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Centroid of a Body

Centroid of a Body

The centroid is an important concept in engineering, physics, and mechanics. It is the geometric center of a body. It always lies within the body except in cases with holes or cavities. When the material that a body is composed of is uniform or homogeneous, the centroid coincides with its center of mass or the center of gravity.
For a homogeneous body with constant density, the centroid can usually be found using equations representing a balance of the moments of the body's volume. If the...

Centroid for the Paraboloid of Revolution

Centroid for the Paraboloid of Revolution

The paraboloid of revolution is an axially symmetric surface generated by rotating a parabola around its axis. This shape has several applications in mechanical engineering due to its advantageous structural properties, such as strength against stress concentration points and rotational symmetry.
The centroid for the paraboloid of revolution is the point where all the mass of the paraboloid is concentrated. This centroid is important for engineering applications, as it determines how forces are...

Gaussian Elimination: Problem Solving

Gaussian Elimination: Problem Solving

Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...

Centroid of a Body: Problem Solving

Centroid of a Body: Problem Solving

The centroid of a body is a crucial concept in engineering and physics. Finding the centroid of a body can help determine its stability, its balance point, and even its design. In this context, consider a thin wire bent in the form of a quarter circular arc. Polar coordinates are used to calculate the centroid. The wire is first divided into small differential elements of a length equal to the radius multiplied by the differential angle.
The x-coordinates and y-coordinates of each element's...

Induced-fit Model

Induced-fit Model

Most chemical reactions in cells require enzymes—biological catalysts that speed up the reaction without being consumed or permanently changed. They reduce the activation energy needed to convert the reactants into products. Enzymes are proteins, that usually work by binding to a substrate—a reactant molecule that they act upon.
Enzymes exhibit substrate specificity, meaning that they can only bind to certain substrates. This is mainly determined by the shape and chemical...

Inclusive Fitness

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Most altruistic behavior—in which one animal helps another at a cost to themselves—occurs between relatives. Scientists think these altruistic behaviors evolved because they increase the inclusive fitness of the animal providing help.

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Related Experiment Video

Updated: Feb 6, 2026

High-Speed Atomic Force Microscopy Imaging of DNA Three-Point-Star Motif Self Assembly Using Photothermal Off-Resonance Tapping

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Star Centroiding Based on Fast Gaussian Fitting for Star Sensors.

Xiaowei Wan¹, Gangyi Wang², Xinguo Wei³

¹School of Instrumentation Science and Opto-electronics Engineering, Beihang University, 37 Xueyuan Rd., Haidian District, Beijing 100191, China. sengesky@buaa.edu.cn.

Sensors (Basel, Switzerland)

|August 30, 2018

Summary

A new fast Gaussian fitting (FGF) algorithm improves star sensor accuracy and efficiency. This method significantly speeds up Gaussian fitting (GF) for real-time star centroiding applications.

Keywords:

Gaussian fitting real-time star centroiding star sensor

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Area of Science:

Aerospace Engineering
Computer Vision
Image Processing

Background:

The Gaussian fitting (GF) algorithm is the most accurate for star centroiding in star sensors due to star spot intensity distribution.
However, GF's high computational complexity limits its use in real-time applications.

Purpose of the Study:

To develop a computationally efficient star centroiding algorithm that maintains high accuracy.
To introduce the fast Gaussian fitting (FGF) method to approximate GF solutions for improved speed.

Main Methods:

Developed the fast Gaussian fitting (FGF) method, approximating GF in closed-form for speed.
Proposed a novel algorithm using two sequential FGF steps: initial parameter estimation and accurate centroid calculation using noise intensity.

Main Results:

The proposed algorithm achieves accuracy comparable to GF and superior to existing methods.
It demonstrates a significant speed improvement, approximately 15 times faster than GF.
Validation performed on simulated and real star sensor images confirmed performance.

Conclusions:

The novel two-step FGF algorithm offers a balance of high accuracy and efficiency.
Its speed makes it suitable for real-time star sensor applications.
This method enhances the feasibility of advanced star tracking and navigation systems.