This new characterization enables an efficient inclusion test, performing almost linearly with data size and dimensionality.

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Area of Science:

  • Computational Geometry
  • Geometric Algorithms

Background:

  • Convex hulls are fundamental in computational geometry.
  • Efficiently testing point inclusion within convex hulls is crucial for various applications.

Purpose of the Study:

  • To present a new characterization for the interior of a convex hull.
  • To develop an efficient point inclusion test based on this characterization.

Main Methods:

  • Developing a novel geometric characterization of the convex hull interior.
  • Implementing an inclusion test algorithm derived from the new characterization.

Main Results:

  • A new mathematical description of the convex hull interior is established.
  • The developed inclusion test demonstrates near-linear average-case performance relative to the number of points and dimensionality.

Conclusions:

  • The novel characterization provides a more effective way to understand convex hull interiors.
  • The efficient inclusion test has significant implications for geometric data processing and analysis.