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Related Concept Videos

Sampling Theorem01:15

Sampling Theorem

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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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Sampling Methods: Overview01:06

Sampling Methods: Overview

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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of...
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Sampling Plans01:23

Sampling Plans

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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
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Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

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Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...
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Stratified Sampling Method01:16

Stratified Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a stratified sample, divide the population into groups called strata and then take a...
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Volumes of Solids of Revolution01:29

Volumes of Solids of Revolution

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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...
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Related Experiment Video

Updated: Apr 30, 2026

An Unbiased Approach of Sampling TEM Sections in Neuroscience
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Conservative sampling of solids in image space.

Yuen-Shan Leung, Charlie C L Wang

    IEEE Computer Graphics and Applications
    |May 9, 2014
    PubMed
    Summary

    Conservative sampling converts boundary-representation (B-rep) models into layered depth images (LDIs). This efficient graphics hardware-compatible method accurately bounds models for versatile applications.

    Area of Science:

    • Computer Graphics
    • Geometric Modeling

    Background:

    • Boundary-representation (B-rep) solid models are fundamental in computer-aided design and manufacturing.
    • Efficiently sampling and representing complex B-rep models is crucial for various geometric computations.
    • Existing methods may lack efficiency or hardware compatibility for real-time applications.

    Purpose of the Study:

    • To introduce a novel conservative sampling technique for B-rep solid models.
    • To generate Layered Depth Images (LDIs) that accurately represent the input B-rep models.
    • To demonstrate the efficiency and versatility of the proposed LDI generation method.

    Main Methods:

    • Conservative sampling algorithm applied to B-rep solid models.
    • Generation of Layered Depth Images (LDIs) with guaranteed boundary closure.

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  • Implementation using shader programs compatible with standard graphics hardware.

    • Main Results:

    • The conservative sampling method produces LDIs with closed boundaries.
    • The generated LDIs are guaranteed to bound the original B-rep models on sampled rays.
    • The approach is efficient and fully implementable on modern graphics hardware.

    Conclusions:

    • Conservative sampling offers an efficient and hardware-accelerated method for generating LDIs from B-rep models.
    • The resulting LDIs are accurate and suitable for advanced geometric processing tasks.
    • The technique's versatility is highlighted through applications in volume intersection and Minkowski sum computation.