Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Spherical Coordinates01:23

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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...
Volumes of Solids of Revolution01:29

Volumes of Solids of Revolution

Volumes of irregularly shaped objects can be systematically determined using the concept of solids of revolution. This approach begins with a region defined by a curve in a two-dimensional plane. When this region is rotated about a fixed line, known as the axis of revolution, it generates a three-dimensional object with rotational symmetry. Such objects frequently arise in mathematical modeling, physics, and engineering applications.When the region being rotated lies directly against the axis...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Partial Fractions01:28

Partial Fractions

A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
Trigonometric Substitution01:23

Trigonometric Substitution

Trigonometric substitution is a technique used to simplify integrals that contain square root expressions involving quadratic forms. It is particularly effective when the integrand includes terms resembling those found in standard geometric equations, such as circles or ellipses.Molniya satellites follow highly elliptical orbits, repeatedly sweeping out the same regions of space as they revolve around Earth. To estimate the area enclosed by such an orbit, the path is modeled as an ellipse...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

TLR agonists enhance responsiveness of inflammatory innate immune cells in HLA-B*57-positive HIV patients.

Journal of molecular medicine (Berlin, Germany)·2020
Same author

Survival of HIV/HCV co-infected patients before introduction of HCV direct acting antivirals (DAA).

Scientific reports·2019
Same author

Packing volumes by spheres.

IEEE transactions on pattern analysis and machine intelligence·2011
Same author

A roadmap for bridging basic and applied research in forensic entomology.

Annual review of entomology·2010
Same author

Stress optic coefficient and stress profile in optical fibers.

Applied optics·2010
Same author

Multimode optical fiber displacement sensor.

Applied optics·2010
Same journal

Relation DETR+: Exploring Explicit Position Relation Prior for Dense Prediction.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

RBF++: Quantifying and Optimizing Reasoning Boundaries across Measurable and Unmeasurable Capabilities for Chain-of-Thought Reasoning.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

CAFE: Cross-View Adaptive Fusion and Cluster Center Enhancement for Robust Multi-View Clustering.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

DIVER: Reinforced Diffusion Breaks Imitation Bottlenecks in End-to-End Autonomous Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Ethics-Aware Safe Reinforcement Learning for Rare-Event Risk Control in Interactive Urban Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Learning Shape Anchors for Holistic Indoor Scene Understanding.

IEEE transactions on pattern analysis and machine intelligence·2026
See all related articles

Related Experiment Video

Updated: May 29, 2026

High-resolution Single Particle Analysis from Electron Cryo-microscopy Images Using SPHIRE
13:28

High-resolution Single Particle Analysis from Electron Cryo-microscopy Images Using SPHIRE

Published on: May 16, 2017

A refinement of a spherical decomposition algorithm.

R Mohr1

  • 1Department of Computer and Information Science, Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, PA 19104; CRIN, C.O. 140, 54047 Nancy Cedex, Franc.

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

This study refines the O'Rourke-Badler spherical decomposition algorithm, significantly improving computational efficiency. The enhanced algorithm reduces complexity from cubic (O(n3)) to quadratic (O(n2)).

More Related Videos

High-throughput Image Analysis of Tumor Spheroids: A User-friendly Software Application to Measure the Size of Spheroids Automatically and Accurately
08:39

High-throughput Image Analysis of Tumor Spheroids: A User-friendly Software Application to Measure the Size of Spheroids Automatically and Accurately

Published on: July 8, 2014

Related Experiment Videos

Last Updated: May 29, 2026

High-resolution Single Particle Analysis from Electron Cryo-microscopy Images Using SPHIRE
13:28

High-resolution Single Particle Analysis from Electron Cryo-microscopy Images Using SPHIRE

Published on: May 16, 2017

High-throughput Image Analysis of Tumor Spheroids: A User-friendly Software Application to Measure the Size of Spheroids Automatically and Accurately
08:39

High-throughput Image Analysis of Tumor Spheroids: A User-friendly Software Application to Measure the Size of Spheroids Automatically and Accurately

Published on: July 8, 2014

Area of Science:

  • Computational geometry
  • Computer-aided design (CAD)

Background:

  • Spherical decomposition is crucial for complex geometric modeling.
  • Existing algorithms like O'Rourke-Badler have high computational complexity.

Purpose of the Study:

  • To propose a refined spherical decomposition algorithm.
  • To reduce the algorithmic complexity of spherical decomposition.

Main Methods:

  • Modification of the O'Rourke-Badler spherical decomposition algorithm.
  • Analysis of algorithmic complexity.

Main Results:

  • The refined algorithm achieves a complexity of O(n2).
  • This represents a significant reduction from the original O(n3) complexity.

Conclusions:

  • The proposed refinement offers a more efficient approach to spherical decomposition.
  • This advancement has implications for improving performance in CAD and geometric modeling applications.